{"id":8977,"date":"2017-04-27T21:56:05","date_gmt":"2017-04-27T21:56:05","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/prealgebra\/?post_type=chapter&p=8977"},"modified":"2020-07-02T05:42:53","modified_gmt":"2020-07-02T05:42:53","slug":"problem-set-fractions","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/cpcc-algebra-trig-I-support\/chapter\/problem-set-fractions\/","title":{"raw":"Problem Set: Fractions","rendered":"Problem Set: Fractions"},"content":{"raw":"

Representing parts of a whole<\/h2>\r\n

Using Models to Represent Fractions<\/h3>\r\nIn the following exercises, name the fraction of each figure that is shaded.\r\n

Exercise 1<\/h4>\r\n\"In\r\n[reveal-answer q=\"878598\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"878598\"]\r\n\r\n\u24d0 = [latex]\\Large\\frac{1}{4}[\/latex]\r\n\r\n\u24d1 = [latex]\\Large\\frac{3}{4}[\/latex]\r\n\r\n\u24d2 = [latex]\\Large\\frac{3}{8}[\/latex]\r\n\r\n\u24d3 = [latex]\\Large\\frac{5}{9}[\/latex][\/hidden-answer]\r\n

Exercise 2<\/h4>\r\n\"In\r\n

Using Models to Represent Fractions<\/h3>\r\nIn the following exercises, shade parts of circles or squares to model the following fractions.\r\n
    \r\n \t
  1. [latex]\\Large\\frac{1}{2}[\/latex]\r\n[reveal-answer q=\"519092\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"519092\"]\"A[\/hidden-answer]<\/li>\r\n \t
  2. [latex]\\Large\\frac{1}{3}[\/latex]<\/li>\r\n \t
  3. [latex]\\Large\\frac{3}{4}[\/latex]\r\n[reveal-answer q=\"259387\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"259387\"]\"A[\/hidden-answer]<\/li>\r\n \t
  4. [latex]\\Large\\frac{2}{5}[\/latex]<\/li>\r\n \t
  5. [latex]\\Large\\frac{5}{6}[\/latex]\r\n[reveal-answer q=\"282088\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"282088\"]\"A[\/hidden-answer]<\/li>\r\n \t
  6. [latex]\\Large\\frac{7}{8}[\/latex]<\/li>\r\n \t
  7. [latex]\\Large\\frac{5}{8}[\/latex]\r\n[reveal-answer q=\"956270\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"956270\"]\"A[\/hidden-answer]<\/li>\r\n \t
  8. [latex]\\Large\\frac{7}{10}[\/latex]<\/li>\r\n<\/ol>\r\n

    Model Improper Fractions and Mixed Numbers<\/h3>\r\nIn the following exercises, use fraction circles to make wholes, if possible, with the following pieces.\r\n
      \r\n \t
    1. [latex]3[\/latex] thirds\r\n[reveal-answer q=\"195280\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"195280\"]\"A[\/hidden-answer]<\/li>\r\n \t
    2. [latex]8[\/latex] eighths<\/li>\r\n \t
    3. [latex]7[\/latex] sixths\r\n[reveal-answer q=\"488102\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"488102\"]\"Two[\/hidden-answer]<\/li>\r\n \t
    4. [latex]4[\/latex] thirds<\/li>\r\n \t
    5. [latex]7[\/latex] fifths\r\n[reveal-answer q=\"285906\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"285906\"]\"Two[\/hidden-answer]<\/li>\r\n \t
    6. [latex]7[\/latex] fourths<\/li>\r\n<\/ol>\r\n

      Model Improper Fractions and Mixed Numbers<\/h3>\r\nIn the following exercises, name the improper fractions. Then write each improper fraction as a mixed number.\r\n

      Exercise 1<\/h4>\r\n\"In\r\n[reveal-answer q=\"112281\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"112281\"]\u24d0 [latex]\\Large\\frac{5}{4}\\normalsize =1\\Large\\frac{1}{4}[\/latex] \u24d1 [latex]\\Large\\frac{7}{4}\\normalsize =1\\Large\\frac{3}{4}[\/latex] \u24d2 [latex]\\Large\\frac{11}{8}\\normalsize =1\\Large\\frac{3}{8}[\/latex][\/hidden-answer]\r\n

      Exercise 2<\/h4>\r\n\"In\r\n

      Exercise 3<\/h4>\r\n\"In\r\n[reveal-answer q=\"210069\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"210069\"]\u24d0 [latex]\\Large\\frac{11}{4}\\normalsize =2\\Large\\frac{3}{4}[\/latex] \u24d1 [latex]\\Large\\frac{19}{8}\\normalsize =2\\Large\\frac{3}{8}[\/latex][\/hidden-answer]\r\n

      Model Improper Fractions and Mixed Numbers<\/h3>\r\nIn the following exercises, draw fraction circles to model the given fraction.\r\n
        \r\n \t
      1. [latex]\\Large\\frac{3}{3}[\/latex]<\/li>\r\n \t
      2. [latex]\\Large\\frac{4}{4}[\/latex]\r\n[reveal-answer q=\"51709\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"51709\"]\"A[\/hidden-answer]<\/li>\r\n \t
      3. [latex]\\Large\\frac{7}{4}[\/latex]<\/li>\r\n \t
      4. [latex]\\Large\\frac{5}{3}[\/latex]\r\n[reveal-answer q=\"860009\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"860009\"]\"Two[\/hidden-answer]<\/li>\r\n \t
      5. [latex]\\Large\\frac{11}{6}[\/latex]<\/li>\r\n \t
      6. [latex]\\Large\\frac{13}{8}[\/latex]\r\n[reveal-answer q=\"654972\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"654972\"]\"Two[\/hidden-answer]<\/li>\r\n \t
      7. [latex]\\Large\\frac{10}{3}[\/latex]<\/li>\r\n \t
      8. [latex]\\Large\\frac{9}{4}[\/latex]\r\n[reveal-answer q=\"348858\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"348858\"]\"Three[\/hidden-answer]<\/li>\r\n<\/ol>\r\n

        Converting Between Improper Fractions and Mixed Numbers<\/h2>\r\n

        Write an Improper Fraction as a Mixed Number<\/h3>\r\nIn the following exercises, rewrite the improper fraction as a mixed number.\r\n
          \r\n \t
        1. [latex]\\Large\\frac{3}{2}[\/latex]<\/li>\r\n \t
        2. [latex]\\Large\\frac{5}{3}[\/latex]\r\n[reveal-answer q=\"532821\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"532821\"][latex]1\\Large\\frac{2}{3}[\/latex][\/hidden-answer]<\/li>\r\n \t
        3. [latex]\\Large\\frac{11}{4}[\/latex]<\/li>\r\n \t
        4. [latex]\\Large\\frac{13}{5}[\/latex]\r\n[reveal-answer q=\"862316\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"862316\"][latex]2\\Large\\frac{3}{5}[\/latex][\/hidden-answer]<\/li>\r\n \t
        5. [latex]\\Large\\frac{25}{6}[\/latex]<\/li>\r\n \t
        6. [latex]\\Large\\frac{28}{9}[\/latex]\r\n[reveal-answer q=\"629032\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"629032\"][latex]3\\Large\\frac{1}{9}[\/latex][\/hidden-answer]<\/li>\r\n \t
        7. [latex]\\Large\\frac{42}{13}[\/latex]<\/li>\r\n \t
        8. [latex]\\Large\\frac{47}{15}[\/latex]\r\n[reveal-answer q=\"423697\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"423697\"][latex]3\\Large\\frac{2}{15}[\/latex][\/hidden-answer]<\/li>\r\n<\/ol>\r\n

          Write a Mixed Number as an Improper Fraction<\/h3>\r\nIn the following exercises, rewrite the mixed number as an improper fraction.\r\n
            \r\n \t
          1. [latex]1\\Large\\frac{2}{3}[\/latex]<\/li>\r\n \t
          2. [latex]1\\Large\\frac{2}{5}[\/latex]\r\n[reveal-answer q=\"402846\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"402846\"][latex]\\Large\\frac{7}{5}[\/latex][\/hidden-answer]<\/li>\r\n \t
          3. [latex]2\\Large\\frac{1}{4}[\/latex]<\/li>\r\n \t
          4. [latex]2\\Large\\frac{5}{6}[\/latex]\r\n[reveal-answer q=\"268851\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"268851\"][latex]\\Large\\frac{17}{6}[\/latex][\/hidden-answer]<\/li>\r\n \t
          5. [latex]2\\Large\\frac{7}{9}[\/latex]<\/li>\r\n \t
          6. [latex]2\\Large\\frac{5}{7}[\/latex]\r\n[reveal-answer q=\"703536\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"703536\"][latex]\\Large\\frac{19}{7}[\/latex][\/hidden-answer]<\/li>\r\n \t
          7. [latex]3\\Large\\frac{4}{7}[\/latex]<\/li>\r\n \t
          8. [latex]3\\Large\\frac{5}{9}[\/latex]\r\n[reveal-answer q=\"475096\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"475096\"][latex]\\Large\\frac{32}{9}[\/latex][\/hidden-answer]<\/li>\r\n<\/ol>\r\n

            Modeling and Finding Equivalent Fractions<\/h2>\r\n

            Modeling Equivalent Fractions<\/h3>\r\nIn the following exercises, use fraction tiles or draw a figure to find equivalent fractions.\r\n
              \r\n \t
            1. How many sixths equal one-third?<\/li>\r\n \t
            2. How many twelfths equal one-third?\r\n[reveal-answer q=\"46235\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"46235\"]4[\/hidden-answer]<\/li>\r\n \t
            3. How many eighths equal three-fourths?<\/li>\r\n \t
            4. How many twelfths equal three-fourths?\r\n[reveal-answer q=\"880114\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"880114\"]9[\/hidden-answer]<\/li>\r\n \t
            5. How many fourths equal three-halves?<\/li>\r\n \t
            6. How many sixths equal three-halves?\r\n[reveal-answer q=\"8258\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"8258\"]9[\/hidden-answer]<\/li>\r\n<\/ol>\r\n

              Finding Equivalent Fractions<\/h3>\r\nIn the following exercises, find three fractions equivalent to the given fraction. Show your work, using figures or algebra.\r\n
                \r\n \t
              1. [latex]\\Large\\frac{1}{4}[\/latex]<\/li>\r\n \t
              2. [latex]\\Large\\frac{1}{3}[\/latex][reveal-answer q=\"74953\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"74953\"]Answers may vary. Correct answers include [latex]\\Large\\frac{2}{6},\\Large\\frac{3}{9},\\Large\\frac{4}{12}[\/latex].[\/hidden-answer]<\/li>\r\n \t
              3. [latex]\\Large\\frac{3}{8}[\/latex]<\/li>\r\n \t
              4. [latex]\\Large\\frac{5}{6}[\/latex][reveal-answer q=\"25227\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"25227\"]Answers may vary. Correct answers include [latex]\\Large\\frac{10}{12},\\Large\\frac{15}{18},\\Large\\frac{20}{24}[\/latex].[\/hidden-answer]<\/li>\r\n \t
              5. [latex]\\Large\\frac{2}{7}[\/latex]<\/li>\r\n \t
              6. [latex]\\Large\\frac{5}{9}[\/latex][reveal-answer q=\"443374\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"443374\"]Answers may vary. Correct answers include [latex]\\Large\\frac{10}{18},\\Large\\frac{15}{27},\\Large\\frac{20}{36}[\/latex].[\/hidden-answer]<\/li>\r\n<\/ol>\r\n

                Locating and Ordering Fractions and Mixed Numbers on the Number Line<\/h2>\r\n

                Locating Fractions on the Number Line<\/h3>\r\nIn the following exercises, plot the numbers on a number line.\r\n
                  \r\n \t
                1. [latex]\\Large\\frac{2}{3},\\Large\\frac{5}{4},\\Large\\frac{12}{5}[\/latex]<\/li>\r\n \t
                2. [latex]\\Large\\frac{1}{3},\\Large\\frac{7}{4},\\Large\\frac{13}{5}[\/latex][reveal-answer q=\"585980\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"585980\"]\"A[\/hidden-answer]<\/li>\r\n \t
                3. [latex]\\Large\\frac{1}{4},\\Large\\frac{9}{5},\\Large\\frac{11}{3}[\/latex]<\/li>\r\n \t
                4. [latex]\\Large\\frac{7}{10},\\Large\\frac{5}{2},\\Large\\frac{13}{8},\\normalsize\r\n3[\/latex][reveal-answer q=\"395060\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"395060\"]\"A[\/hidden-answer]<\/li>\r\n \t
                5. [latex]2\\Large\\frac{1}{3}\\normalsize ,-2\\Large\\frac{1}{3}[\/latex]<\/li>\r\n \t
                6. [latex]1\\Large\\frac{3}{4}\\normalsize ,-1\\Large\\frac{3}{5}[\/latex][reveal-answer q=\"528460\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"528460\"]\"A[\/hidden-answer]<\/li>\r\n \t
                7. [latex]\\Large\\frac{3}{4},-\\Large\\frac{3}{4}\\normalsize ,1\\Large\\frac{2}{3}\\normalsize ,-1\\Large\\frac{2}{3},\\Large\\frac{5}{2},-\\Large\\frac{5}{2}[\/latex]<\/li>\r\n \t
                8. [latex]\\Large\\frac{2}{5},-\\Large\\frac{2}{5}\\normalsize ,1\\Large\\frac{3}{4}\\normalsize ,-1\\Large\\frac{3}{4},\\Large\\frac{8}{3},-\\Large\\frac{8}{3}[\/latex][reveal-answer q=\"728759\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"728759\"]\"A[\/hidden-answer]<\/li>\r\n<\/ol>\r\n

                  Ordering Fractions on the Number Line<\/h3>\r\nIn the following exercises, order each of the following pairs of numbers, using [latex]&lt[\/latex] or [latex]&gt[\/latex].\r\n
                    \r\n \t
                  1. [latex]-1\\text{ __}-\\Large\\frac{1}{4}[\/latex]<\/li>\r\n \t
                  2. [latex]-1\\text{ __}-\\Large\\frac{1}{3}[\/latex]\r\n[reveal-answer q=\"282249\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"282249\"]<[\/hidden-answer]<\/li>\r\n \t
                  3. [latex]-2\\Large\\frac{1}{2}\\normalsize\\text{ __}-3[\/latex]<\/li>\r\n \t
                  4. [latex]-1\\Large\\frac{3}{4}\\normalsize\\text{ __}-2[\/latex]\r\n[reveal-answer q=\"402654\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"402654\"]>[\/hidden-answer]<\/li>\r\n \t
                  5. [latex]-\\Large\\frac{5}{12}\\text{ __}-\\Large\\frac{7}{12}[\/latex]<\/li>\r\n \t
                  6. [latex]-\\Large\\frac{9}{10}\\text{ __}-\\Large\\frac{3}{10}[\/latex]\r\n[reveal-answer q=\"25622\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"25622\"]<[\/hidden-answer]<\/li>\r\n \t
                  7. [latex]-3\\text{ __}-\\Large\\frac{13}{5}[\/latex]<\/li>\r\n \t
                  8. [latex]-4\\text{ __}-\\Large\\frac{23}{6}[\/latex]\r\n[reveal-answer q=\"680158\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"680158\"]<[\/hidden-answer]<\/li>\r\n<\/ol>\r\n
                    \r\n

                    Everyday Math<\/h3>\r\n

                    Music Measures<\/h4>\r\nA choreographed dance is broken into counts. A [latex]\\Large\\frac{1}{1}[\/latex] count has one step in a count, a [latex]\\Large\\frac{1}{2}[\/latex] count has two steps in a count and a [latex]\\Large\\frac{1}{3}[\/latex] count has three steps in a count. How many steps would be in a [latex]\\Large\\frac{1}{5}[\/latex] count? What type of count has four steps in it?\r\n

                    Music Measures<\/h4>\r\nFractions are used often in music. In [latex]\\Large\\frac{4}{4}[\/latex] time, there are four quarter notes in one measure.\r\n
                      \r\n \t
                    1. How many measures would eight quarter notes make?\r\n[reveal-answer q=\"612478\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"612478\"]2[\/hidden-answer]<\/li>\r\n \t
                    2. The song \"Happy Birthday to You\" has [latex]24[\/latex] quarter notes. How many measures are there in \"Happy Birthday to You?\"\r\n[reveal-answer q=\"849617\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"849617\"]6[\/hidden-answer]<\/li>\r\n<\/ol>\r\n

                      Baking<\/h4>\r\nNina is making five pans of fudge to serve after a music recital. For each pan, she needs [latex]\\Large\\frac{1}{2}[\/latex] cup of walnuts.\r\n
                        \r\n \t
                      1. How many cups of walnuts does she need for five pans of fudge?<\/li>\r\n \t
                      2. Do you think it is easier to measure this amount when you use an improper fraction or a mixed number? Why?<\/li>\r\n<\/ol>\r\n<\/div>\r\n
                        \r\n

                        Writing Exercises<\/h3>\r\nGive an example from your life experience (outside of school) where it was important to understand fractions.\r\n\r\n[practice-area rows=\"4\"][\/practice-area]\r\n\r\nExplain how you locate the improper fraction [latex]\\Large\\frac{21}{4}[\/latex] on a number line on which only the whole numbers from [latex]0[\/latex] through [latex]10[\/latex] are marked.\r\n\r\n[practice-area rows=\"4\"][\/practice-area]\r\n\r\n<\/div>\r\n

                        Multiplying and Dividing Fractions<\/h2>\r\n

                        Simplify Fractions<\/h3>\r\nIn the following exercises, simplify each fraction. Do not convert any improper fractions to mixed numbers.\r\n
                          \r\n \t
                        1. [latex]\\Large\\frac{7}{21}[\/latex]\r\n[reveal-answer q=\"494096\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"494096\"][latex]\\Large\\frac{1}{3}[\/latex][\/hidden-answer]<\/li>\r\n \t
                        2. [latex]\\Large\\frac{8}{24}[\/latex]<\/li>\r\n \t
                        3. [latex]\\Large\\frac{15}{20}[\/latex]\r\n[reveal-answer q=\"603689\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"603689\"][latex]\\Large\\frac{3}{4}[\/latex][\/hidden-answer]<\/li>\r\n \t
                        4. [latex]\\Large\\frac{12}{18}[\/latex]<\/li>\r\n \t
                        5. [latex]-\\Large\\frac{40}{88}[\/latex]\r\n[reveal-answer q=\"460011\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"460011\"][latex]-\\Large\\frac{5}{11}[\/latex][\/hidden-answer]<\/li>\r\n \t
                        6. [latex]-\\Large\\frac{63}{99}[\/latex]<\/li>\r\n \t
                        7. [latex]-\\Large\\frac{108}{63}[\/latex]\r\n[reveal-answer q=\"381069\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"381069\"][latex]-\\Large\\frac{12}{7}[\/latex][\/hidden-answer]<\/li>\r\n \t
                        8. [latex]-\\Large\\frac{104}{48}[\/latex]<\/li>\r\n \t
                        9. [latex]\\Large\\frac{120}{252}[\/latex]\r\n[reveal-answer q=\"110116\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"110116\"][latex]\\Large\\frac{10}{21}[\/latex][\/hidden-answer]<\/li>\r\n \t
                        10. [latex]\\Large\\frac{182}{294}[\/latex]<\/li>\r\n \t
                        11. [latex]-\\Large\\frac{168}{192}[\/latex]\r\n[reveal-answer q=\"943000\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"943000\"][latex]-\\Large\\frac{7}{8}[\/latex][\/hidden-answer]<\/li>\r\n \t
                        12. [latex]-\\Large\\frac{140}{224}[\/latex]<\/li>\r\n \t
                        13. [latex]\\Large\\frac{11x}{11y}[\/latex]\r\n[reveal-answer q=\"522365\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"522365\"][latex]\\Large\\frac{x}{y}[\/latex][\/hidden-answer]<\/li>\r\n \t
                        14. [latex]\\Large\\frac{15a}{15b}[\/latex]<\/li>\r\n \t
                        15. [latex]-\\Large\\frac{3x}{12y}[\/latex]\r\n[reveal-answer q=\"257307\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"257307\"][latex]-\\Large\\frac{x}{4y}[\/latex][\/hidden-answer]<\/li>\r\n \t
                        16. [latex]-\\Large\\frac{4x}{32y}[\/latex]<\/li>\r\n \t
                        17. [latex]\\Large\\frac{14{x}^{2}}{21y}[\/latex]\r\n[reveal-answer q=\"900010\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"900010\"][latex]\\Large\\frac{2{x}^{2}}{3y}[\/latex][\/hidden-answer]<\/li>\r\n \t
                        18. [latex]\\Large\\frac{24a}{32{b}^{2}}[\/latex]<\/li>\r\n<\/ol>\r\n

                          Multiply and Simplify Fractions<\/h3>\r\nIn the following exercises, multiply, and write the answer in simplified form.\r\n
                            \r\n \t
                          1. [latex]\\Large\\frac{2}{5}\\cdot\\Large\\frac{1}{3}[\/latex]\r\n[reveal-answer q=\"964952\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"964952\"][latex]\\Large\\frac{2}{15}[\/latex][\/hidden-answer]<\/li>\r\n \t
                          2. [latex]\\Large\\frac{1}{2}\\cdot\\Large\\frac{3}{8}[\/latex]<\/li>\r\n \t
                          3. [latex]\\Large\\frac{3}{4}\\cdot\\Large\\frac{9}{10}[\/latex]\r\n[reveal-answer q=\"32111\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"32111\"][latex]\\Large\\frac{27}{40}[\/latex][\/hidden-answer]<\/li>\r\n \t
                          4. [latex]\\Large\\frac{4}{5}\\cdot\\Large\\frac{2}{7}[\/latex]<\/li>\r\n \t
                          5. [latex]-\\Large\\frac{2}{3}\\left(-\\Large\\frac{3}{8}\\right)[\/latex]\r\n[reveal-answer q=\"138602\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"138602\"][latex]\\Large\\frac{1}{4}[\/latex][\/hidden-answer]<\/li>\r\n \t
                          6. [latex]-\\Large\\frac{3}{4}\\left(-\\Large\\frac{4}{9}\\right)[\/latex]<\/li>\r\n \t
                          7. [latex]-\\Large\\frac{5}{9}\\cdot\\Large\\frac{3}{10}[\/latex]\r\n[reveal-answer q=\"830871\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"830871\"][latex]-\\Large\\frac{1}{6}[\/latex][\/hidden-answer]<\/li>\r\n \t
                          8. [latex]-\\Large\\frac{3}{8}\\cdot\\Large\\frac{4}{15}[\/latex]<\/li>\r\n \t
                          9. [latex]\\Large\\frac{7}{12}\\left(-\\Large\\frac{8}{21}\\right)[\/latex]\r\n[reveal-answer q=\"700400\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"700400\"][latex]-\\Large\\frac{2}{9}[\/latex][\/hidden-answer]<\/li>\r\n \t
                          10. [latex]\\Large\\frac{5}{12}\\left(-\\Large\\frac{8}{15}\\right)[\/latex][latex]\\left(-\\Large\\frac{14}{15}\\right)\\left(\\Large\\frac{9}{20}\\right)[\/latex]\r\n[reveal-answer q=\"42142\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"42142\"][latex]-\\Large\\frac{21}{50}[\/latex][\/hidden-answer]<\/li>\r\n \t
                          11. [latex]\\left(-\\Large\\frac{9}{10}\\right)\\left(\\Large\\frac{25}{33}\\right)[\/latex]<\/li>\r\n \t
                          12. [latex]\\left(-\\Large\\frac{63}{84}\\right)\\left(-\\Large\\frac{44}{90}\\right)[\/latex]\r\n[reveal-answer q=\"45036\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"45036\"][latex]\\Large\\frac{11}{30}[\/latex][\/hidden-answer]<\/li>\r\n \t
                          13. [latex]\\left(-\\Large\\frac{33}{60}\\right)\\left(-\\Large\\frac{40}{88}\\right)[\/latex]<\/li>\r\n \t
                          14. [latex]4\\cdot\\Large\\frac{5}{11}[\/latex]<\/li>\r\n \t
                          15. [latex]\\Large\\frac{20}{11}[\/latex]<\/li>\r\n \t
                          16. [latex]5\\cdot\\Large\\frac{8}{3}[\/latex]<\/li>\r\n \t
                          17. [latex]\\Large\\frac{3}{7}\\normalsize\\cdot 21n[\/latex]\r\n[reveal-answer q=\"668006\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"668006\"]9n[\/hidden-answer]<\/li>\r\n \t
                          18. [latex]\\Large\\frac{5}{6}\\normalsize\\cdot 30m[\/latex]<\/li>\r\n \t
                          19. [latex]-28p\\left(-\\Large\\frac{1}{4}\\right)[\/latex]\r\n[reveal-answer q=\"298971\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"298971\"]7p[\/hidden-answer]<\/li>\r\n \t
                          20. [latex]-51q\\left(-\\Large\\frac{1}{3}\\right)[\/latex]<\/li>\r\n \t
                          21. [latex]-8\\Large\\left(\\frac{17}{4}\\right)[\/latex]\r\n[reveal-answer q=\"460650\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"460650\"]\u221234[\/hidden-answer]<\/li>\r\n \t
                          22. [latex]\\Large\\frac{14}{5}\\normalsize\\left(-15\\right)[\/latex]<\/li>\r\n \t
                          23. [latex]-1\\Large\\left(-\\frac{3}{8}\\right)[\/latex]<\/li>\r\n \t
                          24. [latex]\\Large\\frac{3}{8}[\/latex]<\/li>\r\n \t
                          25. [latex]\\left(-1\\right)\\Large\\left(-\\frac{6}{7}\\right)[\/latex]<\/li>\r\n \t
                          26. [latex]{\\Large\\left(\\frac{2}{3}\\right)}^{3}[\/latex]<\/li>\r\n \t
                          27. [latex]\\Large\\frac{8}{27}[\/latex]<\/li>\r\n \t
                          28. [latex]{\\Large\\left(\\frac{4}{5}\\right)}^{2}[\/latex]<\/li>\r\n \t
                          29. [latex]{\\Large\\left(\\frac{6}{5}\\right)}^{4}[\/latex]<\/li>\r\n \t
                          30. [latex]\\Large\\frac{1296}{625}[\/latex]<\/li>\r\n \t
                          31. [latex]{\\Large\\left(\\frac{4}{7}\\right)}^{4}[\/latex]<\/li>\r\n<\/ol>\r\n

                            Find Reciprocals<\/strong><\/h3>\r\nIn the following exercises, find the reciprocal.\r\n
                              \r\n \t
                            1. [latex]\\Large\\frac{3}{4}[\/latex]\r\n[reveal-answer q=\"411246\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"411246\"][latex]\\Large\\frac{4}{3}[\/latex][\/hidden-answer]<\/li>\r\n \t
                            2. [latex]\\Large\\frac{2}{3}[\/latex]<\/li>\r\n \t
                            3. [latex]-\\Large\\frac{5}{17}[\/latex]\r\n[reveal-answer q=\"997878\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"997878\"][latex]-\\Large\\frac{17}{5}[\/latex][\/hidden-answer]<\/li>\r\n \t
                            4. [latex]-\\Large\\frac{6}{19}[\/latex]<\/li>\r\n \t
                            5. [latex]\\Large\\frac{11}{8}[\/latex]\r\n[reveal-answer q=\"895207\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"895207\"][latex]\\Large\\frac{8}{11}[\/latex][\/hidden-answer]<\/li>\r\n \t
                            6. [latex]-13[\/latex]<\/li>\r\n \t
                            7. [latex]-19[\/latex]\r\n[reveal-answer q=\"246229\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"246229\"][latex]-\\Large\\frac{1}{19}[\/latex][\/hidden-answer]<\/li>\r\n \t
                            8. [latex]-1[\/latex]\r\n[reveal-answer q=\"315899\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"315899\"][latex]1[\/latex][\/hidden-answer]<\/li>\r\n<\/ol>\r\n

                              Divide and Simplify Fractions<\/h3>\r\nIn the following exercises, divide, and write the answer in simplified form.\r\n
                                \r\n \t
                              1. [latex]\\Large\\frac{1}{2}\\normalsize\\div\\Large\\frac{1}{4}[\/latex]<\/li>\r\n \t
                              2. [latex]\\Large\\frac{1}{2}\\normalsize\\div\\Large\\frac{1}{8}[\/latex]\r\n[reveal-answer q=\"198822\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"198822\"]4[\/hidden-answer]<\/li>\r\n \t
                              3. [latex]\\Large\\frac{3}{4}\\normalsize\\div\\Large\\frac{2}{3}[\/latex]<\/li>\r\n \t
                              4. [latex]\\Large\\frac{4}{5}\\normalsize\\div\\Large\\frac{3}{4}[\/latex]<\/li>\r\n \t
                              5. [latex]\\Large\\frac{16}{15}[\/latex]<\/li>\r\n \t
                              6. [latex]-\\Large\\frac{4}{5}\\normalsize\\div\\Large\\frac{4}{7}[\/latex]<\/li>\r\n \t
                              7. [latex]-\\Large\\frac{3}{4}\\normalsize\\div\\Large\\frac{3}{5}[\/latex]<\/li>\r\n \t
                              8. [latex]-\\Large\\frac{5}{4}[\/latex]<\/li>\r\n \t
                              9. [latex]-\\Large\\frac{7}{9}\\normalsize\\div\\Large\\left(-\\frac{7}{9}\\right)[\/latex]<\/li>\r\n \t
                              10. [latex]-\\Large\\frac{5}{6}\\normalsize\\div\\Large\\left(-\\frac{5}{6}\\right)[\/latex]\r\n[reveal-answer q=\"24846\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"24846\"]1[\/hidden-answer]<\/li>\r\n \t
                              11. [latex]\\Large\\frac{3}{4}\\normalsize\\div\\Large\\frac{x}{11}[\/latex]<\/li>\r\n \t
                              12. [latex]\\Large\\frac{2}{5}\\normalsize\\div\\Large\\frac{y}{9}[\/latex]<\/li>\r\n \t
                              13. [latex]\\Large\\frac{18}{5y}[\/latex]<\/li>\r\n \t
                              14. [latex]\\Large\\frac{5}{8}\\normalsize\\div\\Large\\frac{a}{10}[\/latex]<\/li>\r\n \t
                              15. [latex]\\Large\\frac{5}{6}\\normalsize\\div\\Large\\frac{c}{15}[\/latex]<\/li>\r\n \t
                              16. [latex]\\Large\\frac{25}{2c}[\/latex]<\/li>\r\n \t
                              17. [latex]\\Large\\frac{5}{18}\\normalsize\\div\\Large\\left(-\\frac{15}{24}\\right)[\/latex]<\/li>\r\n \t
                              18. [latex]\\Large\\frac{7}{18}\\normalsize\\div\\Large\\left(-\\frac{14}{27}\\right)[\/latex]<\/li>\r\n \t
                              19. [latex]-\\Large\\frac{3}{4}[\/latex]<\/li>\r\n \t
                              20. [latex]\\Large\\frac{7p}{12}\\normalsize\\div\\Large\\frac{21p}{8}[\/latex]<\/li>\r\n \t
                              21. [latex]\\Large\\frac{5q}{12}\\normalsize\\div\\Large\\frac{15q}{8}[\/latex]<\/li>\r\n \t
                              22. [latex]\\Large\\frac{2}{9}[\/latex]<\/li>\r\n \t
                              23. [latex]\\Large\\frac{8u}{15}\\normalsize\\div\\Large\\frac{12v}{25}[\/latex]<\/li>\r\n \t
                              24. [latex]\\Large\\frac{12r}{25}\\normalsize\\div\\Large\\frac{18s}{35}[\/latex]<\/li>\r\n \t
                              25. [latex]\\Large\\frac{14r}{15s}[\/latex]<\/li>\r\n \t
                              26. [latex]-5\\normalsize\\div\\Large\\frac{1}{2}[\/latex]<\/li>\r\n \t
                              27. [latex]-3\\normalsize\\div\\Large\\frac{1}{4}[\/latex]\r\n[reveal-answer q=\"141638\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"141638\"]\u221212[\/hidden-answer]<\/li>\r\n \t
                              28. [latex]\\Large\\frac{3}{4}\\normalsize\\div\\left(-12\\right)[\/latex]<\/li>\r\n \t
                              29. [latex]\\Large\\frac{2}{5}\\normalsize\\div\\left(-10\\right)[\/latex]<\/li>\r\n \t
                              30. [latex]-\\Large\\frac{1}{25}[\/latex]<\/li>\r\n \t
                              31. [latex]-18\\normalsize\\div\\Large\\left(-\\frac{9}{2}\\right)[\/latex]<\/li>\r\n \t
                              32. [latex]-15\\normalsize\\div\\Large\\left(-\\frac{5}{3}\\right)[\/latex]\r\n[reveal-answer q=\"454947\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"454947\"]9[\/hidden-answer]<\/li>\r\n \t
                              33. [latex]\\Large\\frac{1}{2}\\normalsize\\div\\Large\\left(-\\frac{3}{4}\\right)\\normalsize\\div\\Large\\frac{7}{8}[\/latex]<\/li>\r\n \t
                              34. [latex]\\Large\\frac{11}{2}\\normalsize\\div\\Large\\frac{7}{8}\\normalsize\\cdot\\Large\\frac{2}{11}[\/latex]<\/li>\r\n<\/ol>\r\n
                                \r\n

                                Everyday Math<\/h3>\r\n

                                Baking<\/h4>\r\n
                                  \r\n \t
                                1. A recipe for chocolate chip cookies calls for [latex]\\Large\\frac{3}{4}[\/latex] cup brown sugar. Imelda wants to double the recipe.\r\nHow much brown sugar will Imelda need? Show your calculation. Write your result as an improper fraction and as a mixed number.<\/li>\r\n \t
                                2. Measuring cups usually come in sets of [latex]\\Large\\frac{1}{8},\\Large\\frac{1}{4},\\Large\\frac{1}{3},\\Large\\frac{1}{2}\\normalsize ,\\text{ and }1[\/latex] cup. Draw a diagram to show two different ways that Imelda could measure the brown sugar needed to double the recipe.<\/li>\r\n<\/ol>\r\n

                                  Baking<\/h4>\r\nNina is making [latex]4[\/latex] pans of fudge to serve after a music recital. For each pan, she needs [latex]\\Large\\frac{2}{3}[\/latex] cup of condensed milk.\r\n
                                    \r\n \t
                                  1. How much condensed milk will Nina need? Show your calculation. Write your result as an improper fraction and as a mixed number.[reveal-answer q=\"732145\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"732145\"][latex]\\Large\\frac{8}{3}\\normalsize =2\\Large\\frac{2}{3}[\/latex][\/hidden-answer]<\/li>\r\n \t
                                  2. Measuring cups usually come in sets of [latex]\\Large\\frac{1}{8},\\Large\\frac{1}{4},\\Large\\frac{1}{3},\\Large\\frac{1}{2}\\normalsize ,\\text{ and }1[\/latex] cup. Draw a diagram to show two different ways that Nina could measure the condensed milk she needs.<\/li>\r\n<\/ol>\r\n

                                    Portions<\/h4>\r\nDon purchased a bulk package of candy that weighs [latex]5[\/latex] pounds. He wants to sell the candy in little bags that hold [latex]\\Large\\frac{1}{4}[\/latex] pound. How many little bags of candy can he fill from the bulk package?\r\n

                                    Portions<\/h4>\r\nKristen has [latex]\\Large\\frac{3}{4}[\/latex] yards of ribbon. She wants to cut it into equal parts to make hair ribbons for her daughter\u2019s [latex]6[\/latex] dolls. How long will each doll\u2019s hair ribbon be?\r\n\r\n[reveal-answer q=\"308784\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"308784\"][latex]\\Large\\frac{1}{8}\\normalsize\\text{yard}[\/latex][\/hidden-answer]\r\n\r\n<\/div>\r\n
                                    \r\n

                                    Writing Exercises<\/h3>\r\nExplain how you find the reciprocal of a fraction.\r\n\r\n[practice-area rows=\"4\"][\/practice-area]\r\n\r\nExplain how you find the reciprocal of a negative fraction.\r\n\r\n[practice-area rows=\"4\"][\/practice-area]\r\n\r\nRafael wanted to order half a medium pizza at a restaurant. The waiter told him that a medium pizza could be cut into [latex]6[\/latex] or [latex]8[\/latex] slices. Would he prefer [latex]3[\/latex] out of [latex]6[\/latex] slices or [latex]4[\/latex] out of [latex]8[\/latex] slices? Rafael replied that since he wasn\u2019t very hungry, he would prefer [latex]3[\/latex] out of [latex]6[\/latex] slices. Explain what is wrong with Rafael\u2019s reasoning.\r\n\r\n[practice-area rows=\"4\"][\/practice-area]\r\n\r\nGive an example from everyday life that demonstrates how [latex]\\Large\\frac{1}{2}\\normalsize\\cdot\\Large\\frac{2}{3}\\normalsize\\text{ is }\\Large\\frac{1}{3}[\/latex].\r\n\r\n[practice-area rows=\"4\"][\/practice-area]\r\n\r\n<\/div>\r\n

                                    Multiplying and Dividing Mixed Numbers and Complex Fractions<\/h2>\r\n

                                    Multiply Mixed Numbers<\/h3>\r\nIn the following exercises, multiply and write the answer in simplified form.\r\n
                                      \r\n \t
                                    1. [latex]4\\Large\\frac{3}{8}\\normalsize\\cdot\\Large\\frac{7}{10}[\/latex]<\/li>\r\n \t
                                    2. [latex]2\\Large\\frac{4}{9}\\normalsize\\cdot\\Large\\frac{6}{7}[\/latex]\r\n[reveal-answer q=\"549290\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"549290\"][latex]\\Large\\frac{44}{21}[\/latex][\/hidden-answer]<\/li>\r\n \t
                                    3. [latex]\\Large\\frac{15}{22}\\normalsize\\cdot 3\\Large\\frac{3}{5}[\/latex]<\/li>\r\n \t
                                    4. [latex]\\Large\\frac{25}{36}\\normalsize\\cdot 6\\Large\\frac{3}{10}[\/latex]\r\n[reveal-answer q=\"587963\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"587963\"][latex]\\Large\\frac{35}{8}[\/latex][\/hidden-answer]<\/li>\r\n \t
                                    5. [latex]4\\Large\\frac{2}{3}\\left(\\normalsize -1\\Large\\frac{1}{8}\\right)[\/latex]<\/li>\r\n \t
                                    6. [latex]2\\Large\\frac{2}{5}\\left(\\normalsize -2\\Large\\frac{2}{9}\\right)[\/latex]\r\n[reveal-answer q=\"855722\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"855722\"][latex]-\\Large\\frac{16}{3}[\/latex][\/hidden-answer]<\/li>\r\n \t
                                    7. [latex]-4\\Large\\frac{4}{9}\\normalsize\\cdot 5\\Large\\frac{13}{16}[\/latex]<\/li>\r\n \t
                                    8. [latex]-1\\Large\\frac{7}{20}\\normalsize\\cdot 2\\Large\\frac{11}{12}[\/latex]\r\n[reveal-answer q=\"387492\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"387492\"][latex]-\\Large\\frac{63}{16}[\/latex][\/hidden-answer]<\/li>\r\n<\/ol>\r\n

                                      Divide Mixed Numbers<\/h3>\r\nIn the following exercises, divide, and write your answer in simplified form.\r\n
                                        \r\n \t
                                      1. [latex]5\\Large\\frac{1}{3}\\normalsize\\div 4[\/latex]<\/li>\r\n \t
                                      2. [latex]13\\Large\\frac{1}{2}\\normalsize\\div 9[\/latex]\r\n[reveal-answer q=\"791086\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"791086\"][latex]\\Large\\frac{3}{2}[\/latex][\/hidden-answer]<\/li>\r\n \t
                                      3. [latex]-12\\Large\\normalsize\\div 3\\Large\\frac{3}{11}[\/latex]<\/li>\r\n \t
                                      4. [latex]-7\\div 5\\Large\\frac{1}{4}[\/latex]\r\n[reveal-answer q=\"302691\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"302691\"][latex]-\\Large\\frac{4}{3}[\/latex][\/hidden-answer]<\/li>\r\n \t
                                      5. [latex]6\\Large\\frac{3}{8}\\normalsize\\div 2\\Large\\frac{1}{8}[\/latex]<\/li>\r\n \t
                                      6. [latex]2\\Large\\frac{1}{5}\\normalsize\\div 1\\Large\\frac{1}{10}[\/latex]\r\n[reveal-answer q=\"354696\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"354696\"]2[\/hidden-answer]<\/li>\r\n \t
                                      7. [latex]-9\\Large\\frac{3}{5}\\normalsize\\div\\Large\\left(\\normalsize -1\\Large\\frac{3}{5}\\right)[\/latex]<\/li>\r\n \t
                                      8. [latex]-18\\Large\\frac{3}{4}\\normalsize\\div\\Large\\left(\\normalsize -3\\Large\\frac{3}{4}\\right)[\/latex]\r\n[reveal-answer q=\"954878\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"954878\"]5[\/hidden-answer]<\/li>\r\n<\/ol>\r\n

                                        Translate Phrases to Expressions with Fractions<\/strong><\/h3>\r\nIn the following exercises, translate each English phrase into an algebraic expression.\r\n
                                          \r\n \t
                                        1. the quotient of [latex]5u[\/latex] and [latex]11[\/latex]<\/li>\r\n \t
                                        2. the quotient of [latex]7v[\/latex] and [latex]13[\/latex]\r\n[reveal-answer q=\"815312\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"815312\"][latex]\\Large\\frac{7v}{13}[\/latex][\/hidden-answer]<\/li>\r\n \t
                                        3. the quotient of [latex]p[\/latex] and [latex]q[\/latex]<\/li>\r\n \t
                                        4. the quotient of [latex]a[\/latex] and [latex]b[\/latex]\r\n[reveal-answer q=\"567799\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"567799\"][latex]\\Large\\frac{a}{b}[\/latex][\/hidden-answer]<\/li>\r\n \t
                                        5. the quotient of [latex]r[\/latex] and the sum of [latex]s[\/latex] and [latex]10[\/latex]<\/li>\r\n \t
                                        6. the quotient of [latex]A[\/latex] and the difference of [latex]3[\/latex] and [latex]B[\/latex]\r\n[reveal-answer q=\"473802\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"473802\"][latex]\\Large\\frac{A}{3-B}[\/latex][\/hidden-answer]<\/li>\r\n<\/ol>\r\n

                                          Simplify Complex Fractions<\/strong><\/h3>\r\nIn the following exercises, simplify the complex fraction.\r\n
                                            \r\n \t
                                          1. [latex]\\displaystyle\\Large\\frac{\\Large\\frac{2}{3}}{\\Large\\frac{8}{9}}[\/latex]<\/li>\r\n \t
                                          2. [latex]\\displaystyle\\Large\\frac{\\Large\\frac{4}{5}}{\\Large\\frac{8}{15}}[\/latex]\r\n[reveal-answer q=\"122074\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"122074\"][latex]\\displaystyle\\frac{3}{2}[\/latex][\/hidden-answer]<\/li>\r\n \t
                                          3. [latex]\\displaystyle\\Large\\frac{-\\Large\\frac{8}{21}}{\\Large\\frac{12}{35}}[\/latex]<\/li>\r\n \t
                                          4. [latex]\\displaystyle\\Large\\frac{-\\Large\\frac{9}{16}}{\\Large\\frac{33}{40}}[\/latex]\r\n[reveal-answer q=\"132446\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"132446\"][latex]-\\Large\\frac{15}{22}[\/latex][\/hidden-answer]<\/li>\r\n \t
                                          5. [latex]\\displaystyle\\frac{-\\Large\\frac{4}{5}}{2}[\/latex]<\/li>\r\n \t
                                          6. [latex]\\displaystyle\\frac{-\\Large\\frac{9}{10}}{3}[\/latex]\r\n[reveal-answer q=\"545507\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"545507\"][latex]-\\Large\\frac{3}{10}[\/latex][\/hidden-answer]<\/li>\r\n \t
                                          7. [latex]\\displaystyle\\frac{\\Large\\frac{2}{5}}{8}[\/latex]<\/li>\r\n \t
                                          8. [latex]\\displaystyle\\frac{\\Large\\frac{5}{3}}{10}[\/latex]\r\n[reveal-answer q=\"408289\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"408289\"][latex]\\displaystyle\\frac{1}{6}[\/latex][\/hidden-answer]<\/li>\r\n \t
                                          9. [latex]\\displaystyle\\Large\\frac{\\Large\\frac{m}{3}}{\\Large\\frac{n}{2}}[\/latex]<\/li>\r\n \t
                                          10. [latex]\\displaystyle\\Large\\frac{\\Large\\frac{r}{5}}{\\Large\\frac{s}{3}}[\/latex]\r\n[reveal-answer q=\"190662\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"190662\"][latex]\\displaystyle\\frac{3r}{5s}[\/latex][\/hidden-answer]<\/li>\r\n \t
                                          11. [latex]\\displaystyle\\Large\\frac{-\\Large\\frac{x}{6}}{-\\Large\\frac{8}{9}}[\/latex]<\/li>\r\n \t
                                          12. [latex]\\displaystyle\\Large\\frac{-\\Large\\frac{3}{8}}{-\\Large\\frac{y}{12}}[\/latex]\r\n[reveal-answer q=\"86948\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"86948\"][latex]\\displaystyle\\frac{9}{2y}[\/latex][\/hidden-answer]<\/li>\r\n \t
                                          13. [latex]\\displaystyle\\frac{2\\Large\\frac{4}{5}}{\\Large\\frac{1}{10}}[\/latex]<\/li>\r\n \t
                                          14. [latex]\\displaystyle\\frac{4\\Large\\frac{2}{3}}{\\Large\\frac{1}{6}}[\/latex]\r\n[reveal-answer q=\"933059\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"933059\"]28[\/hidden-answer]<\/li>\r\n \t
                                          15. [latex]\\displaystyle\\Large\\frac{\\Large\\frac{7}{9}}{\\normalsize -2\\Large\\frac{4}{5}}[\/latex]<\/li>\r\n \t
                                          16. [latex]\\displaystyle\\Large\\frac{\\Large\\frac{3}{8}}{\\normalsize -6\\Large\\frac{3}{4}}[\/latex]\r\n[reveal-answer q=\"341791\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"341791\"][latex]-\\Large\\frac{1}{18}[\/latex][\/hidden-answer]<\/li>\r\n<\/ol>\r\n

                                            Simplify Expressions with a Fraction Bar<\/strong><\/h3>\r\nIn the following exercises, identify the equivalent fractions.\r\n
                                              \r\n \t
                                            1. Which of the following fractions are equivalent to [latex]\\Large\\frac{5}{-11}?[\/latex]\r\n[latex]\\Large\\frac{-5}{-11},\\Large\\frac{-5}{11},\\Large\\frac{5}{11},-\\Large\\frac{5}{11}[\/latex]<\/li>\r\n \t
                                            2. Which of the following fractions are equivalent to [latex]\\Large\\frac{-4}{9}?[\/latex]\r\n[latex]\\Large\\frac{-4}{-9},\\Large\\frac{-4}{9},\\Large\\frac{4}{9},-\\Large\\frac{4}{9}[\/latex]\r\n[reveal-answer q=\"743755\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"743755\"][latex]\\Large\\frac{-4}{9},\\text{}-\\Large\\frac{4}{9}[\/latex][\/hidden-answer]<\/li>\r\n \t
                                            3. Which of the following fractions are equivalent to [latex]-\\Large\\frac{11}{3}?[\/latex]\r\n[latex]\\Large\\frac{-11}{3},\\Large\\frac{11}{3},\\Large\\frac{-11}{-3},\\text{}\\Large\\frac{11}{-3}[\/latex]<\/li>\r\n \t
                                            4. Which of the following fractions are equivalent to [latex]-\\Large\\frac{13}{6}?[\/latex]\r\n[latex]\\Large\\frac{13}{6},\\Large\\frac{13}{-6},\\Large\\frac{-13}{-6},\\Large\\frac{-13}{6}[\/latex]\r\n[reveal-answer q=\"446627\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"446627\"][latex]\\Large\\frac{13}{-6},\\Large\\frac{-13}{6}[\/latex][\/hidden-answer]<\/li>\r\n<\/ol>\r\n

                                              Simplify Fractions<\/strong><\/h3>\r\nIn the following exercises, simplify.\r\n
                                                \r\n \t
                                              1. [latex]\\Large\\frac{4+11}{8}[\/latex]<\/li>\r\n \t
                                              2. [latex]\\Large\\frac{9+3}{7}[\/latex][reveal-answer q=\"371948\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"371948\"][latex]\\Large\\frac{12}{7}[\/latex][\/hidden-answer]<\/li>\r\n \t
                                              3. [latex]\\Large\\frac{22+3}{10}[\/latex]<\/li>\r\n \t
                                              4. [latex]\\Large\\frac{19 - 4}{6}[\/latex][reveal-answer q=\"835322\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"835322\"][latex]\\Large\\frac{5}{2}[\/latex][\/hidden-answer]<\/li>\r\n \t
                                              5. [latex]\\Large\\frac{48}{24 - 15}[\/latex]<\/li>\r\n \t
                                              6. [latex]\\Large\\frac{46}{4+4}[\/latex][reveal-answer q=\"780942\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"780942\"][latex]\\Large\\frac{23}{4}[\/latex][\/hidden-answer]<\/li>\r\n \t
                                              7. [latex]\\Large\\frac{-6+6}{8+4}[\/latex]<\/li>\r\n \t
                                              8. [latex]\\Large\\frac{-6+3}{17 - 8}[\/latex][reveal-answer q=\"524568\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"524568\"][latex]-\\Large\\frac{1}{3}[\/latex][\/hidden-answer]<\/li>\r\n \t
                                              9. [latex]\\Large\\frac{22 - 14}{19 - 13}[\/latex]<\/li>\r\n \t
                                              10. [latex]\\Large\\frac{15+9}{18+12}[\/latex][reveal-answer q=\"746498\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"746498\"][latex]\\Large\\frac{4}{5}[\/latex][\/hidden-answer]<\/li>\r\n \t
                                              11. [latex]\\Large\\frac{5\\cdot 8}{-10}[\/latex]<\/li>\r\n \t
                                              12. [latex]\\Large\\frac{3\\cdot 4}{-24}[\/latex][reveal-answer q=\"588810\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"588810\"][latex]-\\Large\\frac{1}{2}[\/latex][\/hidden-answer]<\/li>\r\n \t
                                              13. [latex]\\Large\\frac{4\\cdot 3}{6\\cdot 6}[\/latex]<\/li>\r\n \t
                                              14. [latex]\\Large\\frac{6\\cdot 6}{9\\cdot 2}[\/latex][reveal-answer q=\"238626\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"238626\"]2[\/hidden-answer]<\/li>\r\n \t
                                              15. [latex]\\Large\\frac{{4}^{2}-1}{25}[\/latex]<\/li>\r\n \t
                                              16. [latex]\\Large\\frac{{7}^{2}+1}{60}[\/latex][reveal-answer q=\"556548\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"556548\"][latex]\\Large\\frac{5}{6}[\/latex][\/hidden-answer]<\/li>\r\n \t
                                              17. [latex]\\Large\\frac{8\\cdot 3+2\\cdot 9}{14+3}[\/latex]<\/li>\r\n \t
                                              18. [latex]\\Large\\frac{9\\cdot 6 - 4\\cdot 7}{22+3}[\/latex][reveal-answer q=\"947150\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"947150\"][latex]\\Large\\frac{26}{25}[\/latex][\/hidden-answer]<\/li>\r\n \t
                                              19. [latex]\\Large\\frac{15\\cdot 5-{5}^{2}}{2\\cdot 10}[\/latex]<\/li>\r\n \t
                                              20. [latex]\\Large\\frac{12\\cdot 9-{3}^{2}}{3\\cdot 18}[\/latex][reveal-answer q=\"500204\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"500204\"][latex]\\Large\\frac{11}{6}[\/latex][\/hidden-answer]<\/li>\r\n \t
                                              21. [latex]\\Large\\frac{5\\cdot 6 - 3\\cdot 4}{4\\cdot 5 - 2\\cdot 3}[\/latex]<\/li>\r\n \t
                                              22. [latex]\\Large\\frac{8\\cdot 9 - 7\\cdot 6}{5\\cdot 6 - 9\\cdot 2}[\/latex][reveal-answer q=\"630418\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"630418\"][latex]\\Large\\frac{5}{2}[\/latex][\/hidden-answer]<\/li>\r\n \t
                                              23. [latex]\\Large\\frac{{5}^{2}-{3}^{2}}{3 - 5}[\/latex]<\/li>\r\n \t
                                              24. [latex]\\Large\\frac{{6}^{2}-{4}^{2}}{4 - 6}[\/latex][reveal-answer q=\"794918\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"794918\"]\u221210[\/hidden-answer]<\/li>\r\n \t
                                              25. [latex]\\Large\\frac{2+4\\left(3\\right)}{-3-{2}^{2}}[\/latex]<\/li>\r\n \t
                                              26. [latex]\\Large\\frac{7+3\\left(5\\right)}{-2-{3}^{2}}[\/latex][reveal-answer q=\"958628\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"958628\"]\u22122[\/hidden-answer]<\/li>\r\n \t
                                              27. [latex]\\Large\\frac{7\\cdot 4 - 2\\left(8 - 5\\right)}{9.3 - 3.5}[\/latex]<\/li>\r\n \t
                                              28. [latex]\\Large\\frac{9\\cdot 7 - 3\\left(12 - 8\\right)}{8.7 - 6.6}[\/latex][reveal-answer q=\"983540\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"983540\"][latex]\\Large\\frac{51}{20}[\/latex][\/hidden-answer]<\/li>\r\n \t
                                              29. [latex]\\Large\\frac{9\\left(8 - 2\\right)-3\\left(15 - 7\\right)}{6\\left(7 - 1\\right)-3\\left(17 - 9\\right)}[\/latex]<\/li>\r\n \t
                                              30. [latex]\\Large\\frac{8\\left(9 - 2\\right)-4\\left(14 - 9\\right)}{7\\left(8 - 3\\right)-3\\left(16 - 9\\right)}[\/latex][reveal-answer q=\"882159\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"882159\"][latex]\\Large\\frac{18}{7}[\/latex][\/hidden-answer]<\/li>\r\n<\/ol>\r\n
                                                \r\n

                                                Everyday Math<\/h3>\r\n

                                                Baking<\/h4>\r\nA recipe for chocolate chip cookies calls for [latex]2\\Large\\frac{1}{4}[\/latex] cups of flour. Graciela wants to double the recipe.\r\n
                                                  \r\n \t
                                                1. \u00a0How much flour will Graciela need? Show your calculation. Write your result as an improper fraction and as a mixed number.<\/li>\r\n \t
                                                2. Measuring cups usually come in sets with cups for [latex]\\Large\\frac{1}{8},\\Large\\frac{1}{4},\\Large\\frac{1}{3},\\Large\\frac{1}{2}\\normalsize ,\\text{ and }1[\/latex] cup. Draw a diagram to show two different ways that Graciela could measure out the flour needed to double the recipe.<\/li>\r\n<\/ol>\r\n

                                                  Baking<\/h4>\r\nA booth at the county fair sells fudge by the pound. Their award winning \"Chocolate Overdose\" fudge contains [latex]2\\Large\\frac{2}{3}[\/latex] cups of chocolate chips per pound.\r\n
                                                    \r\n \t
                                                  1. How many cups of chocolate chips are in a half-pound of the fudge\r\n[reveal-answer q=\"328325\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"328325\"][latex]\\Large\\frac{4}{3}\\normalsize =1\\Large\\frac{1}{3}\\normalsize\\text{cups}[\/latex][\/hidden-answer]<\/li>\r\n \t
                                                  2. The owners of the booth make the fudge in [latex]10[\/latex] -pound batches. How many chocolate chips do they need to make a [latex]10[\/latex] -pound batch? Write your results as improper fractions and as a mixed numbers.\r\n[reveal-answer q=\"192509\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"192509\"][latex]\\Large\\frac{80}{3}\\normalsize =26\\Large\\frac{2}{3}\\normalsize\\text{cups}[\/latex][\/hidden-answer]<\/li>\r\n<\/ol>\r\n<\/div>\r\n
                                                    \r\n

                                                    Writing Exercises<\/h3>\r\nExplain how to find the reciprocal of a mixed number.\r\n\r\n[practice-area rows=\"4\"][\/practice-area]\r\n\r\nExplain how to multiply mixed numbers.\r\n\r\n[practice-area rows=\"4\"][\/practice-area]\r\n\r\nRandy thinks that [latex]3\\Large\\frac{1}{2}\\normalsize\\cdot 5\\Large\\frac{1}{4}[\/latex] is [latex]15\\Large\\frac{1}{8}[\/latex]. Explain what is wrong with Randy\u2019s thinking.\r\n\r\n[practice-area rows=\"4\"][\/practice-area]\r\n\r\nExplain why [latex]-\\Large\\frac{1}{2},\\Large\\frac{-1}{2}[\/latex], and [latex]\\Large\\frac{1}{-2}[\/latex] are equivalent.\r\n\r\n[practice-area rows=\"4\"][\/practice-area]\r\n\r\n<\/div>\r\n

                                                    Adding and Subtracting Fractions With Common Denominators<\/h2>\r\n

                                                    Model Fraction Addition<\/h3>\r\nIn the following exercises, use a model to add the fractions. Show a diagram to illustrate your model.\r\n
                                                      \r\n \t
                                                    1. [latex]\\Large\\frac{2}{5}+\\Large\\frac{1}{5}[\/latex]<\/li>\r\n \t
                                                    2. [latex]\\Large\\frac{3}{10}+\\Large\\frac{4}{10}[\/latex][reveal-answer q=\"446628\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"446628\"]\"A[\/hidden-answer]<\/li>\r\n \t
                                                    3. [latex]\\Large\\frac{7}{10}[\/latex]<\/li>\r\n \t
                                                    4. [latex]\\Large\\frac{1}{6}+\\Large\\frac{3}{6}[\/latex]<\/li>\r\n \t
                                                    5. [latex]\\Large\\frac{3}{8}+\\Large\\frac{3}{8}[\/latex][reveal-answer q=\"568202\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"568202\"]\"A[\/hidden-answer]<\/li>\r\n \t
                                                    6. [latex]\\Large\\frac{3}{4}[\/latex]<\/li>\r\n<\/ol>\r\n

                                                      Add Fractions with a Common Denominator<\/h3>\r\nIn the following exercises, find each sum.\r\n
                                                        \r\n \t
                                                      1. [latex]\\Large\\frac{4}{9}+\\Large\\frac{1}{9}[\/latex]<\/li>\r\n \t
                                                      2. [latex]\\Large\\frac{2}{9}+\\Large\\frac{5}{9}[\/latex][reveal-answer q=\"618493\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"618493\"][latex]\\Large\\frac{7}{9}[\/latex][\/hidden-answer]<\/li>\r\n \t
                                                      3. [latex]\\Large\\frac{6}{13}+\\Large\\frac{7}{13}[\/latex]<\/li>\r\n \t
                                                      4. [latex]\\Large\\frac{9}{15}+\\Large\\frac{7}{15}[\/latex][reveal-answer q=\"544656\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"544656\"][latex]\\Large\\frac{16}{15}[\/latex][\/hidden-answer]<\/li>\r\n \t
                                                      5. [latex]\\Large\\frac{x}{4}+\\Large\\frac{3}{4}[\/latex]<\/li>\r\n \t
                                                      6. [latex]\\Large\\frac{y}{3}+\\Large\\frac{2}{3}[\/latex][reveal-answer q=\"728246\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"728246\"][latex]\\Large\\frac{y+2}{3}[\/latex][\/hidden-answer]<\/li>\r\n \t
                                                      7. [latex]\\Large\\frac{7}{p}+\\Large\\frac{9}{p}[\/latex]<\/li>\r\n \t
                                                      8. [latex]\\Large\\frac{8}{q}+\\Large\\frac{6}{q}[\/latex][reveal-answer q=\"348392\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"348392\"][latex]\\Large\\frac{14}{q}[\/latex][\/hidden-answer]<\/li>\r\n \t
                                                      9. [latex]\\Large\\frac{8b}{9}+\\Large\\frac{3b}{9}[\/latex]<\/li>\r\n \t
                                                      10. [latex]\\Large\\frac{5a}{7}+\\Large\\frac{4a}{7}[\/latex][reveal-answer q=\"659244\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"659244\"][latex]\\Large\\frac{9a}{7}[\/latex][\/hidden-answer]<\/li>\r\n \t
                                                      11. [latex]\\Large\\frac{-12y}{8}+\\Large\\frac{3y}{8}[\/latex]<\/li>\r\n \t
                                                      12. [latex]\\Large\\frac{-11x}{5}+\\Large\\frac{7x}{5}[\/latex][reveal-answer q=\"30535\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"30535\"][latex]\\Large\\frac{-4x}{5}[\/latex][\/hidden-answer]<\/li>\r\n \t
                                                      13. [latex]-\\Large\\frac{1}{8}+\\Large\\left(-\\frac{3}{8}\\right)[\/latex]<\/li>\r\n \t
                                                      14. [latex]-\\Large\\frac{1}{8}+\\Large\\left(-\\frac{5}{8}\\right)[\/latex][reveal-answer q=\"411420\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"411420\"][latex]-\\Large\\frac{3}{4}[\/latex][\/hidden-answer]<\/li>\r\n \t
                                                      15. [latex]-\\Large\\frac{3}{16}+\\Large\\left(-\\frac{7}{16}\\right)[\/latex]<\/li>\r\n \t
                                                      16. [latex]-\\Large\\frac{5}{16}+\\Large\\left(-\\frac{9}{16}\\right)[\/latex][reveal-answer q=\"764769\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"764769\"][latex]-\\Large\\frac{7}{8}[\/latex][\/hidden-answer]<\/li>\r\n \t
                                                      17. [latex]-\\Large\\frac{8}{17}+\\Large\\frac{15}{17}[\/latex]<\/li>\r\n \t
                                                      18. [latex]-\\Large\\frac{9}{19}+\\Large\\frac{17}{19}[\/latex][reveal-answer q=\"259581\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"259581\"][latex]\\Large\\frac{8}{19}[\/latex][\/hidden-answer]<\/li>\r\n \t
                                                      19. [latex]\\Large\\frac{6}{13}+\\Large\\left(-\\frac{10}{13}\\right)+\\Large\\left(-\\frac{12}{13}\\right)[\/latex]<\/li>\r\n \t
                                                      20. [latex]\\Large\\frac{5}{12}+\\Large\\left(-\\frac{7}{12}\\right)+\\Large\\left(-\\frac{11}{12}\\right)[\/latex][reveal-answer q=\"999337\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"999337\"][latex]-\\Large\\frac{13}{12}[\/latex][\/hidden-answer]<\/li>\r\n<\/ol>\r\n

                                                        Model Fraction Subtraction<\/h3>\r\nIn the following exercises, use a model to subtract the fractions. Show a diagram to illustrate your model.\r\n
                                                          \r\n \t
                                                        1. [latex]\\Large\\frac{5}{8}-\\Large\\frac{2}{8}[\/latex]<\/li>\r\n \t
                                                        2. [latex]\\Large\\frac{5}{6}-\\Large\\frac{2}{6}[\/latex][reveal-answer q=\"540632\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"540632\"]\"A[\/hidden-answer]<\/li>\r\n \t
                                                        3. [latex]\\Large\\frac{1}{2}[\/latex]<\/li>\r\n<\/ol>\r\n

                                                          Subtract Fractions with a Common Denominator<\/h3>\r\nIn the following exercises, find the difference.\r\n
                                                            \r\n \t
                                                          1. [latex]\\Large\\frac{4}{5}-\\Large\\frac{1}{5}[\/latex]<\/li>\r\n \t
                                                          2. [latex]\\Large\\frac{4}{5}-\\Large\\frac{3}{5}[\/latex][reveal-answer q=\"382806\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"382806\"][latex]\\Large\\frac{1}{5}[\/latex][\/hidden-answer]<\/li>\r\n \t
                                                          3. [latex]\\Large\\frac{11}{15}-\\Large\\frac{7}{15}[\/latex]<\/li>\r\n \t
                                                          4. [latex]\\Large\\frac{9}{13}-\\Large\\frac{4}{13}[\/latex][reveal-answer q=\"363188\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"363188\"][latex]\\Large\\frac{5}{13}[\/latex][\/hidden-answer]<\/li>\r\n \t
                                                          5. [latex]\\Large\\frac{11}{12}-\\Large\\frac{5}{12}[\/latex]<\/li>\r\n \t
                                                          6. [latex]\\Large\\frac{7}{12}-\\Large\\frac{5}{12}[\/latex][reveal-answer q=\"962772\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"962772\"][latex]\\Large\\frac{1}{6}[\/latex][\/hidden-answer]<\/li>\r\n \t
                                                          7. [latex]\\Large\\frac{4}{21}-\\Large\\frac{19}{21}[\/latex]<\/li>\r\n \t
                                                          8. [latex]-\\Large\\frac{8}{9}-\\Large\\frac{16}{9}[\/latex][reveal-answer q=\"708371\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"708371\"][latex]-\\Large\\frac{8}{3}[\/latex][\/hidden-answer]<\/li>\r\n \t
                                                          9. [latex]\\Large\\frac{y}{17}-\\Large\\frac{9}{17}[\/latex]<\/li>\r\n \t
                                                          10. [latex]\\Large\\frac{x}{19}-\\Large\\frac{8}{19}[\/latex][reveal-answer q=\"847912\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"847912\"][latex]\\Large\\frac{x - 8}{19}[\/latex][\/hidden-answer]<\/li>\r\n \t
                                                          11. [latex]\\Large\\frac{5y}{8}-\\Large\\frac{7}{8}[\/latex]<\/li>\r\n \t
                                                          12. [latex]\\Large\\frac{11z}{13}-\\Large\\frac{8}{13}[\/latex][reveal-answer q=\"626770\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"626770\"][latex]\\Large\\frac{11z - 8}{13}[\/latex][\/hidden-answer]<\/li>\r\n \t
                                                          13. [latex]-\\Large\\frac{8}{d}-\\Large\\frac{3}{d}[\/latex]<\/li>\r\n \t
                                                          14. [latex]-\\Large\\frac{7}{c}-\\Large\\frac{7}{c}[\/latex][reveal-answer q=\"71545\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"71545\"][latex]-\\Large\\frac{14}{c}[\/latex][\/hidden-answer]<\/li>\r\n \t
                                                          15. [latex]-\\Large\\frac{23}{u}-\\Large\\frac{15}{u}[\/latex]<\/li>\r\n \t
                                                          16. [latex]-\\Large\\frac{29}{v}-\\Large\\frac{26}{v}[\/latex][reveal-answer q=\"176688\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"176688\"][latex]-\\Large\\frac{55}{v}[\/latex][\/hidden-answer]<\/li>\r\n \t
                                                          17. [latex]\\Large\\frac{6c}{7}-\\Large\\frac{5c}{7}[\/latex]<\/li>\r\n \t
                                                          18. [latex]\\Large\\frac{12d}{11}-\\Large\\frac{9d}{11}[\/latex][reveal-answer q=\"448633\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"448633\"][latex]\\Large\\frac{3d}{11}[\/latex][\/hidden-answer]<\/li>\r\n \t
                                                          19. [latex]\\Large\\frac{-4r}{13}-\\Large\\frac{5r}{13}[\/latex]<\/li>\r\n \t
                                                          20. [latex]\\Large\\frac{-7s}{3}-\\Large\\frac{7s}{3}[\/latex][reveal-answer q=\"529883\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"529883\"][latex]-\\Large\\frac{14s}{3}[\/latex][\/hidden-answer]<\/li>\r\n \t
                                                          21. [latex]-\\Large\\frac{3}{5}-\\Large\\left(-\\frac{4}{5}\\right)[\/latex]<\/li>\r\n \t
                                                          22. [latex]-\\Large\\frac{3}{7}-\\Large\\left(-\\frac{5}{7}\\right)[\/latex][reveal-answer q=\"999735\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"999735\"][latex]\\Large\\frac{2}{7}[\/latex][\/hidden-answer]<\/li>\r\n \t
                                                          23. [latex]-\\Large\\frac{7}{9}-\\Large\\left(-\\frac{5}{9}\\right)[\/latex]<\/li>\r\n \t
                                                          24. [latex]-\\Large\\frac{8}{11}-\\Large\\left(-\\frac{5}{11}\\right)[\/latex][reveal-answer q=\"43470\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"43470\"][latex]-\\Large\\frac{3}{11}[\/latex][\/hidden-answer]<\/li>\r\n<\/ol>\r\n

                                                            Identify and Use Fraction Operations<\/h3>\r\nIn the following exercises, perform the indicated operation and write your answers in simplified form.\r\n
                                                              \r\n \t
                                                            1. [latex]-\\Large\\frac{5}{18}\\cdot\\Large\\frac{9}{10}[\/latex]<\/li>\r\n \t
                                                            2. [latex]-\\Large\\frac{3}{14}\\cdot\\Large\\frac{7}{12}[\/latex][reveal-answer q=\"261442\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"261442\"][latex]-\\Large\\frac{1}{8}[\/latex][\/hidden-answer]<\/li>\r\n \t
                                                            3. [latex]\\Large\\frac{n}{5}-\\Large\\frac{4}{5}[\/latex]<\/li>\r\n \t
                                                            4. [latex]\\Large\\frac{6}{11}-\\Large\\frac{s}{11}[\/latex][reveal-answer q=\"848778\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"848778\"][latex]\\Large\\frac{6-s}{11}[\/latex][\/hidden-answer]<\/li>\r\n \t
                                                            5. [latex]-\\Large\\frac{7}{24}+\\Large\\frac{2}{24}[\/latex]<\/li>\r\n \t
                                                            6. [latex]-\\Large\\frac{5}{18}+\\Large\\frac{1}{18}[\/latex][reveal-answer q=\"390881\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"390881\"][latex]-\\Large\\frac{2}{9}[\/latex][\/hidden-answer]<\/li>\r\n \t
                                                            7. [latex]\\Large\\frac{8}{15}\\div\\Large\\frac{12}{5}[\/latex]<\/li>\r\n \t
                                                            8. [latex]\\Large\\frac{7}{12}\\div\\Large\\frac{9}{28}[\/latex][reveal-answer q=\"673922\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"673922\"][latex]\\Large\\frac{49}{27}[\/latex][\/hidden-answer]<\/li>\r\n<\/ol>\r\n
                                                              \r\n

                                                              Everyday Math<\/h3>\r\n

                                                              Trail Mix<\/h4>\r\nJacob is mixing together nuts and raisins to make trail mix. He has [latex]\\Large\\frac{6}{10}[\/latex] of a pound of nuts and [latex]\\Large\\frac{3}{10}[\/latex] of a pound of raisins. How much trail mix can he make?\r\n

                                                              Baking<\/h4>\r\nJanet needs [latex]\\Large\\frac{5}{8}[\/latex] of a cup of flour for a recipe she is making. She only has [latex]\\Large\\frac{3}{8}[\/latex] of a cup of flour and will ask to borrow the rest from her next-door neighbor. How much flour does she have to borrow?\r\n\r\n[reveal-answer q=\"255738\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"255738\"][latex]\\Large\\frac{1}{4}\\normalsize\\text{cup}[\/latex][\/hidden-answer]\r\n\r\n<\/div>\r\n
                                                              \r\n

                                                              Writing Exercises<\/h3>\r\nGreg dropped his case of drill bits and three of the bits fell out.\u00a0 The three bits were\u00a0[latex]\\Large\\frac{7}{16}[\/latex],\u00a0[latex]\\Large\\frac{3}{16}[\/latex], and\u00a0[latex]\\Large\\frac{1}{4}[\/latex].\u00a0 The case has slots for the drill bits, and the slots are arranged in order from smallest to largest. Greg needs to put the bits that fell out back in the case in the empty slots. Where do the three bits go? Explain how you know.\r\n\r\nBits in case: [latex]\\Large\\frac{1}{16}[\/latex] , [latex]\\Large\\frac{1}{8}[\/latex] , ___, ___, [latex]\\Large\\frac{5}{16}[\/latex] , [latex]\\Large\\frac{3}{8}[\/latex] , ___, [latex]\\Large\\frac{1}{2}[\/latex] , [latex]\\Large\\frac{9}{16}[\/latex] , [latex]\\Large\\frac{5}{8}[\/latex] .\r\n\r\n[practice-area rows=\"4\"][\/practice-area]\r\n[reveal-answer q=\"384008\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"384008\"]Bits that fell out: [latex]\\Large\\frac{7}{16}[\/latex] , [latex]\\Large\\frac{3}{16}[\/latex] , [latex]\\Large\\frac{1}{4}[\/latex] .[\/hidden-answer]\r\n\r\nAfter a party, Lupe has [latex]\\Large\\frac{5}{12}[\/latex] of a cheese pizza, [latex]\\Large\\frac{4}{12}[\/latex] of a pepperoni pizza, and [latex]\\Large\\frac{4}{12}[\/latex] of a veggie pizza left. Will all the slices fit into [latex]1[\/latex] pizza box? Explain your reasoning.\r\n\r\n[practice-area rows=\"4\"][\/practice-area]\r\n\r\n<\/div>\r\n

                                                              Adding and Subtracting Fractions with Different Denominators<\/h2>\r\n

                                                              Find the Least Common Denominator (LCD)<\/strong><\/h3>\r\nIn the following exercises, find the least common denominator (LCD) for each set of fractions.\r\n
                                                                \r\n \t
                                                              1. [latex]\\Large\\frac{2}{3}\\normalsize\\text{ and }\\Large\\frac{3}{4}[\/latex]<\/li>\r\n \t
                                                              2. [latex]\\Large\\frac{3}{4}\\normalsize\\text{ and }\\Large\\frac{2}{5}[\/latex][reveal-answer q=\"862309\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"862309\"]20[\/hidden-answer]<\/li>\r\n \t
                                                              3. [latex]\\Large\\frac{7}{12}\\normalsize\\text{ and }\\Large\\frac{5}{8}[\/latex]<\/li>\r\n \t
                                                              4. [latex]\\Large\\frac{9}{16}\\normalsize\\text{ and }\\Large\\frac{7}{12}[\/latex][reveal-answer q=\"775609\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"775609\"]48[\/hidden-answer]<\/li>\r\n \t
                                                              5. [latex]\\Large\\frac{13}{30}\\normalsize\\text{ and }\\Large\\frac{25}{42}[\/latex]<\/li>\r\n \t
                                                              6. [latex]\\Large\\frac{23}{30}\\normalsize\\text{ and }\\Large\\frac{5}{48}[\/latex][reveal-answer q=\"902559\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"902559\"]240[\/hidden-answer]<\/li>\r\n \t
                                                              7. [latex]\\Large\\frac{21}{35}\\normalsize\\text{ and }\\Large\\frac{39}{56}[\/latex]<\/li>\r\n \t
                                                              8. [latex]\\Large\\frac{18}{35}\\normalsize\\text{ and }\\Large\\frac{33}{49}[\/latex][reveal-answer q=\"615888\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"615888\"]245[\/hidden-answer]<\/li>\r\n \t
                                                              9. [latex]\\Large\\frac{2}{3}\\normalsize\\text{,}\\Large\\frac{1}{6}\\normalsize,\\text{ and }\\Large\\frac{3}{4}[\/latex]<\/li>\r\n \t
                                                              10. [latex]\\Large\\frac{2}{3}\\normalsize\\text{,}\\Large\\frac{1}{4}\\normalsize,\\text{ and }\\Large\\frac{3}{5}[\/latex][reveal-answer q=\"452588\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"452588\"]60[\/hidden-answer]<\/li>\r\n<\/ol>\r\n

                                                                Convert Fractions to Equivalent Fractions with the LCD<\/h3>\r\nIn the following exercises, convert to equivalent fractions using the LCD.\r\n
                                                                  \r\n \t
                                                                1. [latex]\\Large\\frac{1}{3}\\normalsize\\text{ and }\\Large\\frac{1}{4}\\normalsize,\\text{LCD}=12[\/latex]<\/li>\r\n \t
                                                                2. [latex]\\Large\\frac{1}{4}\\normalsize\\text{ and }\\Large\\frac{1}{5}\\normalsize,\\text{LCD}=20[\/latex][reveal-answer q=\"229861\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"229861\"][latex]\\Large\\frac{5}{20},\\Large\\frac{4}{20}[\/latex][\/hidden-answer]<\/li>\r\n \t
                                                                3. [latex]\\Large\\frac{5}{12}\\normalsize\\text{ and }\\Large\\frac{7}{8}\\normalsize,\\text{LCD}=24[\/latex]<\/li>\r\n \t
                                                                4. [latex]\\Large\\frac{7}{12}\\normalsize\\text{ and }\\Large\\frac{5}{8}\\normalsize,\\text{LCD}=24[\/latex][reveal-answer q=\"318021\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"318021\"][latex]\\Large\\frac{14}{24},\\Large\\frac{15}{24}[\/latex][\/hidden-answer]<\/li>\r\n \t
                                                                5. [latex]\\Large\\frac{13}{16}\\normalsize\\text{ and }\\text{-}\\Large\\frac{11}{12}\\normalsize,\\text{LCD}=48[\/latex]<\/li>\r\n \t
                                                                6. [latex]\\Large\\frac{11}{16}\\normalsize\\text{ and }\\text{-}\\Large\\frac{5}{12}\\normalsize,\\text{LCD}=48[\/latex][reveal-answer q=\"190334\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"190334\"][latex]\\Large\\frac{33}{48},-\\Large\\frac{20}{48}[\/latex][\/hidden-answer]<\/li>\r\n \t
                                                                7. [latex]\\Large\\frac{1}{3},\\Large\\frac{5}{6}\\normalsize,\\text{ and }\\Large\\frac{3}{4}\\normalsize,\\text{LCD}=12[\/latex]<\/li>\r\n \t
                                                                8. [latex]\\Large\\frac{1}{3},\\Large\\frac{3}{4}\\normalsize,\\text{ and }\\Large\\frac{3}{5}\\normalsize,\\text{LCD}=60[\/latex][reveal-answer q=\"185654\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"185654\"][latex]\\Large\\frac{20}{60},\\Large\\frac{45}{60},\\Large\\frac{36}{60}[\/latex][\/hidden-answer]<\/li>\r\n<\/ol>\r\n

                                                                  Add and Subtract Fractions with Different Denominators<\/h3>\r\nIn the following exercises, add or subtract. Write the result in simplified form.\r\n
                                                                    \r\n \t
                                                                  1. [latex]\\Large\\frac{1}{3}+\\Large\\frac{1}{5}[\/latex]<\/li>\r\n \t
                                                                  2. [latex]\\Large\\frac{1}{4}+\\Large\\frac{1}{5}[\/latex][reveal-answer q=\"753288\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"753288\"][latex]\\Large\\frac{9}{20}[\/latex][\/hidden-answer]<\/li>\r\n \t
                                                                  3. [latex]\\Large\\frac{1}{2}+\\Large\\frac{1}{7}[\/latex]<\/li>\r\n \t
                                                                  4. [latex]\\Large\\frac{1}{3}+\\Large\\frac{1}{8}[\/latex][reveal-answer q=\"672489\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"672489\"][latex]\\Large\\frac{11}{24}[\/latex][\/hidden-answer]<\/li>\r\n \t
                                                                  5. [latex]\\Large\\frac{1}{3}-\\Large\\left(-\\frac{1}{9}\\right)[\/latex]<\/li>\r\n \t
                                                                  6. [latex]\\Large\\frac{1}{4}-\\Large\\left(-\\frac{1}{8}\\right)[\/latex][reveal-answer q=\"971364\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"971364\"][latex]\\Large\\frac{3}{8}[\/latex][\/hidden-answer]<\/li>\r\n \t
                                                                  7. [latex]\\Large\\frac{1}{5}-\\Large\\left(-\\frac{1}{10}\\right)[\/latex]<\/li>\r\n \t
                                                                  8. [latex]\\Large\\frac{1}{2}-\\Large\\left(-\\frac{1}{6}\\right)[\/latex][reveal-answer q=\"487001\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"487001\"][latex]\\Large\\frac{2}{3}[\/latex][\/hidden-answer]<\/li>\r\n \t
                                                                  9. [latex]\\Large\\frac{2}{3}+\\Large\\frac{3}{4}[\/latex]<\/li>\r\n \t
                                                                  10. [latex]\\Large\\frac{3}{4}+\\Large\\frac{2}{5}[\/latex][reveal-answer q=\"541133\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"541133\"][latex]\\Large\\frac{23}{20}[\/latex][\/hidden-answer]<\/li>\r\n \t
                                                                  11. [latex]\\Large\\frac{7}{12}+\\Large\\frac{5}{8}[\/latex]<\/li>\r\n \t
                                                                  12. [latex]\\Large\\frac{5}{12}+\\Large\\frac{3}{8}[\/latex][reveal-answer q=\"344923\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"344923\"][latex]\\Large\\frac{19}{24}[\/latex][\/hidden-answer]<\/li>\r\n \t
                                                                  13. [latex]\\Large\\frac{7}{12}-\\Large\\frac{9}{16}[\/latex]<\/li>\r\n \t
                                                                  14. [latex]\\Large\\frac{7}{16}-\\Large\\frac{5}{12}[\/latex][reveal-answer q=\"119310\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"119310\"][latex]\\Large\\frac{1}{48}[\/latex][\/hidden-answer]<\/li>\r\n \t
                                                                  15. [latex]\\Large\\frac{11}{12}-\\Large\\frac{3}{8}[\/latex]<\/li>\r\n \t
                                                                  16. [latex]\\Large\\frac{5}{8}-\\Large\\frac{7}{12}[\/latex][reveal-answer q=\"74608\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"74608\"][latex]\\Large\\frac{1}{24}[\/latex][\/hidden-answer]<\/li>\r\n \t
                                                                  17. [latex]\\Large\\frac{2}{3}-\\Large\\frac{3}{8}[\/latex]<\/li>\r\n \t
                                                                  18. [latex]\\Large\\frac{5}{6}-\\Large\\frac{3}{4}[\/latex][reveal-answer q=\"751581\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"751581\"][latex]\\Large\\frac{1}{12}[\/latex][\/hidden-answer]<\/li>\r\n \t
                                                                  19. [latex]-\\Large\\frac{11}{30}+\\Large\\frac{27}{40}[\/latex]<\/li>\r\n \t
                                                                  20. [latex]-\\Large\\frac{9}{20}+\\Large\\frac{17}{30}[\/latex][reveal-answer q=\"90848\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"90848\"][latex]\\Large\\frac{7}{60}[\/latex][\/hidden-answer]<\/li>\r\n \t
                                                                  21. [latex]-\\Large\\frac{13}{30}+\\Large\\frac{25}{42}[\/latex]<\/li>\r\n \t
                                                                  22. [latex]-\\Large\\frac{23}{30}+\\Large\\frac{5}{48}[\/latex][reveal-answer q=\"238864\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"238864\"][latex]-\\Large\\frac{53}{80}[\/latex][\/hidden-answer]<\/li>\r\n \t
                                                                  23. [latex]-\\Large\\frac{39}{56}-\\Large\\frac{22}{35}[\/latex]<\/li>\r\n \t
                                                                  24. [latex]-\\Large\\frac{33}{49}-\\Large\\frac{18}{35}[\/latex][reveal-answer q=\"950739\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"950739\"][latex]-\\Large\\frac{291}{245}[\/latex][\/hidden-answer]<\/li>\r\n \t
                                                                  25. [latex]-\\Large\\frac{2}{3}-\\Large\\left(-\\frac{3}{4}\\right)[\/latex]<\/li>\r\n \t
                                                                  26. [latex]-\\Large\\frac{3}{4}-\\Large\\left(-\\frac{4}{5}\\right)[\/latex][reveal-answer q=\"811365\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"811365\"][latex]\\Large\\frac{1}{20}[\/latex][\/hidden-answer]<\/li>\r\n \t
                                                                  27. [latex]-\\Large\\frac{9}{16}-\\Large\\left(-\\frac{4}{5}\\right)[\/latex]<\/li>\r\n \t
                                                                  28. [latex]-\\Large\\frac{7}{20}-\\Large\\left(-\\frac{5}{8}\\right)[\/latex][reveal-answer q=\"159970\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"159970\"][latex]\\Large\\frac{11}{40}[\/latex][\/hidden-answer]<\/li>\r\n \t
                                                                  29. [latex]1+\\Large\\frac{7}{8}[\/latex]<\/li>\r\n \t
                                                                  30. [latex]1+\\Large\\frac{5}{6}[\/latex][reveal-answer q=\"941785\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"941785\"][latex]\\Large\\frac{11}{6}[\/latex][\/hidden-answer]<\/li>\r\n \t
                                                                  31. [latex]1-\\Large\\frac{5}{9}[\/latex]<\/li>\r\n \t
                                                                  32. [latex]1-\\Large\\frac{3}{10}[\/latex][reveal-answer q=\"86994\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"86994\"][latex]\\Large\\frac{7}{10}[\/latex][\/hidden-answer]<\/li>\r\n \t
                                                                  33. [latex]\\Large\\frac{x}{3}+\\Large\\frac{1}{4}[\/latex]<\/li>\r\n \t
                                                                  34. [latex]\\Large\\frac{y}{2}+\\Large\\frac{2}{3}[\/latex][reveal-answer q=\"15595\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"15595\"][latex]\\Large\\frac{3y+4}{6}[\/latex][\/hidden-answer]<\/li>\r\n \t
                                                                  35. [latex]\\Large\\frac{y}{4}-\\Large\\frac{3}{5}[\/latex]<\/li>\r\n \t
                                                                  36. [latex]\\Large\\frac{x}{5}-\\Large\\frac{1}{4}[\/latex][reveal-answer q=\"996809\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"996809\"][latex]\\Large\\frac{4x - 5}{20}[\/latex][\/hidden-answer]<\/li>\r\n<\/ol>\r\n

                                                                    Identify and Use Fraction Operations<\/h3>\r\nIn the following exercises, perform the indicated operations. Write your answers in simplified form.\r\n
                                                                      \r\n \t
                                                                    1. [latex]\\Large\\frac{3}{4}+\\Large\\frac{1}{6}[\/latex]<\/li>\r\n \t
                                                                    2. [latex]\\Large\\frac{3}{4}\\div\\Large\\frac{1}{6}[\/latex]<\/li>\r\n \t
                                                                    3. [latex]\\Large\\frac{2}{3}+\\Large\\frac{1}{6}[\/latex][reveal-answer q=\"622045\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"622045\"][latex]\\Large\\frac{5}{6}[\/latex][\/hidden-answer]<\/li>\r\n \t
                                                                    4. [latex]\\Large\\frac{2}{3}\\div\\Large\\frac{1}{6}[\/latex][reveal-answer q=\"887186\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"887186\"][latex]4[\/latex][\/hidden-answer]<\/li>\r\n \t
                                                                    5. [latex]\\text{-}\\Large\\frac{2}{5}-\\Large\\frac{1}{8}[\/latex]<\/li>\r\n \t
                                                                    6. [latex]\\text{-}\\Large\\frac{2}{5}\\cdot\\Large\\frac{1}{8}[\/latex]<\/li>\r\n \t
                                                                    7. [latex]\\text{-}\\Large\\frac{4}{5}-\\Large\\frac{1}{8}[\/latex][reveal-answer q=\"300024\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"300024\"][latex]-\\Large\\frac{37}{40}[\/latex][\/hidden-answer]<\/li>\r\n \t
                                                                    8. [latex]\\text{-}\\Large\\frac{4}{5}\\cdot\\Large\\frac{1}{8}[\/latex][reveal-answer q=\"400078\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"400078\"][latex]-\\Large\\frac{1}{10}[\/latex][\/hidden-answer]<\/li>\r\n \t
                                                                    9. [latex]\\Large\\frac{5}{n}\\div\\Large\\frac{8}{15}[\/latex]<\/li>\r\n \t
                                                                    10. [latex]\\Large\\frac{5}{n}-\\Large\\frac{8}{15}[\/latex]<\/li>\r\n \t
                                                                    11. [latex]\\Large\\frac{3}{a}\\div\\Large\\frac{7}{12}[\/latex][reveal-answer q=\"79292\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"79292\"][latex]\\Large\\frac{9a}{14}[\/latex][\/hidden-answer]<\/li>\r\n \t
                                                                    12. [latex]\\Large\\frac{3}{a}-\\Large\\frac{7}{12}[\/latex][reveal-answer q=\"638108\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"638108\"][latex]\\Large\\frac{9a - 14}{24}[\/latex][\/hidden-answer]<\/li>\r\n \t
                                                                    13. [latex]\\Large\\frac{9}{10}\\cdot\\Large\\left(-\\frac{11}{d}\\right)[\/latex]<\/li>\r\n \t
                                                                    14. [latex]\\Large\\frac{9}{10}+\\Large\\left(-\\frac{11}{d}\\right)[\/latex]<\/li>\r\n \t
                                                                    15. [latex]\\Large\\frac{4}{15}\\cdot\\Large\\left(-\\frac{5}{q}\\right)[\/latex][reveal-answer q=\"196648\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"196648\"][latex]-\\Large\\frac{4}{3q}[\/latex][\/hidden-answer]<\/li>\r\n \t
                                                                    16. [latex]\\Large\\frac{4}{15}+\\Large\\left(-\\frac{5}{q}\\right)[\/latex][reveal-answer q=\"559716\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"559716\"][latex]\\Large\\frac{12 - 25q}{45}[\/latex][\/hidden-answer]<\/li>\r\n \t
                                                                    17. [latex]-\\Large\\frac{3}{8}\\div\\Large\\left(-\\frac{3}{10}\\right)[\/latex]<\/li>\r\n \t
                                                                    18. [latex]-\\Large\\frac{5}{12}\\div\\Large\\left(-\\frac{5}{9}\\right)[\/latex]<\/li>\r\n \t
                                                                    19. [latex]-\\Large\\frac{3}{8}+\\Large\\frac{5}{12}[\/latex]<\/li>\r\n \t
                                                                    20. [latex]-\\Large\\frac{1}{8}+\\Large\\frac{7}{12}[\/latex][reveal-answer q=\"358463\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"358463\"][latex]\\Large\\frac{11}{24}[\/latex][\/hidden-answer]<\/li>\r\n \t
                                                                    21. [latex]\\Large\\frac{5}{6}-\\Large\\frac{1}{9}[\/latex]<\/li>\r\n \t
                                                                    22. [latex]\\Large\\frac{5}{9}-\\Large\\frac{1}{6}[\/latex][reveal-answer q=\"849101\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"849101\"][latex]\\Large\\frac{7}{18}[\/latex][\/hidden-answer]<\/li>\r\n \t
                                                                    23. [latex]\\Large\\frac{3}{8}\\cdot\\Large\\left(-\\frac{10}{21}\\right)[\/latex]<\/li>\r\n \t
                                                                    24. [latex]\\Large\\frac{7}{12}\\cdot\\Large\\left(-\\frac{8}{35}\\right)[\/latex][reveal-answer q=\"447436\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"447436\"][latex]-\\Large\\frac{2}{15}[\/latex][\/hidden-answer]<\/li>\r\n \t
                                                                    25. [latex]-\\Large\\frac{7}{15}-\\Large\\frac{y}{4}[\/latex]<\/li>\r\n \t
                                                                    26. [latex]-\\Large\\frac{3}{8}-\\Large\\frac{x}{11}[\/latex][reveal-answer q=\"920038\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"920038\"][latex]\\Large\\frac{-33 - 8x}{88}[\/latex][\/hidden-answer]<\/li>\r\n \t
                                                                    27. [latex]\\Large\\frac{11}{12a}\\cdot\\Large\\frac{9a}{16}[\/latex]<\/li>\r\n \t
                                                                    28. [latex]\\Large\\frac{10y}{13}\\cdot\\Large\\frac{8}{15y}[\/latex][reveal-answer q=\"738154\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"738154\"][latex]\\Large\\frac{16}{39}[\/latex][\/hidden-answer]<\/li>\r\n<\/ol>\r\n

                                                                      Use the Order of Operations to Simplify Complex Fractions<\/h3>\r\nIn the following exercises, simplify.\r\n
                                                                        \r\n \t
                                                                      1. [latex]\\displaystyle\\frac{{\\Large\\left(\\frac{1}{5}\\right)}^{2}}{2+{3}^{2}}[\/latex]<\/li>\r\n \t
                                                                      2. [latex]\\displaystyle\\frac{{\\Large\\left(\\frac{1}{3}\\right)}^{2}}{5+{2}^{2}}[\/latex][reveal-answer q=\"722095\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"722095\"][latex]\\displaystyle\\frac{1}{81}[\/latex][\/hidden-answer]<\/li>\r\n \t
                                                                      3. [latex]\\displaystyle\\frac{{2}^{3}+{4}^{2}}{{\\Large\\left(\\frac{2}{3}\\right)}^{2}}[\/latex]<\/li>\r\n \t
                                                                      4. [latex]\\displaystyle\\frac{{3}^{3}-{3}^{2}}{{\\Large\\left(\\frac{3}{4}\\right)}^{2}}[\/latex][reveal-answer q=\"563322\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"563322\"]32[\/hidden-answer]<\/li>\r\n \t
                                                                      5. [latex]\\displaystyle\\frac{{\\Large\\left(\\frac{3}{5}\\right)}^{2}}{{\\Large\\left(\\frac{3}{7}\\right)}^{2}}[\/latex]<\/li>\r\n \t
                                                                      6. [latex]\\displaystyle\\frac{{\\Large\\left(\\frac{3}{4}\\right)}^{2}}{{\\Large\\left(\\frac{5}{8}\\right)}^{2}}[\/latex][reveal-answer q=\"718965\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"718965\"][latex]\\displaystyle\\frac{36}{25}[\/latex][\/hidden-answer]<\/li>\r\n \t
                                                                      7. [latex]\\displaystyle\\frac{2}{\\Large\\frac{1}{3}+\\frac{1}{5}}[\/latex]<\/li>\r\n \t
                                                                      8. [latex]\\displaystyle\\frac{5}{\\Large\\frac{1}{4}+\\frac{1}{3}}[\/latex][reveal-answer q=\"920437\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"920437\"][latex]\\displaystyle\\frac{60}{7}[\/latex][\/hidden-answer]<\/li>\r\n \t
                                                                      9. [latex]\\displaystyle\\frac{\\Large\\frac{2}{3}+\\frac{1}{2}}{\\Large\\frac{3}{4}-\\frac{2}{3}}[\/latex]<\/li>\r\n \t
                                                                      10. [latex]\\displaystyle\\frac{\\Large\\frac{3}{4}+\\frac{1}{2}}{\\Large\\frac{5}{6}-\\frac{2}{3}}[\/latex][reveal-answer q=\"854962\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"854962\"][latex]\\displaystyle\\frac{15}{2}[\/latex][\/hidden-answer]<\/li>\r\n \t
                                                                      11. [latex]\\displaystyle\\frac{\\Large\\frac{7}{8}-\\frac{2}{3}}{\\Large\\frac{1}{2}+\\frac{3}{8}}[\/latex]<\/li>\r\n \t
                                                                      12. [latex]\\displaystyle\\frac{\\Large\\frac{3}{4}-\\frac{3}{5}}{\\Large\\frac{1}{4}+\\frac{2}{5}}[\/latex][reveal-answer q=\"828272\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"828272\"][latex]\\displaystyle\\frac{3}{13}[\/latex][\/hidden-answer]<\/li>\r\n<\/ol>\r\n

                                                                        Identify and Use Fraction Operations<\/h3>\r\nIn the following exercises, simplify.\r\n
                                                                          \r\n \t
                                                                        1. [latex]\\Large\\frac{1}{2}+\\frac{2}{3}\\cdot \\frac{5}{12}[\/latex]<\/li>\r\n \t
                                                                        2. [latex]\\Large\\frac{1}{3}+\\frac{2}{5}\\cdot \\frac{3}{4}[\/latex][reveal-answer q=\"385940\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"385940\"][latex]\\Large\\frac{19}{30}[\/latex][\/hidden-answer]<\/li>\r\n \t
                                                                        3. [latex]1-\\Large\\frac{3}{5}\\div \\frac{1}{10}[\/latex]<\/li>\r\n \t
                                                                        4. [latex]1-\\Large\\frac{5}{6}\\div \\frac{1}{12}[\/latex][reveal-answer q=\"996331\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"996331\"]\u22129[\/hidden-answer]<\/li>\r\n \t
                                                                        5. [latex]\\Large\\frac{2}{3}+\\frac{1}{6}+\\frac{3}{4}[\/latex]<\/li>\r\n \t
                                                                        6. [latex]\\Large\\frac{2}{3}+\\frac{1}{4}+\\frac{3}{5}[\/latex][reveal-answer q=\"17991\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"17991\"][latex]\\Large\\frac{91}{60}[\/latex][\/hidden-answer]<\/li>\r\n \t
                                                                        7. [latex]\\Large\\frac{3}{8}-\\frac{1}{6}+\\frac{3}{4}[\/latex]<\/li>\r\n \t
                                                                        8. [latex]\\Large\\frac{2}{5}+\\frac{5}{8}-\\frac{3}{4}[\/latex][reveal-answer q=\"533147\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"533147\"][latex]\\Large\\frac{11}{40}[\/latex][\/hidden-answer]<\/li>\r\n \t
                                                                        9. [latex]12\\Large\\left(\\frac{9}{20}-\\frac{4}{15}\\right)[\/latex]<\/li>\r\n \t
                                                                        10. [latex]8\\Large\\left(\\frac{15}{16}-\\frac{5}{6}\\right)[\/latex][reveal-answer q=\"909081\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"909081\"][latex]\\Large\\frac{5}{6}[\/latex][\/hidden-answer]<\/li>\r\n \t
                                                                        11. [latex]\\Large\\frac{\\LARGE\\frac{5}{8}+\\LARGE\\frac{1}{6}}{\\LARGE\\frac{19}{24}}[\/latex]<\/li>\r\n \t
                                                                        12. [latex]\\LARGE\\frac{\\LARGE\\frac{1}{6}+\\LARGE\\frac{3}{10}}{\\LARGE\\frac{14}{30}}[\/latex][reveal-answer q=\"444744\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"444744\"]1[\/hidden-answer]<\/li>\r\n \t
                                                                        13. [latex]\\Large\\left(\\frac{5}{9}+\\frac{1}{6}\\right)\\div \\left(\\frac{2}{3}-\\frac{1}{2}\\right)[\/latex]<\/li>\r\n \t
                                                                        14. [latex]\\Large\\left(\\frac{3}{4}+\\frac{1}{6}\\right)\\div \\left(\\frac{5}{8}-\\frac{1}{3}\\right)[\/latex][reveal-answer q=\"943314\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"943314\"][latex]\\Large\\frac{22}{7}[\/latex][\/hidden-answer]<\/li>\r\n<\/ol>\r\n

                                                                          Evaluate Variable Expressions with Fractions<\/h3>\r\nIn the following exercises, evaluate the given expression. Express your answers in simplified form, using improper fractions if necessary.\r\n

                                                                          Exercise 1<\/h4>\r\n[latex]x+\\Large\\frac{1}{2}[\/latex] when\r\n
                                                                            \r\n \t
                                                                          1. [latex]x=-\\Large\\frac{1}{8}[\/latex]<\/li>\r\n \t
                                                                          2. [latex]x=-\\Large\\frac{1}{2}[\/latex]<\/li>\r\n<\/ol>\r\n

                                                                            Exercise 2<\/h4>\r\n[latex]x+\\Large\\frac{2}{3}[\/latex] when\r\n
                                                                              \r\n \t
                                                                            1. [latex]x=-\\Large\\frac{1}{6}[\/latex]<\/li>\r\n \t
                                                                            2. [latex]x=-\\Large\\frac{5}{3}[\/latex]<\/li>\r\n<\/ol>\r\n[reveal-answer q=\"720935\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"720935\"]\r\n
                                                                                \r\n \t
                                                                              1. [latex]\\Large\\frac{1}{2}[\/latex]<\/li>\r\n \t
                                                                              2. [latex]-1[\/latex]<\/li>\r\n<\/ol>\r\n[\/hidden-answer]\r\n

                                                                                Exercise 3<\/h4>\r\n[latex]x+\\Large\\left(-\\frac{5}{6}\\right)[\/latex] when\r\n
                                                                                  \r\n \t
                                                                                1. [latex]x=\\Large\\frac{1}{3}[\/latex]<\/li>\r\n \t
                                                                                2. [latex]x=-\\Large\\frac{1}{6}[\/latex]<\/li>\r\n<\/ol>\r\n

                                                                                  Exercise 4<\/h4>\r\n[latex]x+\\Large\\left(-\\frac{11}{12}\\right)[\/latex] when\r\n
                                                                                    \r\n \t
                                                                                  1. [latex]x=\\Large\\frac{11}{12}[\/latex]<\/li>\r\n \t
                                                                                  2. [latex]x=\\Large\\frac{3}{4}[\/latex]<\/li>\r\n<\/ol>\r\n[reveal-answer q=\"267676\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"267676\"]\r\n
                                                                                      \r\n \t
                                                                                    1. [latex]0[\/latex]<\/li>\r\n \t
                                                                                    2. [latex]-\\Large\\frac{1}{6}[\/latex]<\/li>\r\n<\/ol>\r\n[\/hidden-answer]\r\n

                                                                                      Exercise 5<\/h4>\r\n[latex]x-\\Large\\frac{2}{5}[\/latex] when\r\n
                                                                                        \r\n \t
                                                                                      1. [latex]x=\\Large\\frac{3}{5}[\/latex]<\/li>\r\n \t
                                                                                      2. [latex]x=-\\Large\\frac{3}{5}[\/latex]<\/li>\r\n<\/ol>\r\n

                                                                                        Exercise 6<\/h4>\r\n[latex]x-\\Large\\frac{1}{3}[\/latex] when\r\n
                                                                                          \r\n \t
                                                                                        1. [latex]x=\\Large\\frac{2}{3}[\/latex]<\/li>\r\n \t
                                                                                        2. [latex]x=-\\Large\\frac{2}{3}[\/latex]<\/li>\r\n<\/ol>\r\n[reveal-answer q=\"747799\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"747799\"]\r\n
                                                                                            \r\n \t
                                                                                          1. [latex]\\Large\\frac{1}{3}[\/latex]<\/li>\r\n \t
                                                                                          2. [latex]-1[\/latex]<\/li>\r\n<\/ol>\r\n[\/hidden-answer]\r\n

                                                                                            Exercise 7<\/h4>\r\n[latex]\\Large\\frac{7}{10}\\normalsize-w[\/latex] when\r\n
                                                                                              \r\n \t
                                                                                            1. [latex]w=\\Large\\frac{1}{2}[\/latex]<\/li>\r\n \t
                                                                                            2. [latex]w=-\\Large\\frac{1}{2}[\/latex]<\/li>\r\n<\/ol>\r\n

                                                                                              Exercise 8<\/h4>\r\n[latex]\\Large\\frac{5}{12}\\normalsize-w[\/latex] when\r\n
                                                                                                \r\n \t
                                                                                              1. [latex]w=\\Large\\frac{1}{4}[\/latex]<\/li>\r\n \t
                                                                                              2. [latex]w=-\\Large\\frac{1}{4}[\/latex]<\/li>\r\n<\/ol>\r\n[reveal-answer q=\"966582\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"966582\"]\r\n
                                                                                                  \r\n \t
                                                                                                1. [latex]\\Large\\frac{1}{6}[\/latex]<\/li>\r\n \t
                                                                                                2. [latex]\\Large\\frac{2}{3}[\/latex]<\/li>\r\n<\/ol>\r\n[\/hidden-answer]\r\n

                                                                                                  Evaluate Variable Expressions with Fractions<\/h3>\r\nIn the following exercises, evaluate the given expression. Express your answers in simplified form, using improper fractions if necessary.\r\n
                                                                                                    \r\n \t
                                                                                                  1. [latex]4{p}^{2}q[\/latex] when [latex]p=-\\Large\\frac{1}{2}\\normalsize\\text{ and }q=\\Large\\frac{5}{9}[\/latex]<\/li>\r\n \t
                                                                                                  2. [latex]5{m}^{2}n\\text{ when }m=-\\Large\\frac{2}{5}\\normalsize\\text{ and }n=\\Large\\frac{1}{3}[\/latex][reveal-answer q=\"493858\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"493858\"][latex]\\Large\\frac{4}{15}[\/latex][\/hidden-answer]<\/li>\r\n \t
                                                                                                  3. [latex]2{x}^{2}{y}^{3}\\text{ when }x=-\\Large\\frac{2}{3}\\normalsize\\text{ and }y=-\\Large\\frac{1}{2}[\/latex]<\/li>\r\n \t
                                                                                                  4. [latex]8{u}^{2}{v}^{3}\\text{ when }u=-\\Large\\frac{3}{4}\\normalsize\\text{ and }v=-\\Large\\frac{1}{2}[\/latex][reveal-answer q=\"415571\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"415571\"][latex]-\\Large\\frac{9}{16}[\/latex][\/hidden-answer]<\/li>\r\n \t
                                                                                                  5. [latex]\\Large\\frac{u+v}{w}\\normalsize\\text{ when }u=-4,v=-8,w=2[\/latex]<\/li>\r\n \t
                                                                                                  6. [latex]\\Large\\frac{m+n}{p}\\normalsize\\text{ when }m=-6,n=-2,p=4[\/latex][reveal-answer q=\"261966\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"261966\"]\u22122[\/hidden-answer]<\/li>\r\n \t
                                                                                                  7. [latex]\\Large\\frac{a+b}{a-b}\\normalsize\\text{ when }a=-3,b=8[\/latex]<\/li>\r\n \t
                                                                                                  8. [latex]\\Large\\frac{r-s}{r+s}\\normalsize\\text{ when }r=10,s=-5[\/latex][reveal-answer q=\"793819\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"793819\"]3[\/hidden-answer]<\/li>\r\n<\/ol>\r\n
                                                                                                    \r\n

                                                                                                    Everyday Math<\/h3>\r\n

                                                                                                    Decorating<\/h4>\r\nLaronda is making covers for the throw pillows on her sofa. For each pillow cover, she needs [latex]\\Large\\frac{3}{16}[\/latex] yard of print fabric and [latex]\\Large\\frac{3}{8}[\/latex] yard of solid fabric. What is the total amount of fabric Laronda needs for each pillow cover?\r\n

                                                                                                    Baking<\/h4>\r\nVanessa is baking chocolate chip cookies and oatmeal cookies. She needs [latex]1\\Large\\frac{1}{4}[\/latex] cups of sugar for the chocolate chip cookies, and [latex]1\\Large\\frac{1}{8}[\/latex] cups for the oatmeal cookies How much sugar does she need altogether?\r\n\r\n[reveal-answer q=\"316712\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"316712\"][latex]\\text{She needs}2\\Large\\frac{3}{8}\\normalsize\\text{cups}[\/latex][\/hidden-answer]\r\n\r\n<\/div>\r\n
                                                                                                    \r\n

                                                                                                    Writing Exercises<\/h3>\r\nExplain why it is necessary to have a common denominator to add or subtract fractions.\r\n\r\n[practice-area rows=\"4\"][\/practice-area]\r\n\r\nExplain how to find the LCD of two fractions.\r\n\r\n[practice-area rows=\"4\"][\/practice-area]\r\n\r\n<\/div>\r\n

                                                                                                    Adding and Subtracting Mixed Numbers<\/h2>\r\n

                                                                                                    Model Addition of Mixed Numbers<\/h3>\r\nIn the following exercises, use a model to find the sum. Draw a picture to illustrate your model.\r\n
                                                                                                      \r\n \t
                                                                                                    1. [latex]1\\Large\\frac{1}{5}\\normalsize+3\\Large\\frac{1}{5}[\/latex]<\/li>\r\n \t
                                                                                                    2. [latex]2\\Large\\frac{1}{3}\\normalsize+1\\Large\\frac{1}{3}[\/latex][reveal-answer q=\"337849\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"337849\"]\"Four[\/hidden-answer]<\/li>\r\n \t
                                                                                                    3. [latex]3\\Large\\frac{2}{3}[\/latex]<\/li>\r\n \t
                                                                                                    4. [latex]1\\Large\\frac{3}{8}\\normalsize+1\\Large\\frac{7}{8}[\/latex]<\/li>\r\n \t
                                                                                                    5. [latex]1\\Large\\frac{5}{6}\\normalsize+1\\Large\\frac{5}{6}[\/latex][reveal-answer q=\"394103\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"394103\"]\"Four[\/hidden-answer]<\/li>\r\n \t
                                                                                                    6. [latex]3\\Large\\frac{2}{3}[\/latex]<\/li>\r\n<\/ol>\r\n

                                                                                                      Add Mixed Numbers with a Common Denominator<\/h3>\r\nIn the following exercises, add.\r\n
                                                                                                        \r\n \t
                                                                                                      1. [latex]5\\Large\\frac{1}{3}\\normalsize+6\\Large\\frac{1}{3}[\/latex]<\/li>\r\n \t
                                                                                                      2. [latex]2\\Large\\frac{4}{9}\\normalsize+5\\Large\\frac{1}{9}[\/latex][reveal-answer q=\"552342\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"552342\"][latex]7\\Large\\frac{5}{9}[\/latex][\/hidden-answer]<\/li>\r\n \t
                                                                                                      3. [latex]4\\Large\\frac{5}{8}\\normalsize+9\\Large\\frac{3}{8}[\/latex]<\/li>\r\n \t
                                                                                                      4. [latex]7\\Large\\frac{9}{10}\\normalsize+3\\Large\\frac{1}{10}[\/latex][reveal-answer q=\"530292\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"530292\"]11[\/hidden-answer]<\/li>\r\n \t
                                                                                                      5. [latex]3\\Large\\frac{4}{5}\\normalsize+6\\Large\\frac{4}{5}[\/latex]<\/li>\r\n \t
                                                                                                      6. [latex]9\\Large\\frac{2}{3}\\normalsize+1\\Large\\frac{2}{3}[\/latex][reveal-answer q=\"284943\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"284943\"][latex]11\\Large\\frac{1}{3}[\/latex][\/hidden-answer]<\/li>\r\n \t
                                                                                                      7. [latex]6\\Large\\frac{9}{10}\\normalsize+8\\Large\\frac{3}{10}[\/latex]<\/li>\r\n \t
                                                                                                      8. [latex]8\\Large\\frac{4}{9}\\normalsize+2\\Large\\frac{8}{9}[\/latex][reveal-answer q=\"802441\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"802441\"][latex]11\\Large\\frac{1}{3}[\/latex][\/hidden-answer]<\/li>\r\n<\/ol>\r\n

                                                                                                        Model Subtraction of Mixed Numbers<\/h3>\r\nIn the following exercises, use a model to find the difference. Draw a picture to illustrate your model.\r\n
                                                                                                          \r\n \t
                                                                                                        1. [latex]1\\Large\\frac{1}{6}-\\Large\\frac{5}{6}[\/latex]<\/li>\r\n \t
                                                                                                        2. [latex]1\\Large\\frac{1}{8}-\\Large\\frac{5}{8}[\/latex][reveal-answer q=\"771609\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"771609\"]\"A[\/hidden-answer]<\/li>\r\n \t
                                                                                                        3. [latex]\\Large\\frac{1}{2}[\/latex]<\/li>\r\n<\/ol>\r\n

                                                                                                          Subtract Mixed Numbers with a Common Denominator<\/h3>\r\nIn the following exercises, find the difference.\r\n
                                                                                                            \r\n \t
                                                                                                          1. [latex]2\\Large\\frac{7}{8}\\normalsize-1\\Large\\frac{3}{8}[\/latex]<\/li>\r\n \t
                                                                                                          2. [latex]2\\Large\\frac{7}{12}\\normalsize-1\\Large\\frac{5}{12}[\/latex][reveal-answer q=\"405622\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"405622\"][latex]1\\Large\\frac{1}{6}[\/latex][\/hidden-answer]<\/li>\r\n \t
                                                                                                          3. [latex]8\\Large\\frac{17}{20}\\normalsize-4\\Large\\frac{9}{20}[\/latex]<\/li>\r\n \t
                                                                                                          4. [latex]19\\Large\\frac{13}{15}\\normalsize-13\\Large\\frac{7}{15}[\/latex][reveal-answer q=\"500591\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"500591\"][latex]6\\Large\\frac{2}{5}[\/latex][\/hidden-answer]<\/li>\r\n \t
                                                                                                          5. [latex]8\\Large\\frac{3}{7}\\normalsize-4\\Large\\frac{4}{7}[\/latex]<\/li>\r\n \t
                                                                                                          6. [latex]5\\Large\\frac{2}{9}\\normalsize-3\\Large\\frac{4}{9}[\/latex][reveal-answer q=\"964064\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"964064\"][latex]1\\Large\\frac{7}{9}[\/latex][\/hidden-answer]<\/li>\r\n \t
                                                                                                          7. [latex]2\\Large\\frac{5}{8}\\normalsize-1\\Large\\frac{7}{8}[\/latex]<\/li>\r\n \t
                                                                                                          8. [latex]2\\Large\\frac{5}{12}\\normalsize-1\\Large\\frac{7}{12}[\/latex][reveal-answer q=\"74581\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"74581\"][latex]\\Large\\frac{5}{6}[\/latex][\/hidden-answer]<\/li>\r\n<\/ol>\r\n

                                                                                                            Add and Subtract Mixed Numbers with Different Denominators<\/h3>\r\nIn the following exercises, write the sum or difference as a mixed number in simplified form.\r\n
                                                                                                              \r\n \t
                                                                                                            1. [latex]3\\Large\\frac{1}{4}\\normalsize+6\\Large\\frac{1}{3}[\/latex]<\/li>\r\n \t
                                                                                                            2. [latex]2\\Large\\frac{1}{6}\\normalsize+5\\Large\\frac{3}{4}[\/latex][reveal-answer q=\"190923\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"190923\"][latex]7\\Large\\frac{11}{12}[\/latex][\/hidden-answer]<\/li>\r\n \t
                                                                                                            3. [latex]1\\Large\\frac{5}{8}\\normalsize+4\\Large\\frac{1}{2}[\/latex]<\/li>\r\n \t
                                                                                                            4. [latex]7\\Large\\frac{2}{3}\\normalsize+8\\Large\\frac{1}{2}[\/latex][reveal-answer q=\"272502\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"272502\"][latex]16\\Large\\frac{1}{6}[\/latex][\/hidden-answer]<\/li>\r\n \t
                                                                                                            5. [latex]9\\Large\\frac{7}{10}\\normalsize-2\\Large\\frac{1}{3}[\/latex]<\/li>\r\n \t
                                                                                                            6. [latex]6\\Large\\frac{4}{5}\\normalsize-1\\Large\\frac{1}{4}[\/latex][reveal-answer q=\"885381\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"885381\"][latex]5\\Large\\frac{11}{20}[\/latex][\/hidden-answer]<\/li>\r\n \t
                                                                                                            7. [latex]2\\Large\\frac{2}{3}\\normalsize-3\\Large\\frac{1}{2}[\/latex]<\/li>\r\n \t
                                                                                                            8. [latex]2\\Large\\frac{7}{8}\\normalsize-4\\Large\\frac{1}{3}[\/latex][reveal-answer q=\"891413\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"891413\"][latex]-1\\Large\\frac{11}{24}[\/latex][\/hidden-answer]<\/li>\r\n<\/ol>\r\n

                                                                                                              Identify and Use Fraction Operations<\/h3>\r\nIn the following exercises, perform the indicated operation and write the result as a mixed number in simplified form.\r\n
                                                                                                                \r\n \t
                                                                                                              1. [latex]2\\Large\\frac{5}{8}\\normalsize\\cdot 1\\Large\\frac{3}{4}[\/latex]<\/li>\r\n \t
                                                                                                              2. [latex]1\\Large\\frac{2}{3}\\normalsize\\cdot 4\\Large\\frac{1}{6}[\/latex][reveal-answer q=\"97975\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"97975\"][latex]6\\Large\\frac{17}{18}[\/latex][\/hidden-answer]<\/li>\r\n \t
                                                                                                              3. [latex]\\Large\\frac{2}{7}+\\Large\\frac{4}{7}[\/latex]<\/li>\r\n \t
                                                                                                              4. [latex]\\Large\\frac{2}{9}+\\Large\\frac{5}{9}[\/latex][reveal-answer q=\"996446\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"996446\"][latex]\\Large\\frac{7}{9}[\/latex][\/hidden-answer]<\/li>\r\n \t
                                                                                                              5. [latex]1\\Large\\frac{5}{12}\\div\\Large\\frac{1}{12}[\/latex]<\/li>\r\n \t
                                                                                                              6. [latex]2\\Large\\frac{3}{10}\\div\\Large\\frac{1}{10}[\/latex][reveal-answer q=\"985987\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"985987\"]23[\/hidden-answer]<\/li>\r\n \t
                                                                                                              7. [latex]13\\Large\\frac{5}{12}\\normalsize-9\\Large\\frac{7}{12}[\/latex]<\/li>\r\n \t
                                                                                                              8. [latex]15\\Large\\frac{5}{8}\\normalsize-6\\Large\\frac{7}{8}[\/latex][reveal-answer q=\"334569\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"334569\"][latex]8\\Large\\frac{3}{4}[\/latex][\/hidden-answer]<\/li>\r\n \t
                                                                                                              9. [latex]\\Large\\frac{5}{9}-\\Large\\frac{4}{9}[\/latex]<\/li>\r\n \t
                                                                                                              10. [latex]\\Large\\frac{11}{15}-\\Large\\frac{7}{15}[\/latex][reveal-answer q=\"297751\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"297751\"][latex]\\Large\\frac{4}{15}[\/latex][\/hidden-answer]<\/li>\r\n \t
                                                                                                              11. [latex]4-\\Large\\frac{3}{4}[\/latex]<\/li>\r\n \t
                                                                                                              12. [latex]6-\\Large\\frac{2}{5}[\/latex][reveal-answer q=\"154250\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"154250\"][latex]5\\Large\\frac{3}{5}[\/latex][\/hidden-answer]<\/li>\r\n \t
                                                                                                              13. [latex]\\Large\\frac{9}{20}\\div\\Large\\frac{3}{4}[\/latex]<\/li>\r\n \t
                                                                                                              14. [latex]\\Large\\frac{7}{24}\\div\\Large\\frac{14}{3}[\/latex][reveal-answer q=\"343921\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"343921\"][latex]\\Large\\frac{1}{16}[\/latex][\/hidden-answer]<\/li>\r\n \t
                                                                                                              15. [latex]9\\Large\\frac{6}{11}\\normalsize+7\\Large\\frac{10}{11}[\/latex]<\/li>\r\n \t
                                                                                                              16. [latex]8\\Large\\frac{5}{13}\\normalsize+4\\Large\\frac{9}{13}[\/latex][reveal-answer q=\"464046\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"464046\"][latex]13\\Large\\frac{1}{13}[\/latex][\/hidden-answer]<\/li>\r\n \t
                                                                                                              17. [latex]3\\Large\\frac{2}{5}\\normalsize+5\\Large\\frac{3}{4}[\/latex]<\/li>\r\n \t
                                                                                                              18. [latex]2\\Large\\frac{5}{6}\\normalsize+4\\Large\\frac{1}{5}[\/latex][reveal-answer q=\"13796\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"13796\"][latex]7\\Large\\frac{1}{30}[\/latex][\/hidden-answer]<\/li>\r\n \t
                                                                                                              19. [latex]\\Large\\frac{8}{15}\\cdot\\Large\\frac{10}{19}[\/latex]<\/li>\r\n \t
                                                                                                              20. [latex]\\Large\\frac{5}{12}\\cdot\\Large\\frac{8}{9}[\/latex][reveal-answer q=\"589444\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"589444\"][latex]\\Large\\frac{10}{27}[\/latex][\/hidden-answer]<\/li>\r\n \t
                                                                                                              21. [latex]6\\Large\\frac{7}{8}\\normalsize-2\\Large\\frac{1}{3}[\/latex]<\/li>\r\n \t
                                                                                                              22. [latex]6\\Large\\frac{5}{9}\\normalsize-4\\Large\\frac{2}{5}[\/latex][reveal-answer q=\"2219\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"2219\"][latex]2\\Large\\frac{7}{45}[\/latex][\/hidden-answer]<\/li>\r\n \t
                                                                                                              23. [latex]5\\Large\\frac{2}{9}\\normalsize-4\\Large\\frac{4}{5}[\/latex]<\/li>\r\n \t
                                                                                                              24. [latex]4\\Large\\frac{3}{8}\\normalsize-3\\Large\\frac{2}{3}[\/latex][reveal-answer q=\"769619\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"769619\"][latex]\\Large\\frac{17}{24}[\/latex][\/hidden-answer]<\/li>\r\n<\/ol>\r\n
                                                                                                                \r\n

                                                                                                                Everyday Math<\/h3>\r\n

                                                                                                                Sewing<\/h4>\r\nRenata is sewing matching shirts for her husband and son. According to the patterns she will use, she needs [latex]2\\Large\\frac{3}{8}[\/latex] yards of fabric for her husband\u2019s shirt and [latex]1\\Large\\frac{1}{8}[\/latex] yards of fabric for her son\u2019s shirt. How much fabric does she need to make both shirts?\r\n

                                                                                                                Sewing<\/h4>\r\nPauline has [latex]3\\Large\\frac{1}{4}[\/latex] yards of fabric to make a jacket. The jacket uses [latex]2\\Large\\frac{2}{3}[\/latex] yards. How much fabric will she have left after making the jacket?\r\n\r\n[reveal-answer q=\"255878\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"255878\"][latex]\\Large\\frac{7}{12}\\normalsize\\text{yards}[\/latex][\/hidden-answer]\r\n

                                                                                                                Printing<\/h4>\r\nNishant is printing invitations on his computer. The paper is [latex]8\\Large\\frac{1}{2}[\/latex] inches wide, and he sets the print area to have a [latex]1\\Large\\frac{1}{2}[\/latex] -inch border on each side. How wide is the print area on the sheet of paper?\r\n

                                                                                                                Framing a picture<\/h4>\r\nTessa bought a picture frame for her son\u2019s graduation picture. The picture is [latex]8[\/latex] inches wide. The picture frame is [latex]2\\Large\\frac{5}{8}[\/latex] inches wide on each side. How wide will the framed picture be?\r\n\r\n[reveal-answer q=\"71583\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"71583\"][latex]13\\Large\\frac{1}{4}\\normalsize\\text{inches}[\/latex][\/hidden-answer]\r\n\r\n<\/div>\r\n
                                                                                                                \r\n

                                                                                                                Writing Exercises<\/h3>\r\nDraw a diagram and use it to explain how to add [latex]1\\Large\\frac{5}{8}\\normalsize+2\\Large\\frac{7}{8}[\/latex].\r\n\r\n[practice-area rows=\"4\"][\/practice-area]\r\n\r\nEdgar will have to pay [latex]\\$3.75[\/latex] in tolls to drive to the city.\r\n
                                                                                                                  \r\n \t
                                                                                                                1. Explain how he can make change from a [latex]\\$10[\/latex] bill before he leaves so that he has the exact amount he needs.<\/li>\r\n \t
                                                                                                                2. How is Edgar\u2019s situation similar to how you subtract [latex]10 - 3\\Large\\frac{3}{4}?[\/latex]<\/li>\r\n<\/ol>\r\n[practice-area rows=\"4\"][\/practice-area]\r\n\r\nAdd [latex]4\\Large\\frac{5}{12}\\normalsize+3\\Large\\frac{7}{8}[\/latex] twice, first by leaving them as mixed numbers and then by rewriting as improper fractions. Which method do you prefer, and why?\r\n\r\n[practice-area rows=\"4\"][\/practice-area]\r\n\r\nSubtract [latex]3\\Large\\frac{7}{8}\\normalsize-4\\Large\\frac{5}{12}[\/latex] twice, first by leaving them as mixed numbers and then by rewriting as improper fractions. Which method do you prefer, and why?\r\n\r\n[practice-area rows=\"4\"][\/practice-area]\r\n\r\n<\/div>\r\n

                                                                                                                  Solving Equations That Contain Fractions<\/h2>\r\n

                                                                                                                  Determine Whether a Fraction is a Solution of an Equation<\/h3>\r\nIn the following exercises, determine whether each number is a solution of the given equation.\r\n

                                                                                                                  Exercise 1<\/h4>\r\n[latex]x-\\Large\\frac{2}{5}=\\Large\\frac{1}{10}\\normalsize\\text{:}[\/latex]\r\n
                                                                                                                    \r\n \t
                                                                                                                  1. [latex]x=1[\/latex]<\/li>\r\n \t
                                                                                                                  2. [latex]x=\\Large\\frac{1}{2}[\/latex]<\/li>\r\n \t
                                                                                                                  3. [latex]x=-\\Large\\frac{1}{2}[\/latex]<\/li>\r\n<\/ol>\r\n

                                                                                                                    Exercise 2<\/h4>\r\n[latex]y-\\Large\\frac{1}{3}=\\Large\\frac{5}{12}\\normalsize\\text{:}[\/latex]\r\n
                                                                                                                      \r\n \t
                                                                                                                    1. [latex]y=1[\/latex]<\/li>\r\n \t
                                                                                                                    2. [latex]y=\\Large\\frac{3}{4}[\/latex]<\/li>\r\n \t
                                                                                                                    3. [latex]y=-\\Large\\frac{3}{4}[\/latex]<\/li>\r\n<\/ol>\r\n[reveal-answer q=\"895058\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"895058\"]\r\n
                                                                                                                        \r\n \t
                                                                                                                      1. no<\/li>\r\n \t
                                                                                                                      2. yes<\/li>\r\n \t
                                                                                                                      3. no<\/li>\r\n<\/ol>\r\n[\/hidden-answer]\r\n

                                                                                                                        Exercise 3<\/h4>\r\n[latex]h+\\Large\\frac{3}{4}=\\Large\\frac{2}{5}\\normalsize\\text{:}[\/latex]\r\n
                                                                                                                          \r\n \t
                                                                                                                        1. [latex]h=1[\/latex]<\/li>\r\n \t
                                                                                                                        2. [latex]h=\\Large\\frac{7}{20}[\/latex]<\/li>\r\n \t
                                                                                                                        3. [latex]h=-\\Large\\frac{7}{20}[\/latex]<\/li>\r\n<\/ol>\r\n

                                                                                                                          Exercise 4<\/h4>\r\n[latex]k+\\Large\\frac{2}{5}=\\Large\\frac{5}{6}\\normalsize\\text{:}[\/latex]\r\n
                                                                                                                            \r\n \t
                                                                                                                          1. [latex]k=1[\/latex]<\/li>\r\n \t
                                                                                                                          2. [latex]k=\\Large\\frac{13}{30}[\/latex]<\/li>\r\n \t
                                                                                                                          3. [latex]k=-\\Large\\frac{13}{30}[\/latex]<\/li>\r\n<\/ol>\r\n[reveal-answer q=\"238527\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"238527\"]\r\n
                                                                                                                              \r\n \t
                                                                                                                            1. no<\/li>\r\n \t
                                                                                                                            2. yes<\/li>\r\n \t
                                                                                                                            3. no<\/li>\r\n<\/ol>\r\n[\/hidden-answer]\r\n

                                                                                                                              Solve Equations with Fractions using the Addition, Subtraction, and Division Properties of Equality<\/h3>\r\nIn the following exercises, solve.\r\n
                                                                                                                                \r\n \t
                                                                                                                              1. [latex]y+\\Large\\frac{1}{3}=\\Large\\frac{4}{3}[\/latex]<\/li>\r\n \t
                                                                                                                              2. [latex]m+\\Large\\frac{3}{8}=\\Large\\frac{7}{8}[\/latex][reveal-answer q=\"536167\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"536167\"][latex]m=\\Large\\frac{1}{2}[\/latex][\/hidden-answer]<\/li>\r\n \t
                                                                                                                              3. [latex]f+\\Large\\frac{9}{10}=\\Large\\frac{2}{5}[\/latex]<\/li>\r\n \t
                                                                                                                              4. [latex]h+\\Large\\frac{5}{6}=\\Large\\frac{1}{6}[\/latex][reveal-answer q=\"85819\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"85819\"][latex]h=-\\Large\\frac{2}{3}[\/latex][\/hidden-answer]<\/li>\r\n \t
                                                                                                                              5. [latex]a-\\Large\\frac{5}{8}=-\\Large\\frac{7}{8}[\/latex]<\/li>\r\n \t
                                                                                                                              6. [latex]c-\\Large\\frac{1}{4}=-\\Large\\frac{5}{4}[\/latex][reveal-answer q=\"986921\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"986921\"]c<\/em> = \u22121[\/hidden-answer]<\/li>\r\n \t
                                                                                                                              7. [latex]x-\\Large\\left(-\\frac{3}{20}\\right)=-\\Large\\frac{11}{20}[\/latex]<\/li>\r\n \t
                                                                                                                              8. [latex]z-\\Large\\left(-\\frac{5}{12}\\right)=-\\Large\\frac{7}{12}[\/latex][reveal-answer q=\"176642\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"176642\"]z<\/em> = \u22121[\/hidden-answer]<\/li>\r\n \t
                                                                                                                              9. [latex]n-\\Large\\frac{1}{6}=\\Large\\frac{3}{4}[\/latex]<\/li>\r\n \t
                                                                                                                              10. [latex]p-\\Large\\frac{3}{10}=\\Large\\frac{5}{8}[\/latex][reveal-answer q=\"707306\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"707306\"][latex]p=\\Large\\frac{37}{40}[\/latex][\/hidden-answer]<\/li>\r\n \t
                                                                                                                              11. [latex]s+\\Large\\left(-\\frac{1}{2}\\right)=-\\Large\\frac{8}{9}[\/latex]<\/li>\r\n \t
                                                                                                                              12. [latex]k+\\Large\\left(-\\frac{1}{3}\\right)=-\\Large\\frac{4}{5}[\/latex][reveal-answer q=\"154189\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"154189\"][latex]k=-\\Large\\frac{7}{15}[\/latex][\/hidden-answer]<\/li>\r\n \t
                                                                                                                              13. [latex]5j=17[\/latex]<\/li>\r\n \t
                                                                                                                              14. [latex]7k=18[\/latex][reveal-answer q=\"588394\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"588394\"][latex]k=\\Large\\frac{18}{7}[\/latex][\/hidden-answer]<\/li>\r\n \t
                                                                                                                              15. [latex]-4w=26[\/latex]<\/li>\r\n \t
                                                                                                                              16. [latex]-9v=33[\/latex][reveal-answer q=\"904907\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"904907\"][latex]v=-\\Large\\frac{11}{3}[\/latex][\/hidden-answer]<\/li>\r\n<\/ol>\r\n

                                                                                                                                Solve Equations with Fractions Using the Multiplication Property of Equality<\/h3>\r\nIn the following exercises, solve.\r\n
                                                                                                                                  \r\n \t
                                                                                                                                1. [latex]\\Large\\frac{f}{4}\\normalsize=-20[\/latex]<\/li>\r\n \t
                                                                                                                                2. [latex]\\Large\\frac{b}{3}\\normalsize=-9[\/latex][reveal-answer q=\"607280\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"607280\"]b<\/em> = \u221227[\/hidden-answer]<\/li>\r\n \t
                                                                                                                                3. [latex]\\Large\\frac{y}{7}\\normalsize=-21[\/latex]<\/li>\r\n \t
                                                                                                                                4. [latex]\\Large\\frac{x}{8}\\normalsize=-32[\/latex][reveal-answer q=\"147049\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"147049\"]x<\/em> = \u2212256[\/hidden-answer]<\/li>\r\n \t
                                                                                                                                5. [latex]\\Large\\frac{p}{-5}\\normalsize=-40[\/latex]<\/li>\r\n \t
                                                                                                                                6. [latex]\\Large\\frac{q}{-4}\\normalsize=-40[\/latex][reveal-answer q=\"225446\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"225446\"]q<\/em> = 160[\/hidden-answer]<\/li>\r\n \t
                                                                                                                                7. [latex]\\Large\\frac{r}{-12}\\normalsize=-6[\/latex]<\/li>\r\n \t
                                                                                                                                8. [latex]\\Large\\frac{s}{-15}\\normalsize=-3[\/latex][reveal-answer q=\"283880\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"283880\"]s<\/em> = 45[\/hidden-answer]<\/li>\r\n \t
                                                                                                                                9. [latex]-x=23[\/latex]<\/li>\r\n \t
                                                                                                                                10. [latex]-y=42[\/latex][reveal-answer q=\"223816\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"223816\"]y<\/em> = \u221242[\/hidden-answer]<\/li>\r\n \t
                                                                                                                                11. [latex]-h=-\\Large\\frac{5}{12}[\/latex]<\/li>\r\n \t
                                                                                                                                12. [latex]-k=-\\Large\\frac{17}{20}[\/latex][reveal-answer q=\"404506\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"404506\"][latex]k=\\Large\\frac{17}{20}[\/latex][\/hidden-answer]<\/li>\r\n \t
                                                                                                                                13. [latex]\\Large\\frac{4}{5}\\normalsize n=20[\/latex]<\/li>\r\n \t
                                                                                                                                14. [latex]\\Large\\frac{3}{10}\\normalsize p=30[\/latex][reveal-answer q=\"504934\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"504934\"]p<\/em> = 100[\/hidden-answer]<\/li>\r\n \t
                                                                                                                                15. [latex]\\Large\\frac{3}{8}\\normalsize q=-48[\/latex]<\/li>\r\n \t
                                                                                                                                16. [latex]\\Large\\frac{5}{2}\\normalsize m=-40[\/latex][reveal-answer q=\"15940\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"15940\"]m<\/em> = \u221216[\/hidden-answer]<\/li>\r\n \t
                                                                                                                                17. [latex]-\\Large\\frac{2}{9}\\normalsize a=16[\/latex]<\/li>\r\n \t
                                                                                                                                18. [latex]-\\Large\\frac{3}{7}\\normalsize b=9[\/latex][reveal-answer q=\"671560\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"671560\"]b<\/em> = \u221221[\/hidden-answer]<\/li>\r\n \t
                                                                                                                                19. [latex]-\\Large\\frac{6}{11}\\normalsize u=-24[\/latex]<\/li>\r\n \t
                                                                                                                                20. [latex]-\\Large\\frac{5}{12}\\normalsize v=-15[\/latex][reveal-answer q=\"700100\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"700100\"]v<\/em> = 36[\/hidden-answer]<\/li>\r\n<\/ol>\r\n

                                                                                                                                  Mixed Practice<\/h3>\r\nIn the following exercises, solve.\r\n
                                                                                                                                    \r\n \t
                                                                                                                                  1. [latex]3x=0[\/latex]<\/li>\r\n \t
                                                                                                                                  2. [latex]8y=0[\/latex][reveal-answer q=\"726603\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"726603\"]y<\/em> = 0[\/hidden-answer]<\/li>\r\n \t
                                                                                                                                  3. [latex]4f=\\Large\\frac{4}{5}[\/latex]<\/li>\r\n \t
                                                                                                                                  4. [latex]7g=\\Large\\frac{7}{9}[\/latex][reveal-answer q=\"477348\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"477348\"][latex]g=\\Large\\frac{1}{9}[\/latex][\/hidden-answer]<\/li>\r\n \t
                                                                                                                                  5. [latex]p+\\Large\\frac{2}{3}=\\Large\\frac{1}{12}[\/latex]<\/li>\r\n \t
                                                                                                                                  6. [latex]q+\\Large\\frac{5}{6}=\\Large\\frac{1}{12}[\/latex][reveal-answer q=\"260456\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"260456\"][latex]q=-\\Large\\frac{3}{4}[\/latex][\/hidden-answer]<\/li>\r\n \t
                                                                                                                                  7. [latex]\\Large\\frac{7}{8}\\normalsize m=\\Large\\frac{1}{10}[\/latex]<\/li>\r\n \t
                                                                                                                                  8. [latex]\\Large\\frac{1}{4}\\normalsize n=\\Large\\frac{7}{10}[\/latex][reveal-answer q=\"170581\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"170581\"][latex]n=\\Large\\frac{14}{5}[\/latex][\/hidden-answer]<\/li>\r\n \t
                                                                                                                                  9. [latex]-\\Large\\frac{2}{5}\\normalsize=x+\\Large\\frac{3}{4}[\/latex]<\/li>\r\n \t
                                                                                                                                  10. [latex]-\\Large\\frac{2}{3}\\normalsize=y+\\Large\\frac{3}{8}[\/latex][reveal-answer q=\"222054\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"222054\"][latex]y=-\\Large\\frac{25}{24}[\/latex][\/hidden-answer]<\/li>\r\n \t
                                                                                                                                  11. [latex]\\Large\\frac{11}{20}\\normalsize=\\text{-}\\mathit{\\text{f}}[\/latex]<\/li>\r\n \t
                                                                                                                                  12. [latex]\\Large\\frac{8}{15}\\normalsize=\\text{-}\\mathit{\\text{d}}[\/latex][reveal-answer q=\"839638\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"839638\"][latex]d=-\\Large\\frac{8}{15}[\/latex][\/hidden-answer]<\/li>\r\n<\/ol>\r\n

                                                                                                                                    Translate Sentences to Equations and Solve<\/h3>\r\nIn the following exercises, translate to an algebraic equation and solve.\r\n
                                                                                                                                      \r\n \t
                                                                                                                                    1. [latex]n[\/latex] divided by eight is [latex]-16[\/latex].<\/li>\r\n \t
                                                                                                                                    2. [latex]n[\/latex] divided by six is [latex]-24[\/latex].[reveal-answer q=\"864607\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"864607\"][latex]\\Large\\frac{n}{6}\\normalsize=-24;n=-144[\/latex][\/hidden-answer]<\/li>\r\n \t
                                                                                                                                    3. [latex]m[\/latex] divided by [latex]-9[\/latex] is [latex]-7[\/latex].<\/li>\r\n \t
                                                                                                                                    4. [latex]m[\/latex] divided by [latex]-7[\/latex] is [latex]-8[\/latex].[reveal-answer q=\"521109\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"521109\"][latex]\\Large\\frac{m}{-7}\\normalsize=-8;m=56[\/latex][\/hidden-answer]<\/li>\r\n \t
                                                                                                                                    5. The quotient of [latex]f[\/latex] and [latex]-3[\/latex] is [latex]-18[\/latex].<\/li>\r\n \t
                                                                                                                                    6. The quotient of [latex]f[\/latex] and [latex]-4[\/latex] is [latex]-20[\/latex].[reveal-answer q=\"792024\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"792024\"][latex]\\Large\\frac{f}{-4}\\normalsize=-20;f=80[\/latex][\/hidden-answer]<\/li>\r\n \t
                                                                                                                                    7. The quotient of [latex]g[\/latex] and twelve is [latex]8[\/latex].<\/li>\r\n \t
                                                                                                                                    8. The quotient of [latex]g[\/latex] and nine is [latex]14[\/latex].[reveal-answer q=\"541905\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"541905\"][latex]\\Large\\frac{g}{9}\\normalsize=14;g=126[\/latex][\/hidden-answer]<\/li>\r\n \t
                                                                                                                                    9. Three-fourths of [latex]q[\/latex] is [latex]12[\/latex].<\/li>\r\n \t
                                                                                                                                    10. Two-fifths of [latex]q[\/latex] is [latex]20[\/latex].[reveal-answer q=\"115355\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"115355\"][latex]\\Large\\frac{2}{5}\\normalsize q=20;q=50[\/latex][\/hidden-answer]<\/li>\r\n \t
                                                                                                                                    11. Seven-tenths of [latex]p[\/latex] is [latex]-63[\/latex].<\/li>\r\n \t
                                                                                                                                    12. Four-ninths of [latex]p[\/latex] is [latex]-28[\/latex].[reveal-answer q=\"195488\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"195488\"][latex]\\Large\\frac{4}{9}\\normalsize p=-28;p=-63[\/latex][\/hidden-answer]<\/li>\r\n \t
                                                                                                                                    13. [latex]m[\/latex] divided by [latex]4[\/latex] equals negative [latex]6[\/latex].<\/li>\r\n \t
                                                                                                                                    14. The quotient of [latex]h[\/latex] and [latex]2[\/latex] is [latex]43[\/latex].[reveal-answer q=\"147291\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"147291\"][latex]\\Large\\frac{h}{2}\\normalsize=43[\/latex][\/hidden-answer]<\/li>\r\n \t
                                                                                                                                    15. Three-fourths of [latex]z[\/latex] is the same as [latex]15[\/latex].<\/li>\r\n \t
                                                                                                                                    16. The quotient of [latex]a[\/latex] and [latex]\\Large\\frac{2}{3}[\/latex] is [latex]\\Large\\frac{3}{4}[\/latex].[reveal-answer q=\"25901\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"25901\"][latex]\\Large\\frac{a}{\\LARGE\\frac{2}{3}}=\\Large\\frac{3}{4}[\/latex][\/hidden-answer]<\/li>\r\n \t
                                                                                                                                    17. The sum of five-sixths and [latex]x[\/latex] is [latex]\\Large\\frac{1}{2}[\/latex].<\/li>\r\n \t
                                                                                                                                    18. The sum of three-fourths and [latex]x[\/latex] is [latex]\\Large\\frac{1}{8}[\/latex].[reveal-answer q=\"492619\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"492619\"][latex]\\Large\\frac{3}{4}\\normalsize+x=\\Large\\frac{1}{8}\\normalsize ;x=-\\Large\\frac{5}{8}[\/latex][\/hidden-answer]<\/li>\r\n \t
                                                                                                                                    19. The difference of [latex]y[\/latex] and one-fourth is [latex]-\\Large\\frac{1}{8}[\/latex].<\/li>\r\n \t
                                                                                                                                    20. The difference of [latex]y[\/latex] and one-third is [latex]-\\Large\\frac{1}{6}[\/latex].[reveal-answer q=\"476499\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"476499\"][latex]y-\\Large\\frac{1}{3}=-\\Large\\frac{1}{6}\\normalsize ;y=\\Large\\frac{1}{6}[\/latex][\/hidden-answer]<\/li>\r\n<\/ol>\r\n
                                                                                                                                      \r\n

                                                                                                                                      Everyday Math<\/h3>\r\n

                                                                                                                                      Shopping<\/h4>\r\nTeresa bought a pair of shoes on sale for [latex]\\$48[\/latex]. The sale price was [latex]\\Large\\frac{2}{3}[\/latex] of the regular price. Find the regular price of the shoes by solving the equation [latex]\\Large\\frac{2}{3}\\normalsize p=48[\/latex]\r\n

                                                                                                                                      Playhouse<\/h4>\r\nThe table in a child\u2019s playhouse is [latex]\\Large\\frac{3}{5}[\/latex] of an adult-size table. The playhouse table is [latex]18[\/latex] inches high. Find the height of an adult-size table by solving the equation [latex]\\Large\\frac{3}{5}\\normalsize h=18[\/latex].\r\n\r\n[reveal-answer q=\"137031\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"137031\"]30 inches[\/hidden-answer]\r\n\r\n<\/div>\r\n
                                                                                                                                      \r\n

                                                                                                                                      Writing Exercises<\/h3>\r\nThere are three methods to solve the equation [latex]-y=15[\/latex]. Which method do you prefer? Why?\r\n\r\n[practice-area rows=\"4\"][\/practice-area]\r\n\r\nRichard thinks the solution to the equation [latex]\\Large\\frac{3}{4}\\normalsize x=24[\/latex] is [latex]16[\/latex]. Explain why Richard is wrong.\r\n\r\n[practice-area rows=\"4\"][\/practice-area]\r\n\r\n<\/div>\r\n

                                                                                                                                      Chapter Review Exercises<\/h2>\r\n
                                                                                                                                      \r\n

                                                                                                                                      Visualize Fractions<\/h3>\r\nIn the following exercises, name the fraction of each figure that is shaded.\r\n

                                                                                                                                      Using Models to Represent Fractions<\/h4>\r\n

                                                                                                                                      Exercise 1<\/h5>\r\n\"A\r\n
                                                                                                                                      Exercise 2<\/h5>\r\n\"A\r\n\r\n[reveal-answer q=\"99723\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"99723\"][latex]\\Large\\frac{5}{9}[\/latex][\/hidden-answer]\r\n

                                                                                                                                      Using Models to Represent Mixed Numbers<\/h4>\r\nIn the following exercises, name the improper fractions. Then write each improper fraction as a mixed number.\r\n

                                                                                                                                      Exercise 1<\/h5>\r\n\"Two\r\n
                                                                                                                                      Exercise 2<\/h5>\r\n\"Two\r\n\r\n[reveal-answer q=\"500028\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"500028\"][latex]\\Large\\frac{3}{2}[\/latex][\/hidden-answer]\r\n

                                                                                                                                      Write an Improper Fraction as a Mixed Number<\/h4>\r\nIn the following exercises, convert the improper fraction to a mixed number.\r\n
                                                                                                                                        \r\n \t
                                                                                                                                      1. [latex]\\Large\\frac{58}{15}[\/latex]<\/li>\r\n \t
                                                                                                                                      2. [latex]\\Large\\frac{63}{11}[\/latex][reveal-answer q=\"225999\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"225999\"][latex]5\\Large\\frac{8}{11}[\/latex][\/hidden-answer]<\/li>\r\n<\/ol>\r\n

                                                                                                                                        Write a Mixed Number as an Improper Fraction<\/h4>\r\nIn the following exercises, convert the mixed number to an improper fraction.\r\n
                                                                                                                                          \r\n \t
                                                                                                                                        1. [latex]12\\Large\\frac{1}{4}[\/latex]<\/li>\r\n \t
                                                                                                                                        2. [latex]9\\Large\\frac{4}{5}[\/latex][reveal-answer q=\"165405\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"165405\"][latex]\\Large\\frac{49}{5}[\/latex][\/hidden-answer]<\/li>\r\n \t
                                                                                                                                        3. Find three fractions equivalent to [latex]\\Large\\frac{2}{5}[\/latex]. Show your work, using figures or algebra.<\/li>\r\n \t
                                                                                                                                        4. Find three fractions equivalent to [latex]-\\Large\\frac{4}{3}[\/latex]. Show your work, using figures or algebra.<\/li>\r\n<\/ol>\r\n

                                                                                                                                          Locating Fractions on the Number Line<\/h4>\r\nIn the following exercises, locate the numbers on a number line.\r\n
                                                                                                                                            \r\n \t
                                                                                                                                          1. [latex]\\Large\\frac{5}{8},\\Large\\frac{4}{3},\\normalsize 3\\Large\\frac{3}{4},\\normalsize4[\/latex]<\/li>\r\n \t
                                                                                                                                          2. [latex]\\Large\\frac{1}{4},-\\Large\\frac{1}{4},\\normalsize 1\\Large\\frac{1}{3},\\normalsize -1\\Large\\frac{1}{3},\\Large\\frac{7}{2},-\\Large\\frac{7}{2}[\/latex][reveal-answer q=\"76970\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"76970\"]\"A[\/hidden-answer]<\/li>\r\n<\/ol>\r\n

                                                                                                                                            Ordering Fractions on the Number Line<\/h4>\r\nIn the following exercises, order each pair of numbers, using [latex]&lt[\/latex] or [latex]&gt[\/latex].\r\n
                                                                                                                                              \r\n \t
                                                                                                                                            1. [latex]-1\\text{ ___}-\\Large\\frac{2}{5}[\/latex]<\/li>\r\n \t
                                                                                                                                            2. [latex]-2\\Large\\frac{1}{2}\\normalsize\\text{ ___}- 3[\/latex]<\/li>\r\n<\/ol>\r\n<\/div>\r\n
                                                                                                                                              \r\n

                                                                                                                                              Multiply and Divide Fractions<\/h3>\r\n

                                                                                                                                              Simplify Fractions<\/h4>\r\nIn the following exercises, simplify.\r\n
                                                                                                                                                \r\n \t
                                                                                                                                              1. [latex]-\\Large\\frac{63}{84}[\/latex]<\/li>\r\n \t
                                                                                                                                              2. [latex]-\\Large\\frac{90}{120}[\/latex][reveal-answer q=\"142717\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"142717\"][latex]-\\Large\\frac{3}{4}[\/latex][\/hidden-answer]<\/li>\r\n \t
                                                                                                                                              3. [latex]-\\Large\\frac{14a}{14b}[\/latex]<\/li>\r\n \t
                                                                                                                                              4. [latex]-\\Large\\frac{8x}{8y}[\/latex][reveal-answer q=\"430551\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"430551\"][latex]-\\Large\\frac{x}{y}[\/latex][\/hidden-answer]<\/li>\r\n<\/ol>\r\n

                                                                                                                                                Multiply Fractions<\/h4>\r\nIn the following exercises, multiply.\r\n
                                                                                                                                                  \r\n \t
                                                                                                                                                1. [latex]\\Large\\frac{2}{5}\\cdot\\Large\\frac{8}{13}[\/latex]<\/li>\r\n \t
                                                                                                                                                2. [latex]-\\Large\\frac{1}{3}\\cdot\\Large\\frac{12}{7}[\/latex][reveal-answer q=\"591640\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"591640\"][latex]-\\Large\\frac{4}{7}[\/latex][\/hidden-answer]<\/li>\r\n \t
                                                                                                                                                3. [latex]\\Large\\frac{2}{9}\\cdot\\Large\\left(-\\Large\\frac{45}{32}\\right)[\/latex]<\/li>\r\n \t
                                                                                                                                                4. [latex]6m\\cdot\\Large\\frac{4}{11}[\/latex][reveal-answer q=\"467548\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"467548\"][latex]\\Large\\frac{24}{11}\\normalsize m[\/latex][\/hidden-answer]<\/li>\r\n \t
                                                                                                                                                5. [latex]-\\Large\\frac{1}{4}\\normalsize\\left(-32\\right)[\/latex]<\/li>\r\n \t
                                                                                                                                                6. [latex]3\\Large\\frac{1}{5}\\normalsize\\cdot 1\\Large\\frac{7}{8}[\/latex][reveal-answer q=\"168571\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"168571\"]6[\/hidden-answer]<\/li>\r\n<\/ol>\r\n

                                                                                                                                                  Find Reciprocals<\/h4>\r\nIn the following exercises, find the reciprocal.\r\n
                                                                                                                                                    \r\n \t
                                                                                                                                                  1. [latex]\\Large\\frac{2}{9}[\/latex]<\/li>\r\n \t
                                                                                                                                                  2. [latex]\\Large\\frac{15}{4}[\/latex][reveal-answer q=\"864177\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"864177\"][latex]\\Large\\frac{4}{15}[\/latex][\/hidden-answer]<\/li>\r\n \t
                                                                                                                                                  3. [latex]3[\/latex]<\/li>\r\n \t
                                                                                                                                                  4. [latex]-\\Large\\frac{1}{4}[\/latex][reveal-answer q=\"61325\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"61325\"]\u22124[\/hidden-answer]<\/li>\r\n<\/ol>\r\n
                                                                                                                                                    Exercise 5<\/h5>\r\nFill in the chart.\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n
                                                                                                                                                    <\/th>\r\nOpposite<\/th>\r\nAbsolute Value<\/th>\r\nReciprocal<\/th>\r\n<\/tr>\r\n<\/thead>\r\n
                                                                                                                                                    [latex]-\\Large\\frac{5}{13}[\/latex]<\/td>\r\n<\/td>\r\n<\/td>\r\n<\/td>\r\n<\/tr>\r\n
                                                                                                                                                    [latex]\\Large\\frac{3}{10}[\/latex]<\/td>\r\n<\/td>\r\n<\/td>\r\n<\/td>\r\n<\/tr>\r\n
                                                                                                                                                    [latex]\\Large\\frac{9}{4}[\/latex]<\/td>\r\n<\/td>\r\n<\/td>\r\n<\/td>\r\n<\/tr>\r\n
                                                                                                                                                    [latex]-12[\/latex]<\/td>\r\n<\/td>\r\n<\/td>\r\n<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n

                                                                                                                                                    Divide Fractions<\/h4>\r\nIn the following exercises, divide.\r\n
                                                                                                                                                      \r\n \t
                                                                                                                                                    1. [latex]\\Large\\frac{2}{3}\\div\\Large\\frac{1}{6}[\/latex][reveal-answer q=\"839245\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"839245\"]4[\/hidden-answer]<\/li>\r\n \t
                                                                                                                                                    2. [latex]\\Large\\left(-\\frac{3x}{5}\\right)\\div\\Large\\left(-\\frac{2y}{3}\\right)[\/latex]<\/li>\r\n \t
                                                                                                                                                    3. [latex]\\Large\\frac{4}{5}\\normalsize\\div 3[\/latex][reveal-answer q=\"440534\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"440534\"][latex]\\Large\\frac{4}{15}[\/latex][\/hidden-answer]<\/li>\r\n \t
                                                                                                                                                    4. [latex]8\\div 2\\Large\\frac{2}{3}[\/latex]<\/li>\r\n \t
                                                                                                                                                    5. [latex]8\\Large\\frac{2}{3}\\normalsize\\div 1\\Large\\frac{1}{12}[\/latex][reveal-answer q=\"926775\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"926775\"]8[\/hidden-answer]<\/li>\r\n<\/ol>\r\n<\/div>\r\n
                                                                                                                                                      \r\n

                                                                                                                                                      Multiply and Divide Mixed Numbers and Complex Fractions<\/h3>\r\nIn the following exercises, perform the indicated operation.\r\n
                                                                                                                                                        \r\n \t
                                                                                                                                                      1. [latex]3\\Large\\frac{1}{5}\\normalsize\\cdot 1\\Large\\frac{7}{8}[\/latex]<\/li>\r\n \t
                                                                                                                                                      2. [latex]-5\\Large\\frac{7}{12}\\normalsize\\cdot 4\\Large\\frac{4}{11}[\/latex][reveal-answer q=\"691571\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"691571\"][latex]-\\Large\\frac{268}{11}[\/latex][\/hidden-answer]<\/li>\r\n \t
                                                                                                                                                      3. [latex]8\\div 2\\Large\\frac{2}{3}[\/latex]<\/li>\r\n \t
                                                                                                                                                      4. [latex]8\\Large\\frac{2}{3}\\normalsize\\div 1\\Large\\frac{1}{12}[\/latex][reveal-answer q=\"916626\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"916626\"]8[\/hidden-answer]<\/li>\r\n<\/ol>\r\n

                                                                                                                                                        Translate Phrases to Expressions with Fractions<\/h4>\r\nIn the following exercises, translate the English phrase into an algebraic expression.\r\n
                                                                                                                                                          \r\n \t
                                                                                                                                                        1. the quotient of [latex]8[\/latex] and [latex]y[\/latex]<\/li>\r\n \t
                                                                                                                                                        2. the quotient of [latex]V[\/latex] and the difference of [latex]h[\/latex] and [latex]6[\/latex][reveal-answer q=\"573511\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"573511\"][latex]\\Large\\frac{V}{h - 6}[\/latex][\/hidden-answer]<\/li>\r\n<\/ol>\r\n

                                                                                                                                                          Simplify Complex Fractions<\/h4>\r\nIn the following exercises, simplify the complex fraction\r\n
                                                                                                                                                            \r\n \t
                                                                                                                                                          1. [latex]\\Large\\frac{\\LARGE\\frac{5}{8}}{\\LARGE\\frac{4}{5}}[\/latex]<\/li>\r\n \t
                                                                                                                                                          2. [latex]\\Large\\frac{\\LARGE\\frac{8}{9}}{-4}[\/latex][reveal-answer q=\"698296\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"698296\"][latex]-\\Large\\frac{2}{9}[\/latex][\/hidden-answer]<\/li>\r\n \t
                                                                                                                                                          3. [latex]\\Large\\frac{\\LARGE\\frac{n}{4}}{\\LARGE\\frac{3}{8}}[\/latex]<\/li>\r\n \t
                                                                                                                                                          4. [latex]\\Large\\frac{\\normalsize-1\\LARGE\\frac{5}{6}}{-\\LARGE\\frac{1}{12}}[\/latex][reveal-answer q=\"37865\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"37865\"]22[\/hidden-answer]<\/li>\r\n<\/ol>\r\n

                                                                                                                                                            Simplify Fractions<\/h4>\r\nIn the following exercises, simplify.\r\n
                                                                                                                                                              \r\n \t
                                                                                                                                                            1. [latex]\\Large\\frac{5+16}{5}[\/latex]<\/li>\r\n \t
                                                                                                                                                            2. [latex]\\Large\\frac{8\\cdot 4-{5}^{2}}{3\\cdot 12}[\/latex][reveal-answer q=\"985726\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"985726\"][latex]\\Large\\frac{7}{36}[\/latex][\/hidden-answer]<\/li>\r\n \t
                                                                                                                                                            3. [latex]\\Large\\frac{8\\cdot 7+5\\left(8 - 10\\right)}{9\\cdot 3 - 6\\cdot 4}[\/latex]<\/li>\r\n<\/ol>\r\n<\/div>\r\n
                                                                                                                                                              \r\n

                                                                                                                                                              Add and Subtract Fractions with Common Denominators<\/h3>\r\n

                                                                                                                                                              Add Fractions with a Common Denominator<\/h4>\r\nIn the following exercises, add.\r\n
                                                                                                                                                                \r\n \t
                                                                                                                                                              1. [latex]\\Large\\frac{3}{8}+\\Large\\frac{2}{8}[\/latex][reveal-answer q=\"745460\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"745460\"][latex]\\Large\\frac{5}{8}[\/latex][\/hidden-answer]<\/li>\r\n \t
                                                                                                                                                              2. [latex]\\Large\\frac{4}{5}+\\Large\\frac{1}{5}[\/latex]<\/li>\r\n \t
                                                                                                                                                              3. [latex]\\Large\\frac{2}{5}+\\Large\\frac{1}{5}[\/latex][reveal-answer q=\"34238\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"34238\"][latex]\\Large\\frac{3}{5}[\/latex][\/hidden-answer]<\/li>\r\n \t
                                                                                                                                                              4. [latex]\\Large\\frac{15}{32}+\\Large\\frac{9}{32}[\/latex]<\/li>\r\n \t
                                                                                                                                                              5. [latex]\\Large\\frac{x}{10}+\\Large\\frac{7}{10}[\/latex][reveal-answer q=\"244746\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"244746\"][latex]\\Large\\frac{x+7}{10}[\/latex][\/hidden-answer]<\/li>\r\n<\/ol>\r\n

                                                                                                                                                                Subtract Fractions with a Common Denominator<\/h4>\r\nIn the following exercises, subtract.\r\n
                                                                                                                                                                  \r\n \t
                                                                                                                                                                1. [latex]\\Large\\frac{8}{11}-\\Large\\frac{6}{11}[\/latex]<\/li>\r\n \t
                                                                                                                                                                2. [latex]\\Large\\frac{11}{12}-\\Large\\frac{5}{12}[\/latex][reveal-answer q=\"887169\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"887169\"][latex]\\Large\\frac{1}{2}[\/latex][\/hidden-answer]<\/li>\r\n \t
                                                                                                                                                                3. [latex]\\Large\\frac{4}{5}-\\frac{y}{5}[\/latex]<\/li>\r\n \t
                                                                                                                                                                4. [latex]-\\Large\\frac{31}{30}-\\Large\\frac{7}{30}[\/latex][reveal-answer q=\"329475\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"329475\"][latex]-\\Large\\frac{19}{15}[\/latex][\/hidden-answer]<\/li>\r\n \t
                                                                                                                                                                5. [latex]\\Large\\frac{3}{2}-\\Large\\left(\\frac{3}{2}\\right)[\/latex]<\/li>\r\n \t
                                                                                                                                                                6. [latex]\\Large\\frac{11}{15}-\\Large\\frac{5}{15}-\\Large\\left(-\\frac{2}{15}\\right)[\/latex][reveal-answer q=\"593153\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"593153\"][latex]\\Large\\frac{8}{15}[\/latex][\/hidden-answer]<\/li>\r\n<\/ol>\r\n<\/div>\r\n
                                                                                                                                                                  \r\n

                                                                                                                                                                  Add and Subtract Fractions with Different Denominators<\/h3>\r\n

                                                                                                                                                                  Find the Least Common Denominator (LCD)<\/h4>\r\nIn the following exercises, find the least common denominator.\r\n
                                                                                                                                                                    \r\n \t
                                                                                                                                                                  1. [latex]\\Large\\frac{1}{3}\\normalsize\\text{ and }\\Large\\frac{1}{12}[\/latex]<\/li>\r\n \t
                                                                                                                                                                  2. [latex]\\Large\\frac{1}{3}\\normalsize\\text{ and }\\Large\\frac{4}{5}[\/latex][reveal-answer q=\"823554\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"823554\"]15[\/hidden-answer]<\/li>\r\n \t
                                                                                                                                                                  3. [latex]\\Large\\frac{8}{15}\\normalsize\\text{ and }\\Large\\frac{11}{20}[\/latex]<\/li>\r\n \t
                                                                                                                                                                  4. [latex]\\Large\\frac{3}{4},\\Large\\frac{1}{6},\\normalsize\\text{ and }\\Large\\frac{5}{10}[\/latex][reveal-answer q=\"523424\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"523424\"]60[\/hidden-answer]<\/li>\r\n<\/ol>\r\n

                                                                                                                                                                    Convert Fractions to Equivalent Fractions with the LCD<\/h4>\r\nIn the following exercises, change to equivalent fractions using the given LCD.\r\n
                                                                                                                                                                      \r\n \t
                                                                                                                                                                    1. [latex]\\Large\\frac{1}{3}\\normalsize\\text{ and }\\Large\\frac{1}{5},\\normalsize\\text{LCD}=15[\/latex]<\/li>\r\n \t
                                                                                                                                                                    2. [latex]\\Large\\frac{3}{8}\\normalsize\\text{ and }\\Large\\frac{5}{6},\\normalsize\\text{LCD}=24[\/latex][reveal-answer q=\"79462\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"79462\"][latex]\\Large\\frac{9}{24}\\normalsize\\text{ and }\\Large\\frac{20}{24}[\/latex][\/hidden-answer]<\/li>\r\n \t
                                                                                                                                                                    3. [latex]-\\Large\\frac{9}{16}\\normalsize\\text{ and }\\Large\\frac{5}{12},\\normalsize\\text{LCD}=48[\/latex]<\/li>\r\n \t
                                                                                                                                                                    4. [latex]\\Large\\frac{1}{3}\\normalsize\\text{,}\\Large\\frac{3}{4}\\normalsize\\text{ and }\\Large\\frac{4}{5},\\normalsize\\text{LCD}=60[\/latex][reveal-answer q=\"448503\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"448503\"][latex]\\Large\\frac{20}{60},\\Large\\frac{15}{60}\\normalsize\\text{ and }\\Large\\frac{48}{60}[\/latex][\/hidden-answer]<\/li>\r\n<\/ol>\r\n

                                                                                                                                                                      Identify and Use Fraction Operations<\/h4>\r\nIn the following exercises, perform the indicated operations and simplify.\r\n
                                                                                                                                                                        \r\n \t
                                                                                                                                                                      1. [latex]\\Large\\frac{1}{5}+\\Large\\frac{2}{3}[\/latex]<\/li>\r\n \t
                                                                                                                                                                      2. [latex]\\Large\\frac{11}{12}-\\Large\\frac{2}{3}[\/latex][reveal-answer q=\"976179\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"976179\"][latex]\\Large\\frac{1}{4}[\/latex][\/hidden-answer]<\/li>\r\n \t
                                                                                                                                                                      3. [latex]-\\Large\\frac{9}{10}-\\Large\\frac{3}{4}[\/latex]<\/li>\r\n \t
                                                                                                                                                                      4. [latex]-\\Large\\frac{11}{36}-\\Large\\frac{11}{20}[\/latex][reveal-answer q=\"617886\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"617886\"][latex]-\\Large\\frac{77}{90}[\/latex][\/hidden-answer]<\/li>\r\n \t
                                                                                                                                                                      5. [latex]-\\Large\\frac{22}{25}+\\Large\\frac{9}{40}[\/latex]<\/li>\r\n \t
                                                                                                                                                                      6. [latex]\\Large\\frac{y}{10}-\\Large\\frac{1}{3}[\/latex][reveal-answer q=\"200326\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"200326\"][latex]\\Large\\frac{3y - 10}{30}[\/latex][\/hidden-answer]<\/li>\r\n \t
                                                                                                                                                                      7. [latex]\\Large\\frac{2}{5}+\\Large\\left(-\\frac{5}{9}\\right)[\/latex]<\/li>\r\n \t
                                                                                                                                                                      8. [latex]\\Large\\frac{4}{11}\\div\\Large\\frac{2}{7d}[\/latex][reveal-answer q=\"520162\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"520162\"][latex]\\Large\\frac{14d}{11}[\/latex][\/hidden-answer]<\/li>\r\n \t
                                                                                                                                                                      9. [latex]\\Large\\frac{2}{5}+\\Large\\left(-\\frac{3n}{8}\\right)\\Large\\left(-\\frac{2}{9n}\\right)[\/latex]<\/li>\r\n \t
                                                                                                                                                                      10. [latex]\\Large\\frac{{\\left(\\Large\\frac{2}{3}\\right)}^{2}}{{\\Large\\left(\\frac{5}{8}\\right)}^{2}}[\/latex][reveal-answer q=\"578589\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"578589\"][latex]\\Large\\frac{256}{225}[\/latex][\/hidden-answer]<\/li>\r\n \t
                                                                                                                                                                      11. [latex]\\Large\\left(\\frac{11}{12}+\\Large\\frac{3}{8}\\right)\\div\\Large\\left(\\Large\\frac{5}{6}-\\Large\\frac{1}{10}\\right)[\/latex]<\/li>\r\n<\/ol>\r\n

                                                                                                                                                                        Mixed Practice<\/h4>\r\nIn the following exercises, evaluate.\r\n

                                                                                                                                                                        Exercise 1<\/h5>\r\n[latex]y-\\Large\\frac{4}{5}[\/latex] when\r\n
                                                                                                                                                                          \r\n \t
                                                                                                                                                                        1. [latex]y=-\\Large\\frac{4}{5}[\/latex]<\/li>\r\n \t
                                                                                                                                                                        2. [latex]y=\\Large\\frac{1}{4}[\/latex]<\/li>\r\n<\/ol>\r\n[reveal-answer q=\"480304\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"480304\"]\r\n
                                                                                                                                                                            \r\n \t
                                                                                                                                                                          1. [latex]-\\Large\\frac{8}{5}[\/latex]<\/li>\r\n \t
                                                                                                                                                                          2. [latex]-\\Large\\frac{11}{20}[\/latex]<\/li>\r\n<\/ol>\r\n[\/hidden-answer]\r\n
                                                                                                                                                                            Exercise 2<\/h5>\r\n[latex]6m{n}^{2}[\/latex] when [latex]m=\\Large\\frac{3}{4}\\normalsize\\text{ and }n=-\\Large\\frac{1}{3}[\/latex]\r\n\r\n<\/div>\r\n
                                                                                                                                                                            \r\n

                                                                                                                                                                            Add and Subtract Mixed Numbers<\/h3>\r\nIn the following exercises, perform the indicated operation.\r\n
                                                                                                                                                                              \r\n \t
                                                                                                                                                                            1. [latex]4\\Large\\frac{1}{3}\\normalsize+9\\Large\\frac{1}{3}[\/latex][reveal-answer q=\"97018\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"97018\"][latex]13\\Large\\frac{2}{3}[\/latex][\/hidden-answer]<\/li>\r\n \t
                                                                                                                                                                            2. [latex]6\\Large\\frac{2}{5}\\normalsize+7\\Large\\frac{3}{5}[\/latex]<\/li>\r\n \t
                                                                                                                                                                            3. [latex]5\\Large\\frac{8}{11}\\normalsize+2\\Large\\frac{4}{11}[\/latex][reveal-answer q=\"737880\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"737880\"][latex]8\\Large\\frac{1}{11}[\/latex][\/hidden-answer]<\/li>\r\n \t
                                                                                                                                                                            4. [latex]3\\Large\\frac{5}{8}\\normalsize+3\\Large\\frac{7}{8}[\/latex]<\/li>\r\n \t
                                                                                                                                                                            5. [latex]9\\Large\\frac{13}{20}\\normalsize-4\\Large\\frac{11}{20}[\/latex][reveal-answer q=\"720156\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"720156\"][latex]5\\Large\\frac{1}{10}[\/latex][\/hidden-answer]<\/li>\r\n \t
                                                                                                                                                                            6. [latex]2\\Large\\frac{3}{10}\\normalsize-1\\Large\\frac{9}{10}[\/latex]<\/li>\r\n \t
                                                                                                                                                                            7. [latex]2\\Large\\frac{11}{12}\\normalsize-1\\Large\\frac{7}{12}[\/latex][reveal-answer q=\"779938\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"779938\"][latex]\\Large\\frac{10}{3}[\/latex][\/hidden-answer]<\/li>\r\n \t
                                                                                                                                                                            8. [latex]8\\Large\\frac{6}{11}\\normalsize-2\\Large\\frac{9}{11}[\/latex]<\/li>\r\n<\/ol>\r\n<\/div>\r\n
                                                                                                                                                                              \r\n

                                                                                                                                                                              Solve Equations with Fractions<\/h3>\r\n

                                                                                                                                                                              Determine Whether a Fraction is a Solution of an Equation<\/h4>\r\nIn the following exercises, determine whether the each number is a solution of the given equation.\r\n

                                                                                                                                                                              Exercise 1<\/h5>\r\n[latex]x-\\Large\\frac{1}{2}=\\Large\\frac{1}{6}\\normalsize\\text{:}[\/latex]\r\n
                                                                                                                                                                                \r\n \t
                                                                                                                                                                              1. [latex]x=1[\/latex]<\/li>\r\n \t
                                                                                                                                                                              2. [latex]x=\\Large\\frac{2}{3}[\/latex]<\/li>\r\n \t
                                                                                                                                                                              3. [latex]x=-\\Large\\frac{1}{3}[\/latex]<\/li>\r\n<\/ol>\r\n[reveal-answer q=\"635553\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"635553\"]\r\n
                                                                                                                                                                                  \r\n \t
                                                                                                                                                                                1. no<\/li>\r\n \t
                                                                                                                                                                                2. yes<\/li>\r\n \t
                                                                                                                                                                                3. no<\/li>\r\n<\/ol>\r\n[\/hidden-answer]\r\n
                                                                                                                                                                                  Exercise 2<\/h5>\r\n[latex]y+\\Large\\frac{3}{5}=\\Large\\frac{5}{9}\\normalsize\\text{:}[\/latex]\r\n
                                                                                                                                                                                    \r\n \t
                                                                                                                                                                                  1. [latex]y=\\Large\\frac{1}{2}[\/latex]<\/li>\r\n \t
                                                                                                                                                                                  2. [latex]y=\\Large\\frac{52}{45}[\/latex]<\/li>\r\n \t
                                                                                                                                                                                  3. [latex]y=-\\Large\\frac{2}{45}[\/latex]<\/li>\r\n<\/ol>\r\n

                                                                                                                                                                                    Solve Equations with Fractions using the Addition, Subtraction, and Division Properties of Equality<\/h4>\r\nIn the following exercises, solve the equation.\r\n
                                                                                                                                                                                      \r\n \t
                                                                                                                                                                                    1. [latex]n+\\Large\\frac{9}{11}=\\Large\\frac{4}{11}[\/latex][reveal-answer q=\"551742\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"551742\"][latex]n=-\\Large\\frac{5}{11}[\/latex][\/hidden-answer]<\/li>\r\n \t
                                                                                                                                                                                    2. [latex]x-\\Large\\frac{1}{6}=\\Large\\frac{7}{6}[\/latex]<\/li>\r\n \t
                                                                                                                                                                                    3. [latex]h-\\Large\\left(-\\frac{7}{8}\\right)=-\\Large\\frac{2}{5}[\/latex][reveal-answer q=\"529566\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"529566\"][latex]h=-\\Large\\frac{51}{40}[\/latex][\/hidden-answer]<\/li>\r\n \t
                                                                                                                                                                                    4. [latex]\\Large\\frac{x}{5}\\normalsize=-10[\/latex]<\/li>\r\n \t
                                                                                                                                                                                    5. [latex]-z=23[\/latex][reveal-answer q=\"452156\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"452156\"]z = \u221223[\/hidden-answer]<\/li>\r\n<\/ol>\r\n

                                                                                                                                                                                      Translate Sentences to Equations and Solve<\/h4>\r\nIn the following exercises, translate and solve.\r\n
                                                                                                                                                                                        \r\n \t
                                                                                                                                                                                      1. The sum of two-thirds and [latex]n[\/latex] is [latex]-\\Large\\frac{3}{5}[\/latex].<\/li>\r\n \t
                                                                                                                                                                                      2. The difference of [latex]q[\/latex] and one-tenth is [latex]\\Large\\frac{1}{2}[\/latex].[reveal-answer q=\"959180\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"959180\"][latex]q-\\Large\\frac{1}{10}=\\Large\\frac{1}{2}\\normalsize;q=\\Large\\frac{3}{5}[\/latex][\/hidden-answer]<\/li>\r\n \t
                                                                                                                                                                                      3. The quotient of [latex]p[\/latex] and [latex]-4[\/latex] is [latex]-8[\/latex].<\/li>\r\n \t
                                                                                                                                                                                      4. Three-eighths of [latex]y[\/latex] is [latex]24[\/latex].[reveal-answer q=\"335939\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"335939\"][latex]\\Large\\frac{3}{8}\\normalsize y=24;y=64[\/latex][\/hidden-answer]<\/li>\r\n<\/ol>\r\n<\/div>\r\n
                                                                                                                                                                                        \r\n

                                                                                                                                                                                        Chapter Practice Test<\/h3>\r\nConvert the improper fraction to a mixed number.\r\n
                                                                                                                                                                                          \r\n \t
                                                                                                                                                                                        1. [latex]\\Large\\frac{19}{5}[\/latex]<\/li>\r\n<\/ol>\r\nConvert the mixed number to an improper fraction.\r\n
                                                                                                                                                                                            \r\n \t
                                                                                                                                                                                          1. [latex]3\\Large\\frac{2}{7}[\/latex][reveal-answer q=\"663183\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"663183\"][latex]\\Large\\frac{23}{7}[\/latex][\/hidden-answer]<\/li>\r\n<\/ol>\r\nLocate the numbers on a number line.\r\n
                                                                                                                                                                                              \r\n \t
                                                                                                                                                                                            1. [latex]\\Large\\frac{1}{2}\\normalsize ,1\\Large\\frac{2}{3}\\normalsize ,-2\\Large\\frac{3}{4}\\normalsize ,\\text{ and }\\Large\\frac{9}{4}[\/latex]<\/li>\r\n<\/ol>\r\nIn the following exercises, simplify.\r\n
                                                                                                                                                                                                \r\n \t
                                                                                                                                                                                              1. [latex]\\Large\\frac{5}{20}[\/latex][reveal-answer q=\"940140\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"940140\"][latex]\\Large\\frac{1}{4}[\/latex][\/hidden-answer]<\/li>\r\n \t
                                                                                                                                                                                              2. [latex]\\Large\\frac{18r}{27s}[\/latex]<\/li>\r\n \t
                                                                                                                                                                                              3. [latex]\\Large\\frac{1}{3}\\cdot\\Large\\frac{3}{4}[\/latex][reveal-answer q=\"222332\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"222332\"][latex]\\Large\\frac{1}{4}[\/latex][\/hidden-answer]<\/li>\r\n \t
                                                                                                                                                                                              4. [latex]\\Large\\frac{3}{5}\\normalsize\\cdot 15[\/latex]<\/li>\r\n \t
                                                                                                                                                                                              5. [latex]-36u\\Large\\left(-\\frac{4}{9}\\right)[\/latex][reveal-answer q=\"906918\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"906918\"]16u<\/em>[\/hidden-answer]<\/li>\r\n \t
                                                                                                                                                                                              6. [latex]-5\\Large\\frac{7}{12}\\normalsize\\cdot 4\\Large\\frac{4}{11}[\/latex]<\/li>\r\n \t
                                                                                                                                                                                              7. [latex]-\\Large\\frac{5}{6}\\div\\Large\\frac{5}{12}[\/latex][reveal-answer q=\"589910\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"589910\"]\u22122[\/hidden-answer]<\/li>\r\n \t
                                                                                                                                                                                              8. [latex]\\Large\\frac{7}{11}\\div\\Large\\left(-\\frac{7}{11}\\right)[\/latex]<\/li>\r\n \t
                                                                                                                                                                                              9. [latex]\\Large\\frac{9a}{10}\\div\\Large\\frac{15a}{8}[\/latex][reveal-answer q=\"383040\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"383040\"][latex]\\Large\\frac{12}{25}[\/latex][\/hidden-answer]<\/li>\r\n \t
                                                                                                                                                                                              10. [latex]-6\\Large\\frac{2}{5}\\normalsize\\div 4[\/latex]<\/li>\r\n \t
                                                                                                                                                                                              11. [latex]\\left(-15\\Large\\frac{5}{6}\\right)\\normalsize\\div\\left(-3\\Large\\frac{1}{6}\\right)[\/latex][reveal-answer q=\"592671\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"592671\"]5[\/hidden-answer]<\/li>\r\n \t
                                                                                                                                                                                              12. [latex]\\Large\\frac{-6}{\\LARGE\\frac{6}{11}}[\/latex]<\/li>\r\n \t
                                                                                                                                                                                              13. [latex]\\Large\\frac{\\LARGE\\frac{p}{2}}{\\LARGE\\frac{q}{5}}[\/latex][reveal-answer q=\"763828\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"763828\"][latex]\\Large\\frac{5p}{2q}[\/latex][\/hidden-answer]<\/li>\r\n \t
                                                                                                                                                                                              14. [latex]\\Large\\frac{-\\LARGE\\frac{4}{15}}{-2\\LARGE\\frac{2}{3}}[\/latex]<\/li>\r\n \t
                                                                                                                                                                                              15. [latex]\\Large\\frac{{9}^{2}-{4}^{2}}{9 - 4}[\/latex][reveal-answer q=\"976972\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"976972\"]13[\/hidden-answer]<\/li>\r\n \t
                                                                                                                                                                                              16. [latex]\\Large\\frac{2}{d}+\\Large\\frac{9}{d}[\/latex]<\/li>\r\n \t
                                                                                                                                                                                              17. [latex]-\\Large\\frac{3}{13}+\\Large\\left(-\\frac{4}{13}\\right)[\/latex][reveal-answer q=\"849048\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"849048\"][latex]-\\Large\\frac{7}{13}[\/latex][\/hidden-answer]<\/li>\r\n \t
                                                                                                                                                                                              18. [latex]-\\Large\\frac{22}{25}+\\Large\\frac{9}{40}[\/latex]<\/li>\r\n \t
                                                                                                                                                                                              19. [latex]\\Large\\frac{2}{5}+\\Large\\left(-\\frac{7}{5}\\right)[\/latex][reveal-answer q=\"319104\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"319104\"]\u22121[\/hidden-answer]<\/li>\r\n \t
                                                                                                                                                                                              20. [latex]-\\Large\\frac{3}{10}+\\Large\\left(-\\frac{5}{8}\\right)[\/latex]<\/li>\r\n \t
                                                                                                                                                                                              21. [latex]-\\Large\\frac{3}{4}\\div\\Large\\frac{x}{3}[\/latex][reveal-answer q=\"761632\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"761632\"][latex]-\\Large\\frac{9}{4x}[\/latex][\/hidden-answer]<\/li>\r\n \t
                                                                                                                                                                                              22. [latex]\\Large\\frac{{2}^{3}-{2}^{2}}{{\\LARGE\\left(\\frac{3}{4}\\right)}^{2}}[\/latex]<\/li>\r\n \t
                                                                                                                                                                                              23. [latex]\\Large\\frac{\\LARGE\\frac{5}{14}+\\LARGE\\frac{1}{8}}{\\LARGE\\frac{9}{56}}[\/latex][reveal-answer q=\"427534\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"427534\"]3[\/hidden-answer]<\/li>\r\n<\/ol>\r\nEvaluate [latex]x+\\Large\\frac{1}{3}[\/latex] when\r\n
                                                                                                                                                                                                  \r\n \t
                                                                                                                                                                                                1. [latex]x=\\Large\\frac{2}{3}[\/latex]<\/li>\r\n \t
                                                                                                                                                                                                2. [latex]x=-\\Large\\frac{5}{6}[\/latex]<\/li>\r\n<\/ol>\r\nIn the following exercises, solve the equation.\r\n
                                                                                                                                                                                                    \r\n \t
                                                                                                                                                                                                  1. [latex]y+\\Large\\frac{3}{5}=\\Large\\frac{7}{5}[\/latex][reveal-answer q=\"825853\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"825853\"][latex]y=\\Large\\frac{4}{5}[\/latex][\/hidden-answer]<\/li>\r\n \t
                                                                                                                                                                                                  2. [latex]a-\\Large\\frac{3}{10}=-\\Large\\frac{9}{10}[\/latex]<\/li>\r\n \t
                                                                                                                                                                                                  3. [latex]f+\\Large\\left(-\\frac{2}{3}\\right)=\\Large\\frac{5}{12}[\/latex][reveal-answer q=\"586779\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"586779\"][latex]f=\\Large\\frac{13}{12}[\/latex][\/hidden-answer]<\/li>\r\n \t
                                                                                                                                                                                                  4. [latex]\\Large\\frac{m}{-2}\\normalsize=-16[\/latex]<\/li>\r\n \t
                                                                                                                                                                                                  5. [latex]-\\Large\\frac{2}{3}\\normalsize c=18[\/latex][reveal-answer q=\"406038\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"406038\"]c = \u221227[\/hidden-answer]<\/li>\r\n<\/ol>\r\nTranslate and solve: The quotient of [latex]p[\/latex] and [latex]-4[\/latex] is [latex]-8[\/latex]. Solve for [latex]p[\/late\r\n\r\n<\/div>\r\n

                                                                                                                                                                                                    Contribute!<\/h2>
                                                                                                                                                                                                    Did you have an idea for improving this content? We\u2019d love your input.<\/div>Improve this page<\/a>Learn More<\/a>","rendered":"

                                                                                                                                                                                                    Representing parts of a whole<\/h2>\n

                                                                                                                                                                                                    Using Models to Represent Fractions<\/h3>\n

                                                                                                                                                                                                    In the following exercises, name the fraction of each figure that is shaded.<\/p>\n

                                                                                                                                                                                                    Exercise 1<\/h4>\n

                                                                                                                                                                                                    \"In<\/p>\n

                                                                                                                                                                                                    Show Solution<\/span><\/p>\n
                                                                                                                                                                                                    \n

                                                                                                                                                                                                    \u24d0 = [latex]\\Large\\frac{1}{4}[\/latex]<\/p>\n

                                                                                                                                                                                                    \u24d1 = [latex]\\Large\\frac{3}{4}[\/latex]<\/p>\n

                                                                                                                                                                                                    \u24d2 = [latex]\\Large\\frac{3}{8}[\/latex]<\/p>\n

                                                                                                                                                                                                    \u24d3 = [latex]\\Large\\frac{5}{9}[\/latex]<\/p><\/div>\n<\/div>\n

                                                                                                                                                                                                    Exercise 2<\/h4>\n

                                                                                                                                                                                                    \"In<\/p>\n

                                                                                                                                                                                                    Using Models to Represent Fractions<\/h3>\n

                                                                                                                                                                                                    In the following exercises, shade parts of circles or squares to model the following fractions.<\/p>\n

                                                                                                                                                                                                      \n
                                                                                                                                                                                                    1. [latex]\\Large\\frac{1}{2}[\/latex]\n
                                                                                                                                                                                                      Show Solution<\/span><\/p>\n
                                                                                                                                                                                                      \"A<\/div>\n<\/div>\n<\/li>\n
                                                                                                                                                                                                    2. [latex]\\Large\\frac{1}{3}[\/latex]<\/li>\n
                                                                                                                                                                                                    3. [latex]\\Large\\frac{3}{4}[\/latex]\n
                                                                                                                                                                                                      Show Solution<\/span><\/p>\n
                                                                                                                                                                                                      \"A<\/div>\n<\/div>\n<\/li>\n
                                                                                                                                                                                                    4. [latex]\\Large\\frac{2}{5}[\/latex]<\/li>\n
                                                                                                                                                                                                    5. [latex]\\Large\\frac{5}{6}[\/latex]\n
                                                                                                                                                                                                      Show Solution<\/span><\/p>\n
                                                                                                                                                                                                      \"A<\/div>\n<\/div>\n<\/li>\n
                                                                                                                                                                                                    6. [latex]\\Large\\frac{7}{8}[\/latex]<\/li>\n
                                                                                                                                                                                                    7. [latex]\\Large\\frac{5}{8}[\/latex]\n
                                                                                                                                                                                                      Show Solution<\/span><\/p>\n
                                                                                                                                                                                                      \"A<\/div>\n<\/div>\n<\/li>\n
                                                                                                                                                                                                    8. [latex]\\Large\\frac{7}{10}[\/latex]<\/li>\n<\/ol>\n

                                                                                                                                                                                                      Model Improper Fractions and Mixed Numbers<\/h3>\n

                                                                                                                                                                                                      In the following exercises, use fraction circles to make wholes, if possible, with the following pieces.<\/p>\n

                                                                                                                                                                                                        \n
                                                                                                                                                                                                      1. [latex]3[\/latex] thirds\n
                                                                                                                                                                                                        Show Solution<\/span><\/p>\n
                                                                                                                                                                                                        \"A<\/div>\n<\/div>\n<\/li>\n
                                                                                                                                                                                                      2. [latex]8[\/latex] eighths<\/li>\n
                                                                                                                                                                                                      3. [latex]7[\/latex] sixths\n
                                                                                                                                                                                                        Show Solution<\/span><\/p>\n
                                                                                                                                                                                                        \"Two<\/div>\n<\/div>\n<\/li>\n
                                                                                                                                                                                                      4. [latex]4[\/latex] thirds<\/li>\n
                                                                                                                                                                                                      5. [latex]7[\/latex] fifths\n
                                                                                                                                                                                                        Show Solution<\/span><\/p>\n
                                                                                                                                                                                                        \"Two<\/div>\n<\/div>\n<\/li>\n
                                                                                                                                                                                                      6. [latex]7[\/latex] fourths<\/li>\n<\/ol>\n

                                                                                                                                                                                                        Model Improper Fractions and Mixed Numbers<\/h3>\n

                                                                                                                                                                                                        In the following exercises, name the improper fractions. Then write each improper fraction as a mixed number.<\/p>\n

                                                                                                                                                                                                        Exercise 1<\/h4>\n

                                                                                                                                                                                                        \"In<\/p>\n

                                                                                                                                                                                                        Show Solution<\/span><\/p>\n
                                                                                                                                                                                                        \u24d0 [latex]\\Large\\frac{5}{4}\\normalsize =1\\Large\\frac{1}{4}[\/latex] \u24d1 [latex]\\Large\\frac{7}{4}\\normalsize =1\\Large\\frac{3}{4}[\/latex] \u24d2 [latex]\\Large\\frac{11}{8}\\normalsize =1\\Large\\frac{3}{8}[\/latex]<\/div>\n<\/div>\n

                                                                                                                                                                                                        Exercise 2<\/h4>\n

                                                                                                                                                                                                        \"In<\/p>\n

                                                                                                                                                                                                        Exercise 3<\/h4>\n

                                                                                                                                                                                                        \"In<\/p>\n

                                                                                                                                                                                                        Show Solution<\/span><\/p>\n
                                                                                                                                                                                                        \u24d0 [latex]\\Large\\frac{11}{4}\\normalsize =2\\Large\\frac{3}{4}[\/latex] \u24d1 [latex]\\Large\\frac{19}{8}\\normalsize =2\\Large\\frac{3}{8}[\/latex]<\/div>\n<\/div>\n

                                                                                                                                                                                                        Model Improper Fractions and Mixed Numbers<\/h3>\n

                                                                                                                                                                                                        In the following exercises, draw fraction circles to model the given fraction.<\/p>\n

                                                                                                                                                                                                          \n
                                                                                                                                                                                                        1. [latex]\\Large\\frac{3}{3}[\/latex]<\/li>\n
                                                                                                                                                                                                        2. [latex]\\Large\\frac{4}{4}[\/latex]\n
                                                                                                                                                                                                          Show Solution<\/span><\/p>\n
                                                                                                                                                                                                          \"A<\/div>\n<\/div>\n<\/li>\n
                                                                                                                                                                                                        3. [latex]\\Large\\frac{7}{4}[\/latex]<\/li>\n
                                                                                                                                                                                                        4. [latex]\\Large\\frac{5}{3}[\/latex]\n
                                                                                                                                                                                                          Show Solution<\/span><\/p>\n
                                                                                                                                                                                                          \"Two<\/div>\n<\/div>\n<\/li>\n
                                                                                                                                                                                                        5. [latex]\\Large\\frac{11}{6}[\/latex]<\/li>\n
                                                                                                                                                                                                        6. [latex]\\Large\\frac{13}{8}[\/latex]\n
                                                                                                                                                                                                          Show Solution<\/span><\/p>\n
                                                                                                                                                                                                          \"Two<\/div>\n<\/div>\n<\/li>\n
                                                                                                                                                                                                        7. [latex]\\Large\\frac{10}{3}[\/latex]<\/li>\n
                                                                                                                                                                                                        8. [latex]\\Large\\frac{9}{4}[\/latex]\n
                                                                                                                                                                                                          Show Solution<\/span><\/p>\n
                                                                                                                                                                                                          \"Three<\/div>\n<\/div>\n<\/li>\n<\/ol>\n

                                                                                                                                                                                                          Converting Between Improper Fractions and Mixed Numbers<\/h2>\n

                                                                                                                                                                                                          Write an Improper Fraction as a Mixed Number<\/h3>\n

                                                                                                                                                                                                          In the following exercises, rewrite the improper fraction as a mixed number.<\/p>\n

                                                                                                                                                                                                            \n
                                                                                                                                                                                                          1. [latex]\\Large\\frac{3}{2}[\/latex]<\/li>\n
                                                                                                                                                                                                          2. [latex]\\Large\\frac{5}{3}[\/latex]\n
                                                                                                                                                                                                            Show Solution<\/span><\/p>\n
                                                                                                                                                                                                            [latex]1\\Large\\frac{2}{3}[\/latex]<\/div>\n<\/div>\n<\/li>\n
                                                                                                                                                                                                          3. [latex]\\Large\\frac{11}{4}[\/latex]<\/li>\n
                                                                                                                                                                                                          4. [latex]\\Large\\frac{13}{5}[\/latex]\n
                                                                                                                                                                                                            Show Solution<\/span><\/p>\n
                                                                                                                                                                                                            [latex]2\\Large\\frac{3}{5}[\/latex]<\/div>\n<\/div>\n<\/li>\n
                                                                                                                                                                                                          5. [latex]\\Large\\frac{25}{6}[\/latex]<\/li>\n
                                                                                                                                                                                                          6. [latex]\\Large\\frac{28}{9}[\/latex]\n
                                                                                                                                                                                                            Show Solution<\/span><\/p>\n
                                                                                                                                                                                                            [latex]3\\Large\\frac{1}{9}[\/latex]<\/div>\n<\/div>\n<\/li>\n
                                                                                                                                                                                                          7. [latex]\\Large\\frac{42}{13}[\/latex]<\/li>\n
                                                                                                                                                                                                          8. [latex]\\Large\\frac{47}{15}[\/latex]\n
                                                                                                                                                                                                            Show Solution<\/span><\/p>\n
                                                                                                                                                                                                            [latex]3\\Large\\frac{2}{15}[\/latex]<\/div>\n<\/div>\n<\/li>\n<\/ol>\n

                                                                                                                                                                                                            Write a Mixed Number as an Improper Fraction<\/h3>\n

                                                                                                                                                                                                            In the following exercises, rewrite the mixed number as an improper fraction.<\/p>\n

                                                                                                                                                                                                              \n
                                                                                                                                                                                                            1. [latex]1\\Large\\frac{2}{3}[\/latex]<\/li>\n
                                                                                                                                                                                                            2. [latex]1\\Large\\frac{2}{5}[\/latex]\n
                                                                                                                                                                                                              Show Solution<\/span><\/p>\n
                                                                                                                                                                                                              [latex]\\Large\\frac{7}{5}[\/latex]<\/div>\n<\/div>\n<\/li>\n
                                                                                                                                                                                                            3. [latex]2\\Large\\frac{1}{4}[\/latex]<\/li>\n
                                                                                                                                                                                                            4. [latex]2\\Large\\frac{5}{6}[\/latex]\n
                                                                                                                                                                                                              Show Solution<\/span><\/p>\n
                                                                                                                                                                                                              [latex]\\Large\\frac{17}{6}[\/latex]<\/div>\n<\/div>\n<\/li>\n
                                                                                                                                                                                                            5. [latex]2\\Large\\frac{7}{9}[\/latex]<\/li>\n
                                                                                                                                                                                                            6. [latex]2\\Large\\frac{5}{7}[\/latex]\n
                                                                                                                                                                                                              Show Solution<\/span><\/p>\n
                                                                                                                                                                                                              [latex]\\Large\\frac{19}{7}[\/latex]<\/div>\n<\/div>\n<\/li>\n
                                                                                                                                                                                                            7. [latex]3\\Large\\frac{4}{7}[\/latex]<\/li>\n
                                                                                                                                                                                                            8. [latex]3\\Large\\frac{5}{9}[\/latex]\n
                                                                                                                                                                                                              Show Solution<\/span><\/p>\n
                                                                                                                                                                                                              [latex]\\Large\\frac{32}{9}[\/latex]<\/div>\n<\/div>\n<\/li>\n<\/ol>\n

                                                                                                                                                                                                              Modeling and Finding Equivalent Fractions<\/h2>\n

                                                                                                                                                                                                              Modeling Equivalent Fractions<\/h3>\n

                                                                                                                                                                                                              In the following exercises, use fraction tiles or draw a figure to find equivalent fractions.<\/p>\n

                                                                                                                                                                                                                \n
                                                                                                                                                                                                              1. How many sixths equal one-third?<\/li>\n
                                                                                                                                                                                                              2. How many twelfths equal one-third?\n
                                                                                                                                                                                                                Show Solution<\/span><\/p>\n
                                                                                                                                                                                                                4<\/div>\n<\/div>\n<\/li>\n
                                                                                                                                                                                                              3. How many eighths equal three-fourths?<\/li>\n
                                                                                                                                                                                                              4. How many twelfths equal three-fourths?\n
                                                                                                                                                                                                                Show Solution<\/span><\/p>\n
                                                                                                                                                                                                                9<\/div>\n<\/div>\n<\/li>\n
                                                                                                                                                                                                              5. How many fourths equal three-halves?<\/li>\n
                                                                                                                                                                                                              6. How many sixths equal three-halves?\n
                                                                                                                                                                                                                Show Solution<\/span><\/p>\n
                                                                                                                                                                                                                9<\/div>\n<\/div>\n<\/li>\n<\/ol>\n

                                                                                                                                                                                                                Finding Equivalent Fractions<\/h3>\n

                                                                                                                                                                                                                In the following exercises, find three fractions equivalent to the given fraction. Show your work, using figures or algebra.<\/p>\n

                                                                                                                                                                                                                  \n
                                                                                                                                                                                                                1. [latex]\\Large\\frac{1}{4}[\/latex]<\/li>\n
                                                                                                                                                                                                                2. [latex]\\Large\\frac{1}{3}[\/latex]\n
                                                                                                                                                                                                                  Show Solution<\/span><\/p>\n
                                                                                                                                                                                                                  Answers may vary. Correct answers include [latex]\\Large\\frac{2}{6},\\Large\\frac{3}{9},\\Large\\frac{4}{12}[\/latex].<\/div>\n<\/div>\n<\/li>\n
                                                                                                                                                                                                                3. [latex]\\Large\\frac{3}{8}[\/latex]<\/li>\n
                                                                                                                                                                                                                4. [latex]\\Large\\frac{5}{6}[\/latex]\n
                                                                                                                                                                                                                  Show Solution<\/span><\/p>\n
                                                                                                                                                                                                                  Answers may vary. Correct answers include [latex]\\Large\\frac{10}{12},\\Large\\frac{15}{18},\\Large\\frac{20}{24}[\/latex].<\/div>\n<\/div>\n<\/li>\n
                                                                                                                                                                                                                5. [latex]\\Large\\frac{2}{7}[\/latex]<\/li>\n
                                                                                                                                                                                                                6. [latex]\\Large\\frac{5}{9}[\/latex]\n
                                                                                                                                                                                                                  Show Solution<\/span><\/p>\n
                                                                                                                                                                                                                  Answers may vary. Correct answers include [latex]\\Large\\frac{10}{18},\\Large\\frac{15}{27},\\Large\\frac{20}{36}[\/latex].<\/div>\n<\/div>\n<\/li>\n<\/ol>\n

                                                                                                                                                                                                                  Locating and Ordering Fractions and Mixed Numbers on the Number Line<\/h2>\n

                                                                                                                                                                                                                  Locating Fractions on the Number Line<\/h3>\n

                                                                                                                                                                                                                  In the following exercises, plot the numbers on a number line.<\/p>\n

                                                                                                                                                                                                                    \n
                                                                                                                                                                                                                  1. [latex]\\Large\\frac{2}{3},\\Large\\frac{5}{4},\\Large\\frac{12}{5}[\/latex]<\/li>\n
                                                                                                                                                                                                                  2. [latex]\\Large\\frac{1}{3},\\Large\\frac{7}{4},\\Large\\frac{13}{5}[\/latex]\n
                                                                                                                                                                                                                    Show Solution<\/span><\/p>\n
                                                                                                                                                                                                                    \"A<\/div>\n<\/div>\n<\/li>\n
                                                                                                                                                                                                                  3. [latex]\\Large\\frac{1}{4},\\Large\\frac{9}{5},\\Large\\frac{11}{3}[\/latex]<\/li>\n
                                                                                                                                                                                                                  4. [latex]\\Large\\frac{7}{10},\\Large\\frac{5}{2},\\Large\\frac{13}{8},\\normalsize 3[\/latex]\n
                                                                                                                                                                                                                    Show Solution<\/span><\/p>\n
                                                                                                                                                                                                                    \"A<\/div>\n<\/div>\n<\/li>\n
                                                                                                                                                                                                                  5. [latex]2\\Large\\frac{1}{3}\\normalsize ,-2\\Large\\frac{1}{3}[\/latex]<\/li>\n
                                                                                                                                                                                                                  6. [latex]1\\Large\\frac{3}{4}\\normalsize ,-1\\Large\\frac{3}{5}[\/latex]\n
                                                                                                                                                                                                                    Show Solution<\/span><\/p>\n
                                                                                                                                                                                                                    \"A<\/div>\n<\/div>\n<\/li>\n
                                                                                                                                                                                                                  7. [latex]\\Large\\frac{3}{4},-\\Large\\frac{3}{4}\\normalsize ,1\\Large\\frac{2}{3}\\normalsize ,-1\\Large\\frac{2}{3},\\Large\\frac{5}{2},-\\Large\\frac{5}{2}[\/latex]<\/li>\n
                                                                                                                                                                                                                  8. [latex]\\Large\\frac{2}{5},-\\Large\\frac{2}{5}\\normalsize ,1\\Large\\frac{3}{4}\\normalsize ,-1\\Large\\frac{3}{4},\\Large\\frac{8}{3},-\\Large\\frac{8}{3}[\/latex]\n
                                                                                                                                                                                                                    Show Solution<\/span><\/p>\n
                                                                                                                                                                                                                    \"A<\/div>\n<\/div>\n<\/li>\n<\/ol>\n

                                                                                                                                                                                                                    Ordering Fractions on the Number Line<\/h3>\n

                                                                                                                                                                                                                    In the following exercises, order each of the following pairs of numbers, using [latex]<[\/latex] or [latex]>[\/latex].<\/p>\n

                                                                                                                                                                                                                      \n
                                                                                                                                                                                                                    1. [latex]-1\\text{ __}-\\Large\\frac{1}{4}[\/latex]<\/li>\n
                                                                                                                                                                                                                    2. [latex]-1\\text{ __}-\\Large\\frac{1}{3}[\/latex]\n
                                                                                                                                                                                                                      Show Solution<\/span><\/p>\n
                                                                                                                                                                                                                      <<\/div>\n<\/div>\n<\/li>\n
                                                                                                                                                                                                                    3. [latex]-2\\Large\\frac{1}{2}\\normalsize\\text{ __}-3[\/latex]<\/li>\n
                                                                                                                                                                                                                    4. [latex]-1\\Large\\frac{3}{4}\\normalsize\\text{ __}-2[\/latex]\n
                                                                                                                                                                                                                      Show Solution<\/span><\/p>\n
                                                                                                                                                                                                                      ><\/div>\n<\/div>\n<\/li>\n
                                                                                                                                                                                                                    5. [latex]-\\Large\\frac{5}{12}\\text{ __}-\\Large\\frac{7}{12}[\/latex]<\/li>\n
                                                                                                                                                                                                                    6. [latex]-\\Large\\frac{9}{10}\\text{ __}-\\Large\\frac{3}{10}[\/latex]\n
                                                                                                                                                                                                                      Show Solution<\/span><\/p>\n
                                                                                                                                                                                                                      <<\/div>\n<\/div>\n<\/li>\n
                                                                                                                                                                                                                    7. [latex]-3\\text{ __}-\\Large\\frac{13}{5}[\/latex]<\/li>\n
                                                                                                                                                                                                                    8. [latex]-4\\text{ __}-\\Large\\frac{23}{6}[\/latex]\n
                                                                                                                                                                                                                      Show Solution<\/span><\/p>\n
                                                                                                                                                                                                                      <<\/div>\n<\/div>\n<\/li>\n<\/ol>\n
                                                                                                                                                                                                                      \n

                                                                                                                                                                                                                      Everyday Math<\/h3>\n

                                                                                                                                                                                                                      Music Measures<\/h4>\n

                                                                                                                                                                                                                      A choreographed dance is broken into counts. A [latex]\\Large\\frac{1}{1}[\/latex] count has one step in a count, a [latex]\\Large\\frac{1}{2}[\/latex] count has two steps in a count and a [latex]\\Large\\frac{1}{3}[\/latex] count has three steps in a count. How many steps would be in a [latex]\\Large\\frac{1}{5}[\/latex] count? What type of count has four steps in it?<\/p>\n

                                                                                                                                                                                                                      Music Measures<\/h4>\n

                                                                                                                                                                                                                      Fractions are used often in music. In [latex]\\Large\\frac{4}{4}[\/latex] time, there are four quarter notes in one measure.<\/p>\n

                                                                                                                                                                                                                        \n
                                                                                                                                                                                                                      1. How many measures would eight quarter notes make?\n
                                                                                                                                                                                                                        Show Solution<\/span><\/p>\n
                                                                                                                                                                                                                        2<\/div>\n<\/div>\n<\/li>\n
                                                                                                                                                                                                                      2. The song “Happy Birthday to You” has [latex]24[\/latex] quarter notes. How many measures are there in “Happy Birthday to You?”\n
                                                                                                                                                                                                                        Show Solution<\/span><\/p>\n
                                                                                                                                                                                                                        6<\/div>\n<\/div>\n<\/li>\n<\/ol>\n

                                                                                                                                                                                                                        Baking<\/h4>\n

                                                                                                                                                                                                                        Nina is making five pans of fudge to serve after a music recital. For each pan, she needs [latex]\\Large\\frac{1}{2}[\/latex] cup of walnuts.<\/p>\n

                                                                                                                                                                                                                          \n
                                                                                                                                                                                                                        1. How many cups of walnuts does she need for five pans of fudge?<\/li>\n
                                                                                                                                                                                                                        2. Do you think it is easier to measure this amount when you use an improper fraction or a mixed number? Why?<\/li>\n<\/ol>\n<\/div>\n
                                                                                                                                                                                                                          \n

                                                                                                                                                                                                                          Writing Exercises<\/h3>\n

                                                                                                                                                                                                                          Give an example from your life experience (outside of school) where it was important to understand fractions.<\/p>\n