{"id":9476,"date":"2017-05-02T23:12:19","date_gmt":"2017-05-02T23:12:19","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/prealgebra\/?post_type=chapter&#038;p=9476"},"modified":"2020-09-03T10:46:16","modified_gmt":"2020-09-03T10:46:16","slug":"locating-and-ordering-fractions-and-mixed-numbers-on-the-number-line","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/suny-rockland-developmentalemporium\/chapter\/locating-and-ordering-fractions-and-mixed-numbers-on-the-number-line\/","title":{"raw":"2.1.d - Locating and Ordering Fractions and Mixed Numbers on the Number Line","rendered":"2.1.d &#8211; Locating and Ordering Fractions and Mixed Numbers on the Number Line"},"content":{"raw":"<div class=\"textbox learning-objectives\">\r\n<h3>Learning Outcomes<\/h3>\r\n<ul>\r\n \t<li>Locate fractions and mixed numbers on the number line<\/li>\r\n \t<li>Order fractions and mixed numbers using lists and inequalities<\/li>\r\n<\/ul>\r\n<\/div>\r\nNow we are ready to plot fractions on the number line. This will help us visualize fractions and understand their values.\r\n\r\nLet us locate [latex]{\\dfrac{1}{5}, \\dfrac{4}{5}}, 3, 3{\\dfrac{1}{3}, \\dfrac{7}{4}, \\dfrac{9}{2}}, 5[\/latex], and [latex]{\\dfrac{8}{3}}[\/latex] on the number line.\r\n\r\nWe will start with the whole numbers [latex]3[\/latex] and [latex]5[\/latex] because they are the easiest to plot.\r\n\r\n<img class=\"aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24220803\/CNX_BMath_Figure_04_01_044_img.png\" alt=\"A number line is shown with the numbers 3, 4, and 5. There are red dots at 3 and at 5.\" \/>\r\nThe proper fractions listed are [latex]{\\dfrac{1}{5}}[\/latex] and [latex]{\\dfrac{4}{5}}[\/latex]. We know proper fractions have values less than one, so [latex]{\\dfrac{1}{5}}[\/latex] and [latex]{\\dfrac{4}{5}}[\/latex] are located between the whole numbers [latex]0[\/latex] and [latex]1[\/latex]. The denominators are both [latex]5[\/latex], so we need to divide the segment of the number line between [latex]0[\/latex] and [latex]1[\/latex] into five equal parts. We can do this by drawing four equally spaced marks on the number line, which we can then label as [latex]{\\dfrac{1}{5},\\dfrac{2}{5},\\dfrac{3}{5}}[\/latex], and [latex]{\\dfrac{4}{5}}[\/latex].\r\n\r\nNow plot points at [latex]{\\dfrac{1}{5}}[\/latex] and [latex]{\\dfrac{4}{5}}[\/latex].\r\n\r\n<img class=\"aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24220805\/CNX_BMath_Figure_04_01_045_img.png\" alt=\"A number line is shown. It shows 0, 1 fifth, 2 fifths, 3 fifths, 4 fifths, and 1. There are red dots at 1 fifth and at 4 fifths.\" \/>\r\nThe only mixed number to plot is [latex]3{\\dfrac{1}{3}}[\/latex]. Between what two whole numbers is [latex]3{\\dfrac{1}{3}}[\/latex]? Remember that a mixed number is a whole number plus a proper fraction, so [latex]3{\\dfrac{1}{3}}&gt;3[\/latex]. Since it is greater than [latex]3[\/latex], but not a whole unit greater, [latex]3{\\dfrac{1}{3}}[\/latex] is between [latex]3[\/latex] and [latex]4[\/latex]. We need to divide the portion of the number line between [latex]3[\/latex] and [latex]4[\/latex] into three equal pieces (thirds) and plot [latex]3{\\dfrac{1}{3}}[\/latex] at the first mark.\r\n\r\n<img class=\"aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24220806\/CNX_BMath_Figure_04_01_046_img.png\" alt=\"A number line is shown with whole number 0 through 5. Between 3 and 4, 3 and 1 third and 3 and 2 thirds are labeled. There is a red dot at 3 and 1 third.\" \/>\r\nFinally, look at the improper fractions [latex]{\\dfrac{7}{4},\\dfrac{9}{2}}[\/latex], and [latex]{\\dfrac{8}{3}}[\/latex]. Locating these points will be easier if you change each of them to a mixed number.\r\n<p style=\"text-align: center\">[latex]{\\dfrac{7}{4}}=1{\\dfrac{3}{4}},{\\dfrac{9}{2}}=4{\\dfrac{1}{2}},{\\dfrac{8}{3}}=2{\\dfrac{2}{3}}[\/latex]<\/p>\r\nHere is the number line with all the points plotted.\r\n\r\n<img class=\"aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24220808\/CNX_BMath_Figure_04_01_047_img.png\" alt=\"A number line is shown with whole numbers 0 through 6. Between 0 and 1, 1 fifth and 4 fifths are labeled and shown with red dots. Between 1 and 2, 7 fourths is labeled and shown with a red dot. Between 2 and 3, 8 thirds is labeled and shown with a red dot. Between 3 and 4, 3 and 1 third is labeled and shown with a red dot. Between 4 and 5, 9 halves is labeled and shown with a red dot.\" \/>\r\n<div class=\"textbox exercises\">\r\n<h3>Example<\/h3>\r\nLocate and label the following on a number line: [latex]{\\dfrac{3}{4},\\dfrac{4}{3},\\dfrac{5}{3}},4{\\dfrac{1}{5}}[\/latex], and [latex]{\\dfrac{7}{2}}[\/latex].\r\n\r\nSolution:\r\nStart by locating the proper fraction [latex]{\\dfrac{3}{4}}[\/latex]. It is between [latex]0[\/latex] and [latex]1[\/latex]. To do this, divide the distance between [latex]0[\/latex] and [latex]1[\/latex] into four equal parts. Then plot [latex]{\\dfrac{3}{4}}[\/latex].\r\n\r\n<img class=\"aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24220810\/CNX_BMath_Figure_04_01_048_img.png\" alt=\"A number line is shown. It shows 0, 1 fourth, 2 fourths, 3 fourths, and 1. There is a red dot at 3 fourths.\" \/>\r\nNext, locate the mixed number [latex]4{\\dfrac{1}{5}}[\/latex]. It is between [latex]4[\/latex] and [latex]5[\/latex] on the number line. Divide the number line between [latex]4[\/latex] and [latex]5[\/latex] into five equal parts, and then plot [latex]4{\\dfrac{1}{5}}[\/latex] one-fifth of the way between [latex]4[\/latex] and [latex]5[\/latex] .\r\n\r\n<img class=\"aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24220811\/CNX_BMath_Figure_04_01_049_img.png\" alt=\"A number line is shown. It shows 4, 4 and 1 fifth, 4 and 2 fifths, 4 and 3 fifths, 4 and 4 fifths, and 5. There is a red dot at 4 and 1 fifth.\" \/>\r\nNow locate the improper fractions [latex]{\\dfrac{4}{3}}[\/latex] and [latex]{\\dfrac{5}{3}}[\/latex]. It is easier to plot them if we convert them to mixed numbers first.\r\n\r\n[latex]{\\dfrac{4}{3}}=1{\\dfrac{1}{3}},{\\dfrac{5}{3}}=1{\\dfrac{2}{3}}[\/latex]\r\nDivide the distance between [latex]1[\/latex] and [latex]2[\/latex] into thirds.\r\n\r\n<img class=\"aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24220813\/CNX_BMath_Figure_04_01_050_img.png\" alt=\"A number line is shown. It shows 1, 1 and 1 third, 1 and 2 thirds, and 2. Below 1 it says 3 thirds. Below 1 and 1 third it says 4 thirds. Below 1 and 2 thirds it says 5 thirds. Below 2 it says 6 thirds. There are red dots at 1 and 1 third and 1 and 2 thirds.\" \/>\r\nNext let us plot [latex]{\\dfrac{7}{2}}[\/latex]. We write it as a mixed number, [latex]{\\dfrac{7}{2}}=3{\\dfrac{1}{2}}[\/latex] . Plot it between [latex]3[\/latex] and [latex]4[\/latex].\r\n\r\n<img class=\"aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24220815\/CNX_BMath_Figure_04_01_051_img.png\" alt=\"A number line is shown. It shows 3, 3 and 1 half, and 4. Below 3 it says 6 halves. Below 3 and 1 half it says 7 halves. Below 4 it says 8 halves. There is a red dot at 3 and 1 half.\" \/>\r\nThe number line shows all the numbers located on the number line.\r\n\r\n<img class=\"aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24220817\/CNX_BMath_Figure_04_01_052.png\" alt=\"A number line is shown. It shows the whole numbers 0 through 5. Between any 2 numbers are 10 tick marks. Between 0 and 1, between the 7th and 8th tick mark, 3 fourths is labeled and shown with a red dot. Between 1 and 2, 4 thirds and 5 thirds are labeled and shown with red dots. Between 3 and 4, 7 halves is labeled and shown with a red dot. Between 4 and 5, 4 and 1 fifth is labeled and shown with a red dot.\" \/>\r\n\r\n<\/div>\r\n&nbsp;\r\n<div class=\"textbox key-takeaways\">\r\n<h3>try it<\/h3>\r\n[ohm_question height=\"270\"]146007[\/ohm_question]\r\n\r\n[ohm_question height=\"270\"]146008[\/ohm_question]\r\n\r\n<\/div>\r\nWatch the following video to see more examples of how to locate fractions on a number line.\r\n\r\nhttps:\/\/youtu.be\/EIdmdTRQWTE\r\n\r\n<a href=\"https:\/\/courses.lumenlearning.com\/wm-developmentalemporium\/chapter\/notation-and-definition-of-the-set-of-integers\/\">We previously defined the opposite of a number<\/a>. It is the number that is the same distance from zero on the number line but on the opposite side of zero. We saw, for example, that the opposite of [latex]7[\/latex] is [latex]-7[\/latex] and the opposite of [latex]-7[\/latex] is [latex]7[\/latex].\r\n\r\n<img class=\"aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24220821\/CNX_BMath_Figure_04_01_055_img.png\" alt=\"A number line is shown. It shows the numbers negative 7, 0 and 7. There are red dots at negative 7 and 7. The space between negative 7 and 0 is labeled as 7 units. The space between 0 and 7 is labeled as 7 units.\" \/>\r\nFractions have opposites, too. The opposite of [latex]{\\dfrac{3}{4}}[\/latex] is [latex]-{\\dfrac{3}{4}}[\/latex]. It is the same distance from [latex]0[\/latex] on the number line, but on the opposite side of [latex]0[\/latex].\r\n\r\n<img class=\"aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24220822\/CNX_BMath_Figure_04_01_056_img.png\" alt=\"A number line is shown. It shows the numbers negative 1, negative 3 fourths, 0, 3 fourths, and 1. There are red dots at negative 3 fourths and 3 fourths. The space between negative 3 fourths and 0 is labeled as 3 fourths of a unit. The space between 0 and 3 fourths is labeled as 3 fourths of a unit.\" \/>\r\nThinking of negative fractions as the opposite of positive fractions will help us locate them on the number line. To locate [latex]-{\\dfrac{15}{8}}[\/latex] on the number line, first think of where [latex]{\\dfrac{15}{8}}[\/latex] is located. It is an improper fraction, so we first convert it to the mixed number [latex]1{\\dfrac{7}{8}}[\/latex] and see that it will be between [latex]1[\/latex] and [latex]2[\/latex] on the number line. So its opposite, [latex]-{\\dfrac{15}{8}}[\/latex], will be between [latex]-1[\/latex] and [latex]-2[\/latex] on the number line.\r\n\r\n<img class=\"aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24220824\/CNX_BMath_Figure_04_01_057_img.png\" alt=\"A number line is shown. It shows the numbers negative 2, negative 1, 0, 1, and 2. Between negative 2 and negative 1, negative 1 and 7 eighths is labeled and marked with a red dot. The distance between negative 1 and 7 eighths and 0 is marked as 15 eighths units. Between 1 and 2, 1 and 7 eighths is labeled and marked with a red dot. The distance between 0 and 1 and 7 eighths is marked as 15 eighths units.\" \/>\r\n<div class=\"textbox exercises\">\r\n<h3>Example<\/h3>\r\nLocate and label the following on the number line: [latex]{\\dfrac{1}{4}},-{\\dfrac{1}{4}},1{\\dfrac{1}{3}},-1{\\dfrac{1}{3}},{\\dfrac{5}{2}}[\/latex], and [latex]-{\\dfrac{5}{2}}[\/latex].\r\n[reveal-answer q=\"402611\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"402611\"]\r\n\r\nSolution:\r\nDraw a number line. Mark [latex]0[\/latex] in the middle and then mark several units to the left and right.\r\n\r\nTo locate [latex]{\\dfrac{1}{4}}[\/latex], divide the interval between [latex]0[\/latex] and [latex]1[\/latex] into four equal parts. Each part represents one-quarter of the distance. So plot [latex]{\\dfrac{1}{4}}[\/latex] at the first mark.\r\n\r\n<img class=\"aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24220826\/CNX_BMath_Figure_04_01_058_img.png\" alt=\"A number line is shown. It shows the numbers negative 4, negative 3, negative 2, negative 1, 0, 1, 2, 3, and 4. There are 4 tick marks between negative 1 and 0. There are 4 tick marks between 0 and 1. The first tick mark between 0 and 1 is labeled as 1 fourth and marked with a red dot.\" \/>\r\nTo locate [latex]-{\\dfrac{1}{4}}[\/latex], divide the interval between [latex]0[\/latex] and [latex]-1[\/latex] into four equal parts. Plot [latex]-{\\dfrac{1}{4}}[\/latex] at the first mark to the left of [latex]0[\/latex].\r\n\r\n<img class=\"aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24220827\/CNX_BMath_Figure_04_01_059_img.png\" alt=\"A number line is shown. It shows the numbers negative 4, negative 3, negative 2, negative 1, 0, 1, 2, 3, and 4. There are 4 tick marks between negative 1 and 0. There are 4 tick marks between 0 and 1. The first tick mark between 0 and 1 is labeled as 1 fourth and marked with a red dot. The first tick mark between 0 and negative 1 is labeled as negative 1 fourth and marked with a red dot.\" \/>\r\nSince [latex]1{\\dfrac{1}{3}}[\/latex] is between [latex]1[\/latex] and [latex]2[\/latex], divide the interval between [latex]1[\/latex] and [latex]2[\/latex] into three equal parts. Plot [latex]1{\\dfrac{1}{3}}[\/latex] at the first mark to the right of [latex]1[\/latex]. Then since [latex]-1{\\dfrac{1}{3}}[\/latex] is the opposite of [latex]1{\\dfrac{1}{3}}[\/latex] it is between [latex]-1[\/latex] and [latex]-2[\/latex]. Divide the interval between [latex]-1[\/latex] and [latex]-2[\/latex] into three equal parts. Plot [latex]-1{\\dfrac{1}{3}}[\/latex] at the first mark to the left of [latex]-1[\/latex].\r\n\r\n<img class=\"aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24220829\/CNX_BMath_Figure_04_01_060.png\" alt=\"A number line is shown. The integers from negative 2 to 2 are labeled. Between negative 2 and negative 1, negative 1 and 1 third is labeled and marked with a red dot. Between 1 and 2, 1 and 1 third is labeled and marked with a red dot.\" \/>\r\nTo locate [latex]{\\dfrac{5}{2}}[\/latex] and [latex]-{\\dfrac{5}{2}}[\/latex], it may be helpful to rewrite them as the mixed numbers [latex]2{\\dfrac{1}{2}}[\/latex] and [latex]-2{\\dfrac{1}{2}}[\/latex].\r\n\r\nSince [latex]2{\\dfrac{1}{2}}[\/latex] is between [latex]2[\/latex] and [latex]3[\/latex], divide the interval between [latex]2[\/latex] and [latex]3[\/latex] into two equal parts. Plot [latex]{\\dfrac{5}{2}}[\/latex] at the mark. Then since [latex]-2{\\dfrac{1}{2}}[\/latex] is between [latex]-2[\/latex] and [latex]-3[\/latex], divide the interval between [latex]-2[\/latex] and [latex]-3[\/latex] into two equal parts. Plot [latex]-{\\dfrac{5}{2}}[\/latex] at the mark.\r\n\r\n<img class=\"aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24220831\/CNX_BMath_Figure_04_01_061.png\" alt=\"A number line is shown. The integers from negative 4 to 4 are labeled. Between negative 3 and negative 2, negative 5 halves is labeled and marked with a red dot. Between 2 and 3, 5 halves is labeled and marked with a red dot.\" \/>\r\n\r\n[\/hidden-answer]\r\n\r\n<\/div>\r\n&nbsp;\r\n<div class=\"textbox key-takeaways\">\r\n<h3>Try it<\/h3>\r\n[ohm_question height=\"270\"]146009[\/ohm_question]\r\n\r\n[ohm_question height=\"270\"]146011[\/ohm_question]\r\n\r\n<\/div>\r\nIn the next video we give more examples of how to locate negative and positive fractions on a number line.\r\n\r\nhttps:\/\/youtu.be\/nbSlAAZVQV4\r\n<h2>Order Fractions and Mixed Numbers<\/h2>\r\nWe can use the inequality symbols to order fractions. Remember that [latex]a&gt;b[\/latex] means that [latex]a[\/latex] is to the right of [latex]b[\/latex] on the number line. As we move from left to right on a number line, the values increase.\r\n<div class=\"textbox exercises\">\r\n<h3>Example<\/h3>\r\nOrder each of the following pairs of numbers, using [latex]&amp;lt[\/latex]; or [latex]&gt;:[\/latex]\r\n<ol>\r\n \t<li>[latex]-{\\dfrac{2}{3}}[\/latex] ____ [latex]- 1[\/latex]<\/li>\r\n \t<li>[latex]-3{\\dfrac{1}{2}}[\/latex] ____ [latex]- 3[\/latex]<\/li>\r\n \t<li>[latex]-{\\dfrac{3}{7}}[\/latex] ____ [latex]{\\dfrac{3}{8}}[\/latex]<\/li>\r\n \t<li>[latex]-2[\/latex] ____ [latex]{\\dfrac{-16}{9}}[\/latex]<\/li>\r\n<\/ol>\r\n[reveal-answer q=\"676284\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"676284\"]\r\n\r\nSolution:\r\n\r\n1. [latex]-{\\dfrac{2}{3}}&gt;-1[\/latex]\r\n\r\n<img src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24220835\/CNX_BMath_Figure_04_01_064_img.png\" alt=\"A number line is shown. The integers from negative 3 to 3 are labeled. Negative 1 is marked with a red dot. Between negative 1 and 0, negative 2 thirds is labeled and marked with a red dot.\" \/>\r\n\r\n2. [latex]-3{\\dfrac{1}{2}}&lt;-3[\/latex]\r\n\r\n<img src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24220837\/CNX_BMath_Figure_04_01_065_img.png\" alt=\"A number line is shown. The integers from negative 4 to 4 are labeled. There is a red dot at negative 3. Between negative 4 and negative 3, negative 3 and one half is labeled and marked with a red dot.\" \/>\r\n\r\n3. [latex]-{\\dfrac{3}{7}}&lt;-{\\dfrac{3}{8}}[\/latex]\r\n\r\n<img src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24220838\/CNX_BMath_Figure_04_01_066_img.png\" alt=\"A number line is shown. The numbers negative 3, negative 2, negative 1, 0, 1, 2, and 3 are labeled. Between negative 1 and 0, negative 3 sevenths and negative 3 eighths are labeled and marked with red dots.\" \/>\r\n\r\n4. [latex]-2&lt;{\\dfrac{-16}{9}}[\/latex]\r\n\r\n<img src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24220840\/CNX_BMath_Figure_04_01_067_img.png\" alt=\"A number line is shown. The numbers negative 3, negative 2, negative 1, 0, 1, 2, and 3 are labeled. There is a red dot at negative 2. Between negative 2 and negative 1, negative 16 over 9 is labeled and marked with a red dot.\" \/>\r\n\r\n[\/hidden-answer]\r\n\r\n<\/div>\r\n&nbsp;\r\n<div class=\"textbox key-takeaways\">\r\n<h3>Try it<\/h3>\r\n[ohm_question height=\"270\"]146013[\/ohm_question]\r\n\r\n[ohm_question height=\"270\"]146012[\/ohm_question]\r\n\r\n<\/div>\r\nIn the following video we show another example of how to order integers, fractions and mixed numbers using inequality symbols.\r\n\r\nhttps:\/\/youtu.be\/Phsf_fJgerc","rendered":"<div class=\"textbox learning-objectives\">\n<h3>Learning Outcomes<\/h3>\n<ul>\n<li>Locate fractions and mixed numbers on the number line<\/li>\n<li>Order fractions and mixed numbers using lists and inequalities<\/li>\n<\/ul>\n<\/div>\n<p>Now we are ready to plot fractions on the number line. This will help us visualize fractions and understand their values.<\/p>\n<p>Let us locate [latex]{\\dfrac{1}{5}, \\dfrac{4}{5}}, 3, 3{\\dfrac{1}{3}, \\dfrac{7}{4}, \\dfrac{9}{2}}, 5[\/latex], and [latex]{\\dfrac{8}{3}}[\/latex] on the number line.<\/p>\n<p>We will start with the whole numbers [latex]3[\/latex] and [latex]5[\/latex] because they are the easiest to plot.<\/p>\n<p><img decoding=\"async\" class=\"aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24220803\/CNX_BMath_Figure_04_01_044_img.png\" alt=\"A number line is shown with the numbers 3, 4, and 5. There are red dots at 3 and at 5.\" \/><br \/>\nThe proper fractions listed are [latex]{\\dfrac{1}{5}}[\/latex] and [latex]{\\dfrac{4}{5}}[\/latex]. We know proper fractions have values less than one, so [latex]{\\dfrac{1}{5}}[\/latex] and [latex]{\\dfrac{4}{5}}[\/latex] are located between the whole numbers [latex]0[\/latex] and [latex]1[\/latex]. The denominators are both [latex]5[\/latex], so we need to divide the segment of the number line between [latex]0[\/latex] and [latex]1[\/latex] into five equal parts. We can do this by drawing four equally spaced marks on the number line, which we can then label as [latex]{\\dfrac{1}{5},\\dfrac{2}{5},\\dfrac{3}{5}}[\/latex], and [latex]{\\dfrac{4}{5}}[\/latex].<\/p>\n<p>Now plot points at [latex]{\\dfrac{1}{5}}[\/latex] and [latex]{\\dfrac{4}{5}}[\/latex].<\/p>\n<p><img decoding=\"async\" class=\"aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24220805\/CNX_BMath_Figure_04_01_045_img.png\" alt=\"A number line is shown. It shows 0, 1 fifth, 2 fifths, 3 fifths, 4 fifths, and 1. There are red dots at 1 fifth and at 4 fifths.\" \/><br \/>\nThe only mixed number to plot is [latex]3{\\dfrac{1}{3}}[\/latex]. Between what two whole numbers is [latex]3{\\dfrac{1}{3}}[\/latex]? Remember that a mixed number is a whole number plus a proper fraction, so [latex]3{\\dfrac{1}{3}}>3[\/latex]. Since it is greater than [latex]3[\/latex], but not a whole unit greater, [latex]3{\\dfrac{1}{3}}[\/latex] is between [latex]3[\/latex] and [latex]4[\/latex]. We need to divide the portion of the number line between [latex]3[\/latex] and [latex]4[\/latex] into three equal pieces (thirds) and plot [latex]3{\\dfrac{1}{3}}[\/latex] at the first mark.<\/p>\n<p><img decoding=\"async\" class=\"aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24220806\/CNX_BMath_Figure_04_01_046_img.png\" alt=\"A number line is shown with whole number 0 through 5. Between 3 and 4, 3 and 1 third and 3 and 2 thirds are labeled. There is a red dot at 3 and 1 third.\" \/><br \/>\nFinally, look at the improper fractions [latex]{\\dfrac{7}{4},\\dfrac{9}{2}}[\/latex], and [latex]{\\dfrac{8}{3}}[\/latex]. Locating these points will be easier if you change each of them to a mixed number.<\/p>\n<p style=\"text-align: center\">[latex]{\\dfrac{7}{4}}=1{\\dfrac{3}{4}},{\\dfrac{9}{2}}=4{\\dfrac{1}{2}},{\\dfrac{8}{3}}=2{\\dfrac{2}{3}}[\/latex]<\/p>\n<p>Here is the number line with all the points plotted.<\/p>\n<p><img decoding=\"async\" class=\"aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24220808\/CNX_BMath_Figure_04_01_047_img.png\" alt=\"A number line is shown with whole numbers 0 through 6. Between 0 and 1, 1 fifth and 4 fifths are labeled and shown with red dots. Between 1 and 2, 7 fourths is labeled and shown with a red dot. Between 2 and 3, 8 thirds is labeled and shown with a red dot. Between 3 and 4, 3 and 1 third is labeled and shown with a red dot. Between 4 and 5, 9 halves is labeled and shown with a red dot.\" \/><\/p>\n<div class=\"textbox exercises\">\n<h3>Example<\/h3>\n<p>Locate and label the following on a number line: [latex]{\\dfrac{3}{4},\\dfrac{4}{3},\\dfrac{5}{3}},4{\\dfrac{1}{5}}[\/latex], and [latex]{\\dfrac{7}{2}}[\/latex].<\/p>\n<p>Solution:<br \/>\nStart by locating the proper fraction [latex]{\\dfrac{3}{4}}[\/latex]. It is between [latex]0[\/latex] and [latex]1[\/latex]. To do this, divide the distance between [latex]0[\/latex] and [latex]1[\/latex] into four equal parts. Then plot [latex]{\\dfrac{3}{4}}[\/latex].<\/p>\n<p><img decoding=\"async\" class=\"aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24220810\/CNX_BMath_Figure_04_01_048_img.png\" alt=\"A number line is shown. It shows 0, 1 fourth, 2 fourths, 3 fourths, and 1. There is a red dot at 3 fourths.\" \/><br \/>\nNext, locate the mixed number [latex]4{\\dfrac{1}{5}}[\/latex]. It is between [latex]4[\/latex] and [latex]5[\/latex] on the number line. Divide the number line between [latex]4[\/latex] and [latex]5[\/latex] into five equal parts, and then plot [latex]4{\\dfrac{1}{5}}[\/latex] one-fifth of the way between [latex]4[\/latex] and [latex]5[\/latex] .<\/p>\n<p><img decoding=\"async\" class=\"aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24220811\/CNX_BMath_Figure_04_01_049_img.png\" alt=\"A number line is shown. It shows 4, 4 and 1 fifth, 4 and 2 fifths, 4 and 3 fifths, 4 and 4 fifths, and 5. There is a red dot at 4 and 1 fifth.\" \/><br \/>\nNow locate the improper fractions [latex]{\\dfrac{4}{3}}[\/latex] and [latex]{\\dfrac{5}{3}}[\/latex]. It is easier to plot them if we convert them to mixed numbers first.<\/p>\n<p>[latex]{\\dfrac{4}{3}}=1{\\dfrac{1}{3}},{\\dfrac{5}{3}}=1{\\dfrac{2}{3}}[\/latex]<br \/>\nDivide the distance between [latex]1[\/latex] and [latex]2[\/latex] into thirds.<\/p>\n<p><img decoding=\"async\" class=\"aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24220813\/CNX_BMath_Figure_04_01_050_img.png\" alt=\"A number line is shown. It shows 1, 1 and 1 third, 1 and 2 thirds, and 2. Below 1 it says 3 thirds. Below 1 and 1 third it says 4 thirds. Below 1 and 2 thirds it says 5 thirds. Below 2 it says 6 thirds. There are red dots at 1 and 1 third and 1 and 2 thirds.\" \/><br \/>\nNext let us plot [latex]{\\dfrac{7}{2}}[\/latex]. We write it as a mixed number, [latex]{\\dfrac{7}{2}}=3{\\dfrac{1}{2}}[\/latex] . Plot it between [latex]3[\/latex] and [latex]4[\/latex].<\/p>\n<p><img decoding=\"async\" class=\"aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24220815\/CNX_BMath_Figure_04_01_051_img.png\" alt=\"A number line is shown. It shows 3, 3 and 1 half, and 4. Below 3 it says 6 halves. Below 3 and 1 half it says 7 halves. Below 4 it says 8 halves. There is a red dot at 3 and 1 half.\" \/><br \/>\nThe number line shows all the numbers located on the number line.<\/p>\n<p><img decoding=\"async\" class=\"aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24220817\/CNX_BMath_Figure_04_01_052.png\" alt=\"A number line is shown. It shows the whole numbers 0 through 5. Between any 2 numbers are 10 tick marks. Between 0 and 1, between the 7th and 8th tick mark, 3 fourths is labeled and shown with a red dot. Between 1 and 2, 4 thirds and 5 thirds are labeled and shown with red dots. Between 3 and 4, 7 halves is labeled and shown with a red dot. Between 4 and 5, 4 and 1 fifth is labeled and shown with a red dot.\" \/><\/p>\n<\/div>\n<p>&nbsp;<\/p>\n<div class=\"textbox key-takeaways\">\n<h3>try it<\/h3>\n<p><iframe loading=\"lazy\" id=\"ohm146007\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=146007&theme=oea&iframe_resize_id=ohm146007&show_question_numbers\" width=\"100%\" height=\"270\"><\/iframe><\/p>\n<p><iframe loading=\"lazy\" id=\"ohm146008\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=146008&theme=oea&iframe_resize_id=ohm146008&show_question_numbers\" width=\"100%\" height=\"270\"><\/iframe><\/p>\n<\/div>\n<p>Watch the following video to see more examples of how to locate fractions on a number line.<\/p>\n<p><iframe loading=\"lazy\" id=\"oembed-1\" title=\"Ex:  Identify a Fraction on a Number Line\" width=\"500\" height=\"281\" src=\"https:\/\/www.youtube.com\/embed\/EIdmdTRQWTE?feature=oembed&#38;rel=0\" frameborder=\"0\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/p>\n<p><a href=\"https:\/\/courses.lumenlearning.com\/wm-developmentalemporium\/chapter\/notation-and-definition-of-the-set-of-integers\/\">We previously defined the opposite of a number<\/a>. It is the number that is the same distance from zero on the number line but on the opposite side of zero. We saw, for example, that the opposite of [latex]7[\/latex] is [latex]-7[\/latex] and the opposite of [latex]-7[\/latex] is [latex]7[\/latex].<\/p>\n<p><img decoding=\"async\" class=\"aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24220821\/CNX_BMath_Figure_04_01_055_img.png\" alt=\"A number line is shown. It shows the numbers negative 7, 0 and 7. There are red dots at negative 7 and 7. The space between negative 7 and 0 is labeled as 7 units. The space between 0 and 7 is labeled as 7 units.\" \/><br \/>\nFractions have opposites, too. The opposite of [latex]{\\dfrac{3}{4}}[\/latex] is [latex]-{\\dfrac{3}{4}}[\/latex]. It is the same distance from [latex]0[\/latex] on the number line, but on the opposite side of [latex]0[\/latex].<\/p>\n<p><img decoding=\"async\" class=\"aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24220822\/CNX_BMath_Figure_04_01_056_img.png\" alt=\"A number line is shown. It shows the numbers negative 1, negative 3 fourths, 0, 3 fourths, and 1. There are red dots at negative 3 fourths and 3 fourths. The space between negative 3 fourths and 0 is labeled as 3 fourths of a unit. The space between 0 and 3 fourths is labeled as 3 fourths of a unit.\" \/><br \/>\nThinking of negative fractions as the opposite of positive fractions will help us locate them on the number line. To locate [latex]-{\\dfrac{15}{8}}[\/latex] on the number line, first think of where [latex]{\\dfrac{15}{8}}[\/latex] is located. It is an improper fraction, so we first convert it to the mixed number [latex]1{\\dfrac{7}{8}}[\/latex] and see that it will be between [latex]1[\/latex] and [latex]2[\/latex] on the number line. So its opposite, [latex]-{\\dfrac{15}{8}}[\/latex], will be between [latex]-1[\/latex] and [latex]-2[\/latex] on the number line.<\/p>\n<p><img decoding=\"async\" class=\"aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24220824\/CNX_BMath_Figure_04_01_057_img.png\" alt=\"A number line is shown. It shows the numbers negative 2, negative 1, 0, 1, and 2. Between negative 2 and negative 1, negative 1 and 7 eighths is labeled and marked with a red dot. The distance between negative 1 and 7 eighths and 0 is marked as 15 eighths units. Between 1 and 2, 1 and 7 eighths is labeled and marked with a red dot. The distance between 0 and 1 and 7 eighths is marked as 15 eighths units.\" \/><\/p>\n<div class=\"textbox exercises\">\n<h3>Example<\/h3>\n<p>Locate and label the following on the number line: [latex]{\\dfrac{1}{4}},-{\\dfrac{1}{4}},1{\\dfrac{1}{3}},-1{\\dfrac{1}{3}},{\\dfrac{5}{2}}[\/latex], and [latex]-{\\dfrac{5}{2}}[\/latex].<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q402611\">Show Solution<\/span><\/p>\n<div id=\"q402611\" class=\"hidden-answer\" style=\"display: none\">\n<p>Solution:<br \/>\nDraw a number line. Mark [latex]0[\/latex] in the middle and then mark several units to the left and right.<\/p>\n<p>To locate [latex]{\\dfrac{1}{4}}[\/latex], divide the interval between [latex]0[\/latex] and [latex]1[\/latex] into four equal parts. Each part represents one-quarter of the distance. So plot [latex]{\\dfrac{1}{4}}[\/latex] at the first mark.<\/p>\n<p><img decoding=\"async\" class=\"aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24220826\/CNX_BMath_Figure_04_01_058_img.png\" alt=\"A number line is shown. It shows the numbers negative 4, negative 3, negative 2, negative 1, 0, 1, 2, 3, and 4. There are 4 tick marks between negative 1 and 0. There are 4 tick marks between 0 and 1. The first tick mark between 0 and 1 is labeled as 1 fourth and marked with a red dot.\" \/><br \/>\nTo locate [latex]-{\\dfrac{1}{4}}[\/latex], divide the interval between [latex]0[\/latex] and [latex]-1[\/latex] into four equal parts. Plot [latex]-{\\dfrac{1}{4}}[\/latex] at the first mark to the left of [latex]0[\/latex].<\/p>\n<p><img decoding=\"async\" class=\"aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24220827\/CNX_BMath_Figure_04_01_059_img.png\" alt=\"A number line is shown. It shows the numbers negative 4, negative 3, negative 2, negative 1, 0, 1, 2, 3, and 4. There are 4 tick marks between negative 1 and 0. There are 4 tick marks between 0 and 1. The first tick mark between 0 and 1 is labeled as 1 fourth and marked with a red dot. The first tick mark between 0 and negative 1 is labeled as negative 1 fourth and marked with a red dot.\" \/><br \/>\nSince [latex]1{\\dfrac{1}{3}}[\/latex] is between [latex]1[\/latex] and [latex]2[\/latex], divide the interval between [latex]1[\/latex] and [latex]2[\/latex] into three equal parts. Plot [latex]1{\\dfrac{1}{3}}[\/latex] at the first mark to the right of [latex]1[\/latex]. Then since [latex]-1{\\dfrac{1}{3}}[\/latex] is the opposite of [latex]1{\\dfrac{1}{3}}[\/latex] it is between [latex]-1[\/latex] and [latex]-2[\/latex]. Divide the interval between [latex]-1[\/latex] and [latex]-2[\/latex] into three equal parts. Plot [latex]-1{\\dfrac{1}{3}}[\/latex] at the first mark to the left of [latex]-1[\/latex].<\/p>\n<p><img decoding=\"async\" class=\"aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24220829\/CNX_BMath_Figure_04_01_060.png\" alt=\"A number line is shown. The integers from negative 2 to 2 are labeled. Between negative 2 and negative 1, negative 1 and 1 third is labeled and marked with a red dot. Between 1 and 2, 1 and 1 third is labeled and marked with a red dot.\" \/><br \/>\nTo locate [latex]{\\dfrac{5}{2}}[\/latex] and [latex]-{\\dfrac{5}{2}}[\/latex], it may be helpful to rewrite them as the mixed numbers [latex]2{\\dfrac{1}{2}}[\/latex] and [latex]-2{\\dfrac{1}{2}}[\/latex].<\/p>\n<p>Since [latex]2{\\dfrac{1}{2}}[\/latex] is between [latex]2[\/latex] and [latex]3[\/latex], divide the interval between [latex]2[\/latex] and [latex]3[\/latex] into two equal parts. Plot [latex]{\\dfrac{5}{2}}[\/latex] at the mark. Then since [latex]-2{\\dfrac{1}{2}}[\/latex] is between [latex]-2[\/latex] and [latex]-3[\/latex], divide the interval between [latex]-2[\/latex] and [latex]-3[\/latex] into two equal parts. Plot [latex]-{\\dfrac{5}{2}}[\/latex] at the mark.<\/p>\n<p><img decoding=\"async\" class=\"aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24220831\/CNX_BMath_Figure_04_01_061.png\" alt=\"A number line is shown. The integers from negative 4 to 4 are labeled. Between negative 3 and negative 2, negative 5 halves is labeled and marked with a red dot. Between 2 and 3, 5 halves is labeled and marked with a red dot.\" \/><\/p>\n<\/div>\n<\/div>\n<\/div>\n<p>&nbsp;<\/p>\n<div class=\"textbox key-takeaways\">\n<h3>Try it<\/h3>\n<p><iframe loading=\"lazy\" id=\"ohm146009\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=146009&theme=oea&iframe_resize_id=ohm146009&show_question_numbers\" width=\"100%\" height=\"270\"><\/iframe><\/p>\n<p><iframe loading=\"lazy\" id=\"ohm146011\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=146011&theme=oea&iframe_resize_id=ohm146011&show_question_numbers\" width=\"100%\" height=\"270\"><\/iframe><\/p>\n<\/div>\n<p>In the next video we give more examples of how to locate negative and positive fractions on a number line.<\/p>\n<p><iframe loading=\"lazy\" id=\"oembed-2\" title=\"Determine Negative Proper and Improper Fractions on the Number Line\" width=\"500\" height=\"281\" src=\"https:\/\/www.youtube.com\/embed\/nbSlAAZVQV4?feature=oembed&#38;rel=0\" frameborder=\"0\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/p>\n<h2>Order Fractions and Mixed Numbers<\/h2>\n<p>We can use the inequality symbols to order fractions. Remember that [latex]a>b[\/latex] means that [latex]a[\/latex] is to the right of [latex]b[\/latex] on the number line. As we move from left to right on a number line, the values increase.<\/p>\n<div class=\"textbox exercises\">\n<h3>Example<\/h3>\n<p>Order each of the following pairs of numbers, using [latex]&lt[\/latex]; or [latex]>:[\/latex]<\/p>\n<ol>\n<li>[latex]-{\\dfrac{2}{3}}[\/latex] ____ [latex]- 1[\/latex]<\/li>\n<li>[latex]-3{\\dfrac{1}{2}}[\/latex] ____ [latex]- 3[\/latex]<\/li>\n<li>[latex]-{\\dfrac{3}{7}}[\/latex] ____ [latex]{\\dfrac{3}{8}}[\/latex]<\/li>\n<li>[latex]-2[\/latex] ____ [latex]{\\dfrac{-16}{9}}[\/latex]<\/li>\n<\/ol>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q676284\">Show Solution<\/span><\/p>\n<div id=\"q676284\" class=\"hidden-answer\" style=\"display: none\">\n<p>Solution:<\/p>\n<p>1. [latex]-{\\dfrac{2}{3}}>-1[\/latex]<\/p>\n<p><img decoding=\"async\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24220835\/CNX_BMath_Figure_04_01_064_img.png\" alt=\"A number line is shown. The integers from negative 3 to 3 are labeled. Negative 1 is marked with a red dot. Between negative 1 and 0, negative 2 thirds is labeled and marked with a red dot.\" \/><\/p>\n<p>2. [latex]-3{\\dfrac{1}{2}}<-3[\/latex]\n\n<img decoding=\"async\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24220837\/CNX_BMath_Figure_04_01_065_img.png\" alt=\"A number line is shown. The integers from negative 4 to 4 are labeled. There is a red dot at negative 3. Between negative 4 and negative 3, negative 3 and one half is labeled and marked with a red dot.\" \/><\/p>\n<p>3. [latex]-{\\dfrac{3}{7}}<-{\\dfrac{3}{8}}[\/latex]\n\n<img decoding=\"async\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24220838\/CNX_BMath_Figure_04_01_066_img.png\" alt=\"A number line is shown. The numbers negative 3, negative 2, negative 1, 0, 1, 2, and 3 are labeled. Between negative 1 and 0, negative 3 sevenths and negative 3 eighths are labeled and marked with red dots.\" \/><\/p>\n<p>4. [latex]-2<{\\dfrac{-16}{9}}[\/latex]\n\n<img decoding=\"async\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24220840\/CNX_BMath_Figure_04_01_067_img.png\" alt=\"A number line is shown. The numbers negative 3, negative 2, negative 1, 0, 1, 2, and 3 are labeled. There is a red dot at negative 2. Between negative 2 and negative 1, negative 16 over 9 is labeled and marked with a red dot.\" \/><\/p>\n<\/div>\n<\/div>\n<\/div>\n<p>&nbsp;<\/p>\n<div class=\"textbox key-takeaways\">\n<h3>Try it<\/h3>\n<p><iframe loading=\"lazy\" id=\"ohm146013\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=146013&theme=oea&iframe_resize_id=ohm146013&show_question_numbers\" width=\"100%\" height=\"270\"><\/iframe><\/p>\n<p><iframe loading=\"lazy\" id=\"ohm146012\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=146012&theme=oea&iframe_resize_id=ohm146012&show_question_numbers\" width=\"100%\" height=\"270\"><\/iframe><\/p>\n<\/div>\n<p>In the following video we show another example of how to order integers, fractions and mixed numbers using inequality symbols.<\/p>\n<p><iframe loading=\"lazy\" id=\"oembed-3\" title=\"Compare Integers, Fractions, and Mixed Numbers (Number Line and Common Denom)\" width=\"500\" height=\"281\" src=\"https:\/\/www.youtube.com\/embed\/Phsf_fJgerc?feature=oembed&#38;rel=0\" frameborder=\"0\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/p>\n\n\t\t\t <section class=\"citations-section\" role=\"contentinfo\">\n\t\t\t <h3>Candela Citations<\/h3>\n\t\t\t\t\t <div>\n\t\t\t\t\t\t <div id=\"citation-list-9476\">\n\t\t\t\t\t\t\t <div class=\"licensing\"><div class=\"license-attribution-dropdown-subheading\">CC licensed content, Original<\/div><ul class=\"citation-list\"><li>Question ID: 146007, 146008, 146009, 146011, 146012, 146013. <strong>Authored by<\/strong>: Alyson Day. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/licenses\/by\/4.0\/\">CC BY: Attribution<\/a><\/em>. <strong>License Terms<\/strong>: IMathAS Community License CC-BY + GPL<\/li><\/ul><div class=\"license-attribution-dropdown-subheading\">CC licensed content, Shared previously<\/div><ul class=\"citation-list\"><li>Ex: Identify a Fraction on a Number Line. <strong>Authored by<\/strong>: James Sousa (Mathispower4u.com). <strong>Located at<\/strong>: <a target=\"_blank\" href=\"https:\/\/youtu.be\/EIdmdTRQWTE\">https:\/\/youtu.be\/EIdmdTRQWTE<\/a>. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/licenses\/by\/4.0\/\">CC BY: Attribution<\/a><\/em><\/li><li>Determine Negative Proper and Improper Fractions on the Number Line. <strong>Authored by<\/strong>: James Sousa (Mathispower4u.com). <strong>Located at<\/strong>: <a target=\"_blank\" href=\"https:\/\/youtu.be\/nbSlAAZVQV4\">https:\/\/youtu.be\/nbSlAAZVQV4<\/a>. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/licenses\/by\/4.0\/\">CC BY: Attribution<\/a><\/em><\/li><li>Compare Integers, Fractions, and Mixed Numbers (Number Line and Common Denom). <strong>Authored by<\/strong>: James Sousa (Mathispower4u.com). <strong>Located at<\/strong>: <a target=\"_blank\" href=\"https:\/\/youtu.be\/Phsf_fJgerc\">https:\/\/youtu.be\/Phsf_fJgerc<\/a>. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/licenses\/by\/4.0\/\">CC BY: Attribution<\/a><\/em><\/li><\/ul><div class=\"license-attribution-dropdown-subheading\">CC licensed content, Specific attribution<\/div><ul class=\"citation-list\"><li>Prealgebra. <strong>Provided by<\/strong>: OpenStax. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/licenses\/by\/4.0\/\">CC BY: Attribution<\/a><\/em>. <strong>License Terms<\/strong>: Download for free at http:\/\/cnx.org\/contents\/caa57dab-41c7-455e-bd6f-f443cda5519c@9.757<\/li><\/ul><\/div>\n\t\t\t\t\t\t <\/div>\n\t\t\t\t\t <\/div>\n\t\t\t <\/section>","protected":false},"author":17533,"menu_order":6,"template":"","meta":{"_candela_citation":"[{\"type\":\"cc-attribution\",\"description\":\"Prealgebra\",\"author\":\"\",\"organization\":\"OpenStax\",\"url\":\"\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"Download for free at http:\/\/cnx.org\/contents\/caa57dab-41c7-455e-bd6f-f443cda5519c@9.757\"},{\"type\":\"cc\",\"description\":\"Ex: Identify a Fraction on a Number Line\",\"author\":\"James Sousa (Mathispower4u.com)\",\"organization\":\"\",\"url\":\"https:\/\/youtu.be\/EIdmdTRQWTE\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"\"},{\"type\":\"cc\",\"description\":\"Determine Negative Proper and Improper Fractions on the Number Line\",\"author\":\"James Sousa (Mathispower4u.com)\",\"organization\":\"\",\"url\":\"https:\/\/youtu.be\/nbSlAAZVQV4\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"\"},{\"type\":\"original\",\"description\":\"Question ID: 146007, 146008, 146009, 146011, 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