{"id":3099,"date":"2019-10-23T14:08:50","date_gmt":"2019-10-23T14:08:50","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/mathforlibscoreq\/?post_type=chapter&#038;p=3099"},"modified":"2021-02-06T00:03:10","modified_gmt":"2021-02-06T00:03:10","slug":"summary-review-topics-6","status":"web-only","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/slcc-mathforliberalartscorequisite\/chapter\/summary-review-topics-6\/","title":{"raw":"Summary: Review Topics","rendered":"Summary: Review Topics"},"content":{"raw":"<h2>Key Concepts<\/h2>\r\n<ul>\r\n \t<li><strong>Fraction Addition<\/strong>\r\n<ul id=\"eip-id1170326280061\">\r\n \t<li>If [latex]a,b[\/latex], and [latex]c[\/latex] are numbers where [latex]c\\ne 0[\/latex] , then [latex]{\\Large\\frac{a}{c}}+{\\Large\\frac{b}{c}}={\\Large\\frac{a+c}{c}}[\/latex] .<\/li>\r\n \t<li>To add fractions, add the numerators and place the sum over the common denominator.<\/li>\r\n<\/ul>\r\n<\/li>\r\n \t<li><strong>Fraction Subtraction<\/strong>\r\n<ul id=\"eip-id1170322914726\">\r\n \t<li>If [latex]a,b[\/latex], and [latex]c[\/latex] are numbers where [latex]c\\ne 0[\/latex] , then [latex]{\\Large\\frac{a}{c}}-{\\Large\\frac{b}{c}}={\\Large\\frac{a-b}{c}}[\/latex] .<\/li>\r\n \t<li>To subtract fractions, subtract the numerators and place the difference over the common denominator.<\/li>\r\n<\/ul>\r\n<\/li>\r\n \t<li><strong>Find the prime factorization of a composite number using the tree method.<\/strong>\r\n<ol id=\"eip-id1170195278180\" class=\"stepwise\">\r\n \t<li>Find any factor pair of the given number, and use these numbers to create two branches.<\/li>\r\n \t<li>If a factor is prime, that branch is complete. Circle the prime.<\/li>\r\n \t<li>If a factor is not prime, write it as the product of a factor pair and continue the process.<\/li>\r\n \t<li>Write the composite number as the product of all the circled primes.<\/li>\r\n<\/ol>\r\n<\/li>\r\n \t<li><strong>Find the prime factorization of a composite number using the ladder method.<\/strong>\r\n<ol id=\"eip-id1170195278197\" class=\"stepwise\">\r\n \t<li>Divide the number by the smallest prime.<\/li>\r\n \t<li>Continue dividing by that prime until it no longer divides evenly.<\/li>\r\n \t<li>Divide by the next prime until it no longer divides evenly.<\/li>\r\n \t<li>Continue until the quotient is a prime.<\/li>\r\n \t<li>Write the composite number as the product of all the primes on the sides and top of the ladder.<\/li>\r\n<\/ol>\r\n<\/li>\r\n \t<li><strong>Find the LCM using the prime factors method.<\/strong>\r\n<ol id=\"eip-id1170195278218\" class=\"stepwise\">\r\n \t<li>Find the prime factorization of each number.<\/li>\r\n \t<li>Write each number as a product of primes, matching primes vertically when possible.<\/li>\r\n \t<li>Bring down the primes in each column.<\/li>\r\n \t<li>Multiply the factors to get the LCM.<\/li>\r\n<\/ol>\r\n<\/li>\r\n \t<li><strong>Find the LCM using the prime factors method.<\/strong>\r\n<ol id=\"eip-id1170195278236\" class=\"stepwise\">\r\n \t<li>Find the prime factorization of each number.<\/li>\r\n \t<li>Write each number as a product of primes, matching primes vertically when possible.<\/li>\r\n \t<li>Bring down the primes in each column.<\/li>\r\n \t<li>Multiply the factors to get the LCM.<\/li>\r\n<\/ol>\r\n<\/li>\r\n \t<li><strong>Find the least common denominator (LCD) of two fractions.<\/strong>\r\n<ol id=\"eip-id1170326533417\" class=\"stepwise\">\r\n \t<li>Factor each denominator into its primes.<\/li>\r\n \t<li>List the primes, matching primes in columns when possible.<\/li>\r\n \t<li>Bring down the columns.<\/li>\r\n \t<li>Multiply the factors. The product is the LCM of the denominators.<\/li>\r\n \t<li>The LCM of the denominators is the LCD of the fractions.<\/li>\r\n<\/ol>\r\n<\/li>\r\n \t<li><strong>Equivalent Fractions Property<\/strong>\r\n<ul id=\"eip-id1170322988097\">\r\n \t<li>If [latex]a,b[\/latex] , and [latex]c[\/latex] are whole numbers where [latex]b\\ne 0[\/latex] , [latex]c\\ne 0[\/latex] then[latex]\\Large\\frac{a}{b}=\\Large\\frac{a\\cdot c}{b\\cdot c}[\/latex]\r\nand [latex]\\Large\\frac{a\\cdot c}{b\\cdot c}=\\Large\\frac{a}{b}[\/latex]<\/li>\r\n<\/ul>\r\n<\/li>\r\n \t<li><strong>Convert two fractions to equivalent fractions with their LCD as the common denominator.<\/strong>\r\n<ol id=\"eip-id1170324058309\" class=\"stepwise\">\r\n \t<li>Find the LCD.<\/li>\r\n \t<li>For each fraction, determine the number needed to multiply the denominator to get the LCD.<\/li>\r\n \t<li>Use the Equivalent Fractions Property to multiply the numerator and denominator by the number from Step 2.<\/li>\r\n \t<li>Simplify the numerator and denominator.<\/li>\r\n<\/ol>\r\n<\/li>\r\n \t<li><strong>Add or subtract fractions with different denominators.<\/strong>\r\n<ol id=\"eip-id1170322955166\" class=\"stepwise\">\r\n \t<li>Find the LCD.<\/li>\r\n \t<li>Convert each fraction to an equivalent form with the LCD as the denominator.<\/li>\r\n \t<li>Add or subtract the fractions.<\/li>\r\n \t<li>Write the result in simplified form.<\/li>\r\n<\/ol>\r\n<\/li>\r\n<\/ul>\r\n<h2>Glossary<\/h2>\r\n<dl>\r\n \t<dt><strong>composite number<\/strong><\/dt>\r\n \t<dd>A composite number is a counting number that is not prime<\/dd>\r\n<\/dl>\r\n<dl>\r\n \t<dt><strong>divisibility<\/strong><\/dt>\r\n \t<dd>If a number [latex]m[\/latex] is a multiple of [latex]n[\/latex] , then we say that [latex]m[\/latex] is divisible by [latex]n[\/latex]<\/dd>\r\n<\/dl>\r\n<dl>\r\n \t<dt><strong>least common denominator (LCD)<\/strong><\/dt>\r\n \t<dd>The least common denominator (LCD) of two fractions is the least common multiple (LCM) of their denominators<\/dd>\r\n<\/dl>\r\n<dl>\r\n \t<dt><strong>multiple of a number<\/strong><\/dt>\r\n \t<dd>A number is a multiple of [latex]n[\/latex] if it is the product of a counting number and [latex]n[\/latex]<\/dd>\r\n<\/dl>\r\n<dl>\r\n \t<dt><strong>ratio<\/strong><\/dt>\r\n \t<dd>A ratio compares two numbers or two quantities that are measured with the same unit. The ratio of [latex]a[\/latex] to [latex]b[\/latex] is written [latex]a[\/latex] to [latex]b[\/latex] , [latex]\\Large\\frac{a}{b}[\/latex] , or [latex]a:b[\/latex]<\/dd>\r\n<\/dl>\r\n<dl>\r\n \t<dt><strong>prime number<\/strong><\/dt>\r\n \t<dd>A prime number is a counting number greater than 1 whose only factors are 1 and itself<\/dd>\r\n<\/dl>","rendered":"<h2>Key Concepts<\/h2>\n<ul>\n<li><strong>Fraction Addition<\/strong>\n<ul id=\"eip-id1170326280061\">\n<li>If [latex]a,b[\/latex], and [latex]c[\/latex] are numbers where [latex]c\\ne 0[\/latex] , then [latex]{\\Large\\frac{a}{c}}+{\\Large\\frac{b}{c}}={\\Large\\frac{a+c}{c}}[\/latex] .<\/li>\n<li>To add fractions, add the numerators and place the sum over the common denominator.<\/li>\n<\/ul>\n<\/li>\n<li><strong>Fraction Subtraction<\/strong>\n<ul id=\"eip-id1170322914726\">\n<li>If [latex]a,b[\/latex], and [latex]c[\/latex] are numbers where [latex]c\\ne 0[\/latex] , then [latex]{\\Large\\frac{a}{c}}-{\\Large\\frac{b}{c}}={\\Large\\frac{a-b}{c}}[\/latex] .<\/li>\n<li>To subtract fractions, subtract the numerators and place the difference over the common denominator.<\/li>\n<\/ul>\n<\/li>\n<li><strong>Find the prime factorization of a composite number using the tree method.<\/strong>\n<ol id=\"eip-id1170195278180\" class=\"stepwise\">\n<li>Find any factor pair of the given number, and use these numbers to create two branches.<\/li>\n<li>If a factor is prime, that branch is complete. Circle the prime.<\/li>\n<li>If a factor is not prime, write it as the product of a factor pair and continue the process.<\/li>\n<li>Write the composite number as the product of all the circled primes.<\/li>\n<\/ol>\n<\/li>\n<li><strong>Find the prime factorization of a composite number using the ladder method.<\/strong>\n<ol id=\"eip-id1170195278197\" class=\"stepwise\">\n<li>Divide the number by the smallest prime.<\/li>\n<li>Continue dividing by that prime until it no longer divides evenly.<\/li>\n<li>Divide by the next prime until it no longer divides evenly.<\/li>\n<li>Continue until the quotient is a prime.<\/li>\n<li>Write the composite number as the product of all the primes on the sides and top of the ladder.<\/li>\n<\/ol>\n<\/li>\n<li><strong>Find the LCM using the prime factors method.<\/strong>\n<ol id=\"eip-id1170195278218\" class=\"stepwise\">\n<li>Find the prime factorization of each number.<\/li>\n<li>Write each number as a product of primes, matching primes vertically when possible.<\/li>\n<li>Bring down the primes in each column.<\/li>\n<li>Multiply the factors to get the LCM.<\/li>\n<\/ol>\n<\/li>\n<li><strong>Find the LCM using the prime factors method.<\/strong>\n<ol id=\"eip-id1170195278236\" class=\"stepwise\">\n<li>Find the prime factorization of each number.<\/li>\n<li>Write each number as a product of primes, matching primes vertically when possible.<\/li>\n<li>Bring down the primes in each column.<\/li>\n<li>Multiply the factors to get the LCM.<\/li>\n<\/ol>\n<\/li>\n<li><strong>Find the least common denominator (LCD) of two fractions.<\/strong>\n<ol id=\"eip-id1170326533417\" class=\"stepwise\">\n<li>Factor each denominator into its primes.<\/li>\n<li>List the primes, matching primes in columns when possible.<\/li>\n<li>Bring down the columns.<\/li>\n<li>Multiply the factors. The product is the LCM of the denominators.<\/li>\n<li>The LCM of the denominators is the LCD of the fractions.<\/li>\n<\/ol>\n<\/li>\n<li><strong>Equivalent Fractions Property<\/strong>\n<ul id=\"eip-id1170322988097\">\n<li>If [latex]a,b[\/latex] , and [latex]c[\/latex] are whole numbers where [latex]b\\ne 0[\/latex] , [latex]c\\ne 0[\/latex] then[latex]\\Large\\frac{a}{b}=\\Large\\frac{a\\cdot c}{b\\cdot c}[\/latex]<br \/>\nand [latex]\\Large\\frac{a\\cdot c}{b\\cdot c}=\\Large\\frac{a}{b}[\/latex]<\/li>\n<\/ul>\n<\/li>\n<li><strong>Convert two fractions to equivalent fractions with their LCD as the common denominator.<\/strong>\n<ol id=\"eip-id1170324058309\" class=\"stepwise\">\n<li>Find the LCD.<\/li>\n<li>For each fraction, determine the number needed to multiply the denominator to get the LCD.<\/li>\n<li>Use the Equivalent Fractions Property to multiply the numerator and denominator by the number from Step 2.<\/li>\n<li>Simplify the numerator and denominator.<\/li>\n<\/ol>\n<\/li>\n<li><strong>Add or subtract fractions with different denominators.<\/strong>\n<ol id=\"eip-id1170322955166\" class=\"stepwise\">\n<li>Find the LCD.<\/li>\n<li>Convert each fraction to an equivalent form with the LCD as the denominator.<\/li>\n<li>Add or subtract the fractions.<\/li>\n<li>Write the result in simplified form.<\/li>\n<\/ol>\n<\/li>\n<\/ul>\n<h2>Glossary<\/h2>\n<dl>\n<dt><strong>composite number<\/strong><\/dt>\n<dd>A composite number is a counting number that is not prime<\/dd>\n<\/dl>\n<dl>\n<dt><strong>divisibility<\/strong><\/dt>\n<dd>If a number [latex]m[\/latex] is a multiple of [latex]n[\/latex] , then we say that [latex]m[\/latex] is divisible by [latex]n[\/latex]<\/dd>\n<\/dl>\n<dl>\n<dt><strong>least common denominator (LCD)<\/strong><\/dt>\n<dd>The least common denominator (LCD) of two fractions is the least common multiple (LCM) of their denominators<\/dd>\n<\/dl>\n<dl>\n<dt><strong>multiple of a number<\/strong><\/dt>\n<dd>A number is a multiple of [latex]n[\/latex] if it is the product of a counting number and [latex]n[\/latex]<\/dd>\n<\/dl>\n<dl>\n<dt><strong>ratio<\/strong><\/dt>\n<dd>A ratio compares two numbers or two quantities that are measured with the same unit. The ratio of [latex]a[\/latex] to [latex]b[\/latex] is written [latex]a[\/latex] to [latex]b[\/latex] , [latex]\\Large\\frac{a}{b}[\/latex] , or [latex]a:b[\/latex]<\/dd>\n<\/dl>\n<dl>\n<dt><strong>prime number<\/strong><\/dt>\n<dd>A prime number is a counting number greater than 1 whose only factors are 1 and itself<\/dd>\n<\/dl>\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-3099\">\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><strong>Authored by<\/strong>: Deborah Devlin. <strong>Provided by<\/strong>: Lumen Learning. <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>\n\t\t\t\t\t\t <\/div>\n\t\t\t\t\t <\/div>\n\t\t\t <\/section>","protected":false},"author":25777,"menu_order":9,"template":"","meta":{"_candela_citation":"[{\"type\":\"original\",\"description\":\"\",\"author\":\"Deborah Devlin\",\"organization\":\"Lumen Learning\",\"url\":\"\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"\"}]","CANDELA_OUTCOMES_GUID":"","pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"class_list":["post-3099","chapter","type-chapter","status-web-only","hentry"],"part":329,"_links":{"self":[{"href":"https:\/\/courses.lumenlearning.com\/slcc-mathforliberalartscorequisite\/wp-json\/pressbooks\/v2\/chapters\/3099","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/courses.lumenlearning.com\/slcc-mathforliberalartscorequisite\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/courses.lumenlearning.com\/slcc-mathforliberalartscorequisite\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/slcc-mathforliberalartscorequisite\/wp-json\/wp\/v2\/users\/25777"}],"version-history":[{"count":3,"href":"https:\/\/courses.lumenlearning.com\/slcc-mathforliberalartscorequisite\/wp-json\/pressbooks\/v2\/chapters\/3099\/revisions"}],"predecessor-version":[{"id":4135,"href":"https:\/\/courses.lumenlearning.com\/slcc-mathforliberalartscorequisite\/wp-json\/pressbooks\/v2\/chapters\/3099\/revisions\/4135"}],"part":[{"href":"https:\/\/courses.lumenlearning.com\/slcc-mathforliberalartscorequisite\/wp-json\/pressbooks\/v2\/parts\/329"}],"metadata":[{"href":"https:\/\/courses.lumenlearning.com\/slcc-mathforliberalartscorequisite\/wp-json\/pressbooks\/v2\/chapters\/3099\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/courses.lumenlearning.com\/slcc-mathforliberalartscorequisite\/wp-json\/wp\/v2\/media?parent=3099"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/slcc-mathforliberalartscorequisite\/wp-json\/pressbooks\/v2\/chapter-type?post=3099"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/slcc-mathforliberalartscorequisite\/wp-json\/wp\/v2\/contributor?post=3099"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/slcc-mathforliberalartscorequisite\/wp-json\/wp\/v2\/license?post=3099"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}