{"id":9543,"date":"2017-05-03T15:38:37","date_gmt":"2017-05-03T15:38:37","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/prealgebra\/?post_type=chapter&#038;p=9543"},"modified":"2020-09-03T10:52:54","modified_gmt":"2020-09-03T10:52:54","slug":"summary-adding-and-subtracting-fractions-with-different-denominators","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/suny-rockland-developmentalemporium\/chapter\/summary-adding-and-subtracting-fractions-with-different-denominators\/","title":{"raw":"2.5.d - Summary: Adding and Subtracting Fractions With Different Denominators","rendered":"2.5.d &#8211; Summary: Adding and Subtracting Fractions With Different Denominators"},"content":{"raw":"<h2>\u00a0Key Concepts<\/h2>\r\n<ul id=\"eip-352\">\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 \t<li><strong>Simplify complex fractions.<\/strong>\r\n<ol id=\"eip-id1170322955166\" class=\"stepwise\">\r\n \t<li>Simplify the numerator.<\/li>\r\n \t<li>Simplify the denominator.<\/li>\r\n \t<li>Divide the numerator by the denominator.<\/li>\r\n \t<li>Simplify if possible.<\/li>\r\n<\/ol>\r\n<\/li>\r\n<\/ul>\r\n<h2>Glossary<\/h2>\r\n<dl id=\"fs-id2483777\" class=\"definition\">\r\n \t<dt>least common denominator (LCD)<\/dt>\r\n \t<dd id=\"fs-id2129255\">The least common denominator (LCD) of two fractions is the least common multiple (LCM) of their denominators.<\/dd>\r\n<\/dl>\r\n&nbsp;","rendered":"<h2>\u00a0Key Concepts<\/h2>\n<ul id=\"eip-352\">\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<li><strong>Simplify complex fractions.<\/strong>\n<ol id=\"eip-id1170322955166\" class=\"stepwise\">\n<li>Simplify the numerator.<\/li>\n<li>Simplify the denominator.<\/li>\n<li>Divide the numerator by the denominator.<\/li>\n<li>Simplify if possible.<\/li>\n<\/ol>\n<\/li>\n<\/ul>\n<h2>Glossary<\/h2>\n<dl id=\"fs-id2483777\" class=\"definition\">\n<dt>least common denominator (LCD)<\/dt>\n<dd id=\"fs-id2129255\">The least common denominator (LCD) of two fractions is the least common multiple (LCM) of their denominators.<\/dd>\n<\/dl>\n<p>&nbsp;<\/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-9543\">\n\t\t\t\t\t\t\t <div class=\"licensing\"><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":27,"template":"","meta":{"_candela_citation":"[{\"type\":\"cc-attribution\",\"description\":\"Prealgebra\",\"author\":\"\",\"organization\":\"OpenStax\",\"url\":\"\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"Download 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