{"id":9494,"date":"2017-05-02T23:16:34","date_gmt":"2017-05-02T23:16:34","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/prealgebra\/?post_type=chapter&#038;p=9494"},"modified":"2017-09-26T16:22:04","modified_gmt":"2017-09-26T16:22:04","slug":"summary-multiplying-and-dividing-fractions","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/wm-prealgebra\/chapter\/summary-multiplying-and-dividing-fractions\/","title":{"raw":"Summary: Multiplying and Dividing Fractions","rendered":"Summary: Multiplying and Dividing Fractions"},"content":{"raw":"<h2 data-type=\"title\">Key Concepts<\/h2>\r\n<ul id=\"eip-167\">\r\n \t<li><strong>Equivalent Fractions Property<\/strong>\r\n<ul id=\"eip-id1170323004261\">\r\n \t<li>If [latex]a,b,c[\/latex] are numbers where [latex]b\\ne 0[\/latex] , [latex]c\\ne 0[\/latex] , then [latex]\\Large\\frac{a}{b}\\normalsize=\\Large\\frac{a\\cdot c}{b\\cdot c}[\/latex] and [latex]\\Large\\frac{a\\cdot c}{b\\cdot c}\\normalsize=\\Large\\frac{a}{b}[\/latex] .<\/li>\r\n<\/ul>\r\n<\/li>\r\n \t<li><strong>Simplify a fraction.<\/strong>\r\n<ol id=\"eip-id1170323004302\" class=\"stepwise\" data-number-style=\"arabic\">\r\n \t<li>Rewrite the numerator and denominator to show the common factors. If needed, factor the numerator and denominator into prime numbers.<\/li>\r\n \t<li>Simplify, using the equivalent fractions property, by removing common factors.<\/li>\r\n \t<li>Multiply any remaining factors.<\/li>\r\n<\/ol>\r\n<\/li>\r\n \t<li><strong>Fraction Multiplication<\/strong>\r\n<ul id=\"eip-id1170323004360\">\r\n \t<li>If [latex]a,b,c[\/latex], and [latex]d[\/latex] are numbers where [latex]b\\ne 0[\/latex] and [latex]d\\ne 0[\/latex] , then [latex]\\Large\\frac{a}{b}\\cdot \\frac{c}{d}\\normalsize=\\Large\\frac{ac}{bd}[\/latex] .<\/li>\r\n<\/ul>\r\n<\/li>\r\n \t<li><strong>Reciprocal<\/strong>\r\n<ul id=\"eip-id1170322987712\">\r\n \t<li>A number and its reciprocal have a product of [latex]1[\/latex] . [latex]\\Large\\frac{a}{b}\\cdot \\frac{b}{a}\\normalsize=1[\/latex]\r\n<table id=\"eip-id1170326426110\" style=\"width: 85%;\" summary=\"reciprocal\"><caption>\u00a0<\/caption>\r\n<tbody>\r\n<tr>\r\n<td><strong>Opposite<\/strong><\/td>\r\n<td><strong>Absolute Value<\/strong><\/td>\r\n<td><strong>Reciprocal<\/strong><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>has opposite sign<\/td>\r\n<td>is never negative<\/td>\r\n<td>has same sign, fraction inverts<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<\/li>\r\n<\/ul>\r\n<\/li>\r\n \t<li><strong>Fraction Division<\/strong>\r\n<ul id=\"eip-id1170323913006\">\r\n \t<li>If [latex]a,b,c[\/latex], and [latex]d[\/latex] are numbers where [latex]b\\ne 0[\/latex] , [latex]c\\ne 0[\/latex] and [latex]d\\ne 0[\/latex] , then[latex]\\Large\\frac{a}{b}\\normalsize+\\Large\\frac{c}{d}\\normalsize=\\Large\\frac{a}{b}\\cdot\\Large\\frac{d}{c}[\/latex]<\/li>\r\n \t<li>To divide fractions, multiply the first fraction by the reciprocal of the second.<\/li>\r\n<\/ul>\r\n<\/li>\r\n<\/ul>\r\n<h2 data-type=\"glossary-title\">Glossary<\/h2>\r\n<dl id=\"fs-id2946118\" class=\"definition\">\r\n \t<dt>reciprocal<\/dt>\r\n \t<dd id=\"fs-id2447033\">The reciprocal of the fraction [latex]\\Large\\frac{a}{b}[\/latex] is [latex]\\Large\\frac{b}{a}[\/latex] where [latex]a\\ne 0[\/latex] and [latex]b\\ne 0[\/latex] .<\/dd>\r\n<\/dl>\r\n<dl id=\"fs-id1170326339386\" class=\"definition\">\r\n \t<dt>simplified fraction<\/dt>\r\n \t<dd id=\"fs-id1170326339389\">A fraction is considered simplified if there are no common factors in the numerator and denominator.<\/dd>\r\n<\/dl>","rendered":"<h2 data-type=\"title\">Key Concepts<\/h2>\n<ul id=\"eip-167\">\n<li><strong>Equivalent Fractions Property<\/strong>\n<ul id=\"eip-id1170323004261\">\n<li>If [latex]a,b,c[\/latex] are numbers where [latex]b\\ne 0[\/latex] , [latex]c\\ne 0[\/latex] , then [latex]\\Large\\frac{a}{b}\\normalsize=\\Large\\frac{a\\cdot c}{b\\cdot c}[\/latex] and [latex]\\Large\\frac{a\\cdot c}{b\\cdot c}\\normalsize=\\Large\\frac{a}{b}[\/latex] .<\/li>\n<\/ul>\n<\/li>\n<li><strong>Simplify a fraction.<\/strong>\n<ol id=\"eip-id1170323004302\" class=\"stepwise\" data-number-style=\"arabic\">\n<li>Rewrite the numerator and denominator to show the common factors. If needed, factor the numerator and denominator into prime numbers.<\/li>\n<li>Simplify, using the equivalent fractions property, by removing common factors.<\/li>\n<li>Multiply any remaining factors.<\/li>\n<\/ol>\n<\/li>\n<li><strong>Fraction Multiplication<\/strong>\n<ul id=\"eip-id1170323004360\">\n<li>If [latex]a,b,c[\/latex], and [latex]d[\/latex] are numbers where [latex]b\\ne 0[\/latex] and [latex]d\\ne 0[\/latex] , then [latex]\\Large\\frac{a}{b}\\cdot \\frac{c}{d}\\normalsize=\\Large\\frac{ac}{bd}[\/latex] .<\/li>\n<\/ul>\n<\/li>\n<li><strong>Reciprocal<\/strong>\n<ul id=\"eip-id1170322987712\">\n<li>A number and its reciprocal have a product of [latex]1[\/latex] . [latex]\\Large\\frac{a}{b}\\cdot \\frac{b}{a}\\normalsize=1[\/latex]<br \/>\n<table id=\"eip-id1170326426110\" style=\"width: 85%;\" summary=\"reciprocal\">\n<caption>\u00a0<\/caption>\n<tbody>\n<tr>\n<td><strong>Opposite<\/strong><\/td>\n<td><strong>Absolute Value<\/strong><\/td>\n<td><strong>Reciprocal<\/strong><\/td>\n<\/tr>\n<tr>\n<td>has opposite sign<\/td>\n<td>is never negative<\/td>\n<td>has same sign, fraction inverts<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/li>\n<\/ul>\n<\/li>\n<li><strong>Fraction Division<\/strong>\n<ul id=\"eip-id1170323913006\">\n<li>If [latex]a,b,c[\/latex], and [latex]d[\/latex] are numbers where [latex]b\\ne 0[\/latex] , [latex]c\\ne 0[\/latex] and [latex]d\\ne 0[\/latex] , then[latex]\\Large\\frac{a}{b}\\normalsize+\\Large\\frac{c}{d}\\normalsize=\\Large\\frac{a}{b}\\cdot\\Large\\frac{d}{c}[\/latex]<\/li>\n<li>To divide fractions, multiply the first fraction by the reciprocal of the second.<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<h2 data-type=\"glossary-title\">Glossary<\/h2>\n<dl id=\"fs-id2946118\" class=\"definition\">\n<dt>reciprocal<\/dt>\n<dd id=\"fs-id2447033\">The reciprocal of the fraction [latex]\\Large\\frac{a}{b}[\/latex] is [latex]\\Large\\frac{b}{a}[\/latex] where [latex]a\\ne 0[\/latex] and [latex]b\\ne 0[\/latex] .<\/dd>\n<\/dl>\n<dl id=\"fs-id1170326339386\" class=\"definition\">\n<dt>simplified fraction<\/dt>\n<dd id=\"fs-id1170326339389\">A fraction is considered simplified if there are no common factors in the numerator and denominator.<\/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-9494\">\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":13,"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\"}]","CANDELA_OUTCOMES_GUID":"ba4f7a3a-9529-47e1-952e-7e6b4ca6cc87","pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"class_list":["post-9494","chapter","type-chapter","status-publish","hentry"],"part":6633,"_links":{"self":[{"href":"https:\/\/courses.lumenlearning.com\/wm-prealgebra\/wp-json\/pressbooks\/v2\/chapters\/9494","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/courses.lumenlearning.com\/wm-prealgebra\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/courses.lumenlearning.com\/wm-prealgebra\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/wm-prealgebra\/wp-json\/wp\/v2\/users\/17533"}],"version-history":[{"count":8,"href":"https:\/\/courses.lumenlearning.com\/wm-prealgebra\/wp-json\/pressbooks\/v2\/chapters\/9494\/revisions"}],"predecessor-version":[{"id":15356,"href":"https:\/\/courses.lumenlearning.com\/wm-prealgebra\/wp-json\/pressbooks\/v2\/chapters\/9494\/revisions\/15356"}],"part":[{"href":"https:\/\/courses.lumenlearning.com\/wm-prealgebra\/wp-json\/pressbooks\/v2\/parts\/6633"}],"metadata":[{"href":"https:\/\/courses.lumenlearning.com\/wm-prealgebra\/wp-json\/pressbooks\/v2\/chapters\/9494\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/courses.lumenlearning.com\/wm-prealgebra\/wp-json\/wp\/v2\/media?parent=9494"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/wm-prealgebra\/wp-json\/pressbooks\/v2\/chapter-type?post=9494"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/wm-prealgebra\/wp-json\/wp\/v2\/contributor?post=9494"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/wm-prealgebra\/wp-json\/wp\/v2\/license?post=9494"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}