{"id":10458,"date":"2017-05-26T20:44:31","date_gmt":"2017-05-26T20:44:31","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/prealgebra\/?post_type=chapter&#038;p=10458"},"modified":"2024-04-30T16:45:09","modified_gmt":"2024-04-30T16:45:09","slug":"summary-solving-proportions-and-their-applications","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/wm-developmentalemporium\/chapter\/summary-solving-proportions-and-their-applications\/","title":{"raw":"Summary: Solving Applications of Proportions","rendered":"Summary: Solving Applications of Proportions"},"content":{"raw":"<h2>Key Concepts<\/h2>\r\n<ul id=\"fs-id1166498049771\">\r\n \t<li><strong>Proportion<\/strong>\r\n<ul id=\"eip-id4505152\">\r\n \t<li>A proportion is an equation of the form [latex]{\\Large\\frac{a}{b}}={\\Large\\frac{c}{d}}[\/latex], where [latex]b\\ne 0[\/latex], [latex]d\\ne 0[\/latex].\u00a0 The proportion states two ratios or rates are equal. The proportion is read \"[latex]a[\/latex] is to [latex]b[\/latex], as [latex]c[\/latex] is to [latex]d[\/latex]\".<\/li>\r\n<\/ul>\r\n<\/li>\r\n \t<li><strong>Cross Products of a Proportion<\/strong>\r\n<ul id=\"eip-id1166665440339\">\r\n \t<li>For any proportion of the form [latex]{\\Large\\frac{a}{b}}={\\Large\\frac{c}{d}}[\/latex] , where [latex]b\\ne 0[\/latex] , its cross products are equal: [latex]a\\cdot d=b\\cdot c[\/latex] .<\/li>\r\n<\/ul>\r\n<\/li>\r\n \t<li><strong>Percent Proportion<\/strong>\r\n<ul id=\"eip-id1166625630839\">\r\n \t<li>The amount is to the base as the percent is to 100. [latex]{\\Large\\frac{\\text{amount}}{\\text{base}}}={\\Large\\frac{\\text{percent}}{100}}[\/latex]<\/li>\r\n<\/ul>\r\n<\/li>\r\n<\/ul>\r\n<h2>Glossary<\/h2>\r\n<dl id=\"fs-id1166490867506\" class=\"definition\">\r\n \t<dt>proportion<\/dt>\r\n \t<dd id=\"fs-id1166490867511\">A proportion is an equation of the form [latex]{\\Large\\frac{a}{b}}={\\Large\\frac{c}{d}}[\/latex] , where [latex]b\\ne 0[\/latex] , [latex]d\\ne 0[\/latex] .The proportion states two ratios or rates are equal. The proportion is read \" [latex]a[\/latex] is to [latex]b[\/latex] , as [latex]c[\/latex] is to [latex]d[\/latex] \".<\/dd>\r\n<\/dl>","rendered":"<h2>Key Concepts<\/h2>\n<ul id=\"fs-id1166498049771\">\n<li><strong>Proportion<\/strong>\n<ul id=\"eip-id4505152\">\n<li>A proportion is an equation of the form [latex]{\\Large\\frac{a}{b}}={\\Large\\frac{c}{d}}[\/latex], where [latex]b\\ne 0[\/latex], [latex]d\\ne 0[\/latex].\u00a0 The proportion states two ratios or rates are equal. The proportion is read &#8220;[latex]a[\/latex] is to [latex]b[\/latex], as [latex]c[\/latex] is to [latex]d[\/latex]&#8220;.<\/li>\n<\/ul>\n<\/li>\n<li><strong>Cross Products of a Proportion<\/strong>\n<ul id=\"eip-id1166665440339\">\n<li>For any proportion of the form [latex]{\\Large\\frac{a}{b}}={\\Large\\frac{c}{d}}[\/latex] , where [latex]b\\ne 0[\/latex] , its cross products are equal: [latex]a\\cdot d=b\\cdot c[\/latex] .<\/li>\n<\/ul>\n<\/li>\n<li><strong>Percent Proportion<\/strong>\n<ul id=\"eip-id1166625630839\">\n<li>The amount is to the base as the percent is to 100. [latex]{\\Large\\frac{\\text{amount}}{\\text{base}}}={\\Large\\frac{\\text{percent}}{100}}[\/latex]<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<h2>Glossary<\/h2>\n<dl id=\"fs-id1166490867506\" class=\"definition\">\n<dt>proportion<\/dt>\n<dd id=\"fs-id1166490867511\">A proportion is an equation of the form [latex]{\\Large\\frac{a}{b}}={\\Large\\frac{c}{d}}[\/latex] , where [latex]b\\ne 0[\/latex] , [latex]d\\ne 0[\/latex] .The proportion states two ratios or rates are equal. The proportion is read &#8221; [latex]a[\/latex] is to [latex]b[\/latex] , as [latex]c[\/latex] is to [latex]d[\/latex] &#8220;.<\/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-10458\">\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":25,"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":"0200c0cb67db4495ac69dad760145c40","pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"class_list":["post-10458","chapter","type-chapter","status-publish","hentry"],"part":7176,"_links":{"self":[{"href":"https:\/\/courses.lumenlearning.com\/wm-developmentalemporium\/wp-json\/pressbooks\/v2\/chapters\/10458","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/courses.lumenlearning.com\/wm-developmentalemporium\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/courses.lumenlearning.com\/wm-developmentalemporium\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/wm-developmentalemporium\/wp-json\/wp\/v2\/users\/17533"}],"version-history":[{"count":8,"href":"https:\/\/courses.lumenlearning.com\/wm-developmentalemporium\/wp-json\/pressbooks\/v2\/chapters\/10458\/revisions"}],"predecessor-version":[{"id":20402,"href":"https:\/\/courses.lumenlearning.com\/wm-developmentalemporium\/wp-json\/pressbooks\/v2\/chapters\/10458\/revisions\/20402"}],"part":[{"href":"https:\/\/courses.lumenlearning.com\/wm-developmentalemporium\/wp-json\/pressbooks\/v2\/parts\/7176"}],"metadata":[{"href":"https:\/\/courses.lumenlearning.com\/wm-developmentalemporium\/wp-json\/pressbooks\/v2\/chapters\/10458\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/courses.lumenlearning.com\/wm-developmentalemporium\/wp-json\/wp\/v2\/media?parent=10458"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/wm-developmentalemporium\/wp-json\/pressbooks\/v2\/chapter-type?post=10458"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/wm-developmentalemporium\/wp-json\/wp\/v2\/contributor?post=10458"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/wm-developmentalemporium\/wp-json\/wp\/v2\/license?post=10458"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}