{"id":9484,"date":"2017-05-02T23:12:37","date_gmt":"2017-05-02T23:12:37","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/prealgebra\/?post_type=chapter&#038;p=9484"},"modified":"2017-09-23T22:06:22","modified_gmt":"2017-09-23T22:06:22","slug":"summary-representing-parts-of-a-whole-as-fractions","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/wm-prealgebra\/chapter\/summary-representing-parts-of-a-whole-as-fractions\/","title":{"raw":"Summary: Representing Parts of a Whole as Fractions","rendered":"Summary: Representing Parts of a Whole as Fractions"},"content":{"raw":"<h2>Key Concepts<\/h2>\r\n<ul id=\"eip-894\">\r\n \t<li><strong>Property of One<\/strong>\r\n<ul id=\"eip-id1170324076343\">\r\n \t<li>Any number, except zero, divided by itself is one.\u00a0\u00a0 [latex]{\\Large\\frac{a}{a}}=1[\/latex] , where [latex]a\\ne 0[\/latex]<\/li>\r\n<\/ul>\r\n<\/li>\r\n \t<li><strong>Mixed Numbers<\/strong>\r\n<ul id=\"eip-123\">\r\n \t<li>A <strong>mixed number<\/strong> consists of a whole number [latex]a[\/latex] and a fraction [latex]{\\Large\\frac{b}{c}}[\/latex] where [latex]c\\ne 0[\/latex]<\/li>\r\n \t<li>It is written as follows: [latex]a{\\Large\\frac{b}{c}}\\enspace c\\ne 0[\/latex]<\/li>\r\n<\/ul>\r\n<\/li>\r\n \t<li><strong>Proper and Improper Fractions<\/strong>\r\n<ul id=\"eip-id11703076343\">\r\n \t<li>The fraction [latex]ab[\/latex] is a proper fraction if [latex]a&lt;b[\/latex] and an improper fraction if [latex]a\\ge b[\/latex] .<\/li>\r\n<\/ul>\r\n<\/li>\r\n \t<li><strong>Convert an improper fraction to a mixed number.<\/strong>\r\n<ol id=\"eip-id114076343\" class=\"stepwise\">\r\n \t<li>Divide the denominator into the numerator.<\/li>\r\n \t<li>Identify the quotient, remainder, and divisor.<\/li>\r\n \t<li>Write the mixed number as quotient [latex]{\\large\\frac{\\text{remainder}}{\\text{divisor}}}[\/latex]<\/li>\r\n<\/ol>\r\n<\/li>\r\n \t<li><strong>Convert a mixed number to an improper fraction.<\/strong>\r\n<ol id=\"eip-id114343\" class=\"stepwise\">\r\n \t<li>Multiply the whole number by the denominator.<\/li>\r\n \t<li>Add the numerator to the product found in Step 1.<\/li>\r\n \t<li>Write the final sum over the original denominator.<\/li>\r\n<\/ol>\r\n<\/li>\r\n \t<li><strong>Equivalent Fractions Property<\/strong>\r\n<ul id=\"eip-id11703246343\">\r\n \t<li>If [latex]\\mathrm{a, b,}[\/latex] and [latex]c[\/latex] are 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]<\/li>\r\n<\/ul>\r\n<\/li>\r\n<\/ul>\r\n<h2>Glossary<\/h2>\r\n<dl id=\"fs-id2849922\" class=\"definition\">\r\n \t<dt>equivalent fractions<\/dt>\r\n \t<dd id=\"fs-id3177563\">Equivalent fractions are two or more fractions that have the same value.<\/dd>\r\n<\/dl>\r\n<dl id=\"fs-id2715365\" class=\"definition\">\r\n \t<dt>fraction<\/dt>\r\n \t<dd id=\"fs-id2495919\">A fraction is written [latex]{\\Large\\frac{a}{b}}[\/latex] . in a fraction, [latex]a[\/latex] is the numerator and [latex]b[\/latex] is the denominator. A fraction represents parts of a whole. The denominator [latex]b[\/latex] is the number of equal parts the whole has been divided into, and the numerator [latex]a[\/latex] indicates how many parts are included.<\/dd>\r\n<\/dl>\r\n<dl id=\"fs-id2435034\" class=\"definition\">\r\n \t<dt>mixed number<\/dt>\r\n \t<dd id=\"fs-id3330885\">A mixed number contains<\/dd>\r\n<\/dl>","rendered":"<h2>Key Concepts<\/h2>\n<ul id=\"eip-894\">\n<li><strong>Property of One<\/strong>\n<ul id=\"eip-id1170324076343\">\n<li>Any number, except zero, divided by itself is one.\u00a0\u00a0 [latex]{\\Large\\frac{a}{a}}=1[\/latex] , where [latex]a\\ne 0[\/latex]<\/li>\n<\/ul>\n<\/li>\n<li><strong>Mixed Numbers<\/strong>\n<ul id=\"eip-123\">\n<li>A <strong>mixed number<\/strong> consists of a whole number [latex]a[\/latex] and a fraction [latex]{\\Large\\frac{b}{c}}[\/latex] where [latex]c\\ne 0[\/latex]<\/li>\n<li>It is written as follows: [latex]a{\\Large\\frac{b}{c}}\\enspace c\\ne 0[\/latex]<\/li>\n<\/ul>\n<\/li>\n<li><strong>Proper and Improper Fractions<\/strong>\n<ul id=\"eip-id11703076343\">\n<li>The fraction [latex]ab[\/latex] is a proper fraction if [latex]a<b[\/latex] and an improper fraction if [latex]a\\ge b[\/latex] .<\/li>\n<\/ul>\n<\/li>\n<li><strong>Convert an improper fraction to a mixed number.<\/strong>\n<ol id=\"eip-id114076343\" class=\"stepwise\">\n<li>Divide the denominator into the numerator.<\/li>\n<li>Identify the quotient, remainder, and divisor.<\/li>\n<li>Write the mixed number as quotient [latex]{\\large\\frac{\\text{remainder}}{\\text{divisor}}}[\/latex]<\/li>\n<\/ol>\n<\/li>\n<li><strong>Convert a mixed number to an improper fraction.<\/strong>\n<ol id=\"eip-id114343\" class=\"stepwise\">\n<li>Multiply the whole number by the denominator.<\/li>\n<li>Add the numerator to the product found in Step 1.<\/li>\n<li>Write the final sum over the original denominator.<\/li>\n<\/ol>\n<\/li>\n<li><strong>Equivalent Fractions Property<\/strong>\n<ul id=\"eip-id11703246343\">\n<li>If [latex]\\mathrm{a, b,}[\/latex] and [latex]c[\/latex] are 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]<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<h2>Glossary<\/h2>\n<dl id=\"fs-id2849922\" class=\"definition\">\n<dt>equivalent fractions<\/dt>\n<dd id=\"fs-id3177563\">Equivalent fractions are two or more fractions that have the same value.<\/dd>\n<\/dl>\n<dl id=\"fs-id2715365\" class=\"definition\">\n<dt>fraction<\/dt>\n<dd id=\"fs-id2495919\">A fraction is written [latex]{\\Large\\frac{a}{b}}[\/latex] . in a fraction, [latex]a[\/latex] is the numerator and [latex]b[\/latex] is the denominator. A fraction represents parts of a whole. The denominator [latex]b[\/latex] is the number of equal parts the whole has been divided into, and the numerator [latex]a[\/latex] indicates how many parts are included.<\/dd>\n<\/dl>\n<dl id=\"fs-id2435034\" class=\"definition\">\n<dt>mixed number<\/dt>\n<dd id=\"fs-id3330885\">A mixed number contains<\/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-9484\">\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":7,"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":"e74bee23-c766-459f-ae81-25db35dbe485","pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"class_list":["post-9484","chapter","type-chapter","status-publish","hentry"],"part":6633,"_links":{"self":[{"href":"https:\/\/courses.lumenlearning.com\/wm-prealgebra\/wp-json\/pressbooks\/v2\/chapters\/9484","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":10,"href":"https:\/\/courses.lumenlearning.com\/wm-prealgebra\/wp-json\/pressbooks\/v2\/chapters\/9484\/revisions"}],"predecessor-version":[{"id":15158,"href":"https:\/\/courses.lumenlearning.com\/wm-prealgebra\/wp-json\/pressbooks\/v2\/chapters\/9484\/revisions\/15158"}],"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\/9484\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/courses.lumenlearning.com\/wm-prealgebra\/wp-json\/wp\/v2\/media?parent=9484"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/wm-prealgebra\/wp-json\/pressbooks\/v2\/chapter-type?post=9484"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/wm-prealgebra\/wp-json\/wp\/v2\/contributor?post=9484"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/wm-prealgebra\/wp-json\/wp\/v2\/license?post=9484"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}