{"id":8591,"date":"2023-10-03T19:42:06","date_gmt":"2023-10-03T19:42:06","guid":{"rendered":"https:\/\/content.one.lumenlearning.com\/quantitativereasoning\/?post_type=chapter&#038;p=8591"},"modified":"2024-10-18T20:56:41","modified_gmt":"2024-10-18T20:56:41","slug":"calculations-involving-rational-numbers-learn-it-6","status":"web-only","type":"chapter","link":"https:\/\/content.one.lumenlearning.com\/quantitativereasoning\/chapter\/calculations-involving-rational-numbers-learn-it-6\/","title":{"raw":"Calculations Involving Rational Numbers: Learn It 6","rendered":"Calculations Involving Rational Numbers: Learn It 6"},"content":{"raw":"<h2>Converting Between Improper Fractions and Mixed Numbers<\/h2>\r\n<p>One way to visualize a fraction is as parts of a whole, as in [latex]\\frac{5}{12}[\/latex] of a pizza. But when the numerator is larger than the denominator, as in [latex]\\frac{23}{12}[\/latex], then the idea of parts of a whole seems not to make sense.<\/p>\r\n<p>Such a fraction is an <strong>improper fraction<\/strong>. That kind of fraction could be written as an integer plus a fraction, which is a <strong>mixed number<\/strong>. The fraction [latex]\\frac{23}{12}[\/latex] rewritten as a mixed number would be [latex]1\\frac{11}{12}[\/latex]. Arithmetically, [latex]1\\frac{11}{12}[\/latex] is equivalent to [latex]1 + \\frac{11}{12}[\/latex], which is read as \u201cone and 11 twelfths.\u201d<\/p>\r\n<p>Improper fractions can be rewritten as mixed numbers using division and remainders.<\/p>\r\n<section class=\"textbox questionHelp\">\r\n<p><b>How to: Convert Between Improper Fractions and Mixed Numbers<\/b><\/p>\r\n\r\n\r\nTo find the mixed number representation of an improper fraction, divide the numerator by the denominator. The quotient is the integer part, and the remainder becomes the numerator of the remaining fraction.<\/section>\r\n<section class=\"textbox example\">\r\n<p>Convert [latex]{\\Large\\frac{11}{6}}[\/latex] to a mixed number.<\/p>\r\n\r\n\r\n[reveal-answer q=\"160921\"]Show Solution[\/reveal-answer] [hidden-answer a=\"160921\"]\r\n\r\n\r\n<table id=\"eip-id1168469636042\" class=\"unnumbered unstyled\" style=\"width: 85%;\" summary=\"A division symbol is shown with an 11 on the inside. A 6 is on the outside and is labeled as the divisor. A 6 is below the 11. Below the 6 is a 5 that is labeled as the remainder. Above the division sign, a 1 is labeled as the quotient.\">\r\n<tbody>\r\n<tr>\r\n<td>&nbsp;<\/td>\r\n<td>[latex]{\\Large\\frac{11}{6}}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Divide the denominator into the numerator.<\/td>\r\n<td>Remember [latex]{\\Large\\frac{11}{6}}[\/latex] means [latex]11\\div 6[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>&nbsp;<\/td>\r\n<td><img src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24220740\/CNX_BMath_Figure_04_01_031_img-01.png\" alt=\".\" \/><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Identify the quotient, remainder and divisor.<\/td>\r\n<td>&nbsp;<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Write the mixed number as [latex]\\text{quotient }({\\Large\\frac{\\text{remainder}}{\\text{divisor}}})[\/latex] .<\/td>\r\n<td>[latex]1{\\Large\\frac{5}{6}}[\/latex]<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<p>&nbsp;<\/p>\r\n<p>So, [latex]{\\Large\\frac{11}{6}}=1{\\Large\\frac{5}{6}}[\/latex].<\/p>\r\n\r\n\r\n[\/hidden-answer]<\/section>\r\n<section class=\"textbox example\">\r\n<p>Rewrite [latex]\\frac{48}{13}[\/latex] as a mixed number.<\/p>\r\n\r\n\r\n[reveal-answer q=\"160936\"]Show Solution[\/reveal-answer] [hidden-answer a=\"160936\"] When [latex]48[\/latex] is divided by [latex]13[\/latex], the result is [latex]3[\/latex] with a remainder of [latex]9[\/latex]. So, we can rewrite [latex]\\frac{48}{13}[\/latex] as [latex]3\\frac{9}{13}[\/latex]. [\/hidden-answer]<\/section>\r\n<section class=\"textbox tryIt\">\r\n<p>[ohm2_question hide_question_numbers=1]12700[\/ohm2_question]<\/p>\r\n<\/section>\r\n<p>Similarly, we can convert a mixed number into an improper fraction.<\/p>\r\n<section class=\"textbox questionHelp\">\r\n<p><b>How to: Convert Between Mixed Numbers and Improper Fractions<br \/>\r\n<br \/>\r\n<\/b>To convert a mixed number to an improper fraction, first convert the whole number part to a fraction by writing the whole number as itself divided by [latex]1[\/latex], and then add the two fractions.<b><br \/>\r\n<\/b><\/p>\r\n<\/section>\r\n<p>Alternately, we can multiply the whole number part and the denominator of the fractional part. Next, add that product to the numerator. Finally, express the number as that product divided by the denominator.<\/p>\r\n<section class=\"textbox example\">\r\n<p>Convert the mixed number [latex]4{\\Large\\frac{2}{3}}[\/latex] to an improper fraction.<\/p>\r\n\r\n\r\n[reveal-answer q=\"486918\"]Show Solution[\/reveal-answer] [hidden-answer a=\"486918\"]\r\n\r\n\r\n<table id=\"eip-id1168466233262\" class=\"unnumbered unstyled\" style=\"width: 85%;\" summary=\"The mixed number 4 and 2 thirds is shown. The first step says, \">\r\n<tbody>\r\n<tr>\r\n<td>&nbsp;<\/td>\r\n<td>[latex]4{\\Large\\frac{2}{3}}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Multiply the whole number by the denominator.<\/td>\r\n<td>&nbsp;<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>The whole number is [latex]4[\/latex] and the denominator is [latex]3[\/latex].<\/td>\r\n<td><img src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24220743\/CNX_BMath_Figure_04_01_068_img-01.png\" alt=\".\" \/><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Simplify.<\/td>\r\n<td><img src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24220744\/CNX_BMath_Figure_04_01_068_img-02.png\" alt=\".\" \/><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Add the numerator to the product.<\/td>\r\n<td>&nbsp;<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>The numerator of the mixed number is [latex]2[\/latex].<\/td>\r\n<td><img src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24220745\/CNX_BMath_Figure_04_01_068_img-03.png\" alt=\".\" \/><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Simplify.<\/td>\r\n<td><img src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24220745\/CNX_BMath_Figure_04_01_068_img-04.png\" alt=\".\" \/><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Write the final sum over the original denominator. The denominator is [latex]3[\/latex].<\/td>\r\n<td>[latex]{\\Large\\frac{14}{3}}[\/latex]<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n\r\n\r\n[\/hidden-answer]<\/section>\r\n<section class=\"textbox example\">\r\n<p>Rewrite [latex]5\\frac{4}{9}[\/latex] as an improper fraction.<\/p>\r\n\r\n\r\n[reveal-answer q=\"160931\"]Show Solution[\/reveal-answer] [hidden-answer a=\"160931\"]\r\n\r\n\r\n<ul>\r\n\t<li><strong>Step 1:<\/strong> Multiply the integer part, [latex]5[\/latex], by the denominator, [latex]9[\/latex], which gives [latex]5\u00d79=45[\/latex].<\/li>\r\n\t<li><strong>Step 2:<\/strong> Add that product to the numerator, which gives [latex]45+4=49[\/latex].<\/li>\r\n\t<li><strong>Step 3:<\/strong> Write the number as the sum, [latex]49[\/latex], divided by the denominator, [latex]9[\/latex], which gives [latex]\\frac{49}{9}[\/latex].<\/li>\r\n<\/ul>\r\n\r\n\r\n[\/hidden-answer]<\/section>\r\n<section class=\"textbox tryIt\">\r\n<p>[ohm2_question hide_question_numbers=1]12701[\/ohm2_question]<\/p>\r\n<\/section>\r\n<section class=\"textbox proTip\">\r\n<p>Desmos can be used to convert from a mixed number to an improper fraction. To do so, we use the idea that a mixed number, such as [latex]5\\frac{6}{11}[\/latex], is another way to represent [latex]5+\\frac{6}{11}[\/latex].<\/p>\r\n<p>If [latex]5+\\frac{6}{11}[\/latex] is entered in Desmos, the result is the decimal form of the number. However, clicking the fraction button to the left will convert the decimal to an improper fraction, [latex]\\frac{61}{11}[\/latex]. <br \/>\r\n<br \/>\r\nAs an added bonus, Desmos will automatically reduce the fraction to lowest terms. For more on how to use Desmos to convert an improper fraction to a mixed number, <a href=\"https:\/\/www.youtube.com\/watch?v=M21fk_LtryU\" target=\"_blank\" rel=\"noopener\">watch this video.<\/a><\/p>\r\n<p>You can view the <a href=\"https:\/\/course-building.s3.us-west-2.amazonaws.com\/Quantitative+Reasoning+-+2023+Build\/Transcriptions\/Converting+Improper+Fractions+to+Mixed+Number+on+the+Desmos+Scientific+Calculator.txt\" target=\"_blank\" rel=\"noopener\">transcript for \u201cConverting Improper Fractions to Mixed Number on the Desmos Scientific Calculator\u201d here (opens in new window).<\/a><\/p>\r\n<\/section>","rendered":"<h2>Converting Between Improper Fractions and Mixed Numbers<\/h2>\n<p>One way to visualize a fraction is as parts of a whole, as in [latex]\\frac{5}{12}[\/latex] of a pizza. But when the numerator is larger than the denominator, as in [latex]\\frac{23}{12}[\/latex], then the idea of parts of a whole seems not to make sense.<\/p>\n<p>Such a fraction is an <strong>improper fraction<\/strong>. That kind of fraction could be written as an integer plus a fraction, which is a <strong>mixed number<\/strong>. The fraction [latex]\\frac{23}{12}[\/latex] rewritten as a mixed number would be [latex]1\\frac{11}{12}[\/latex]. Arithmetically, [latex]1\\frac{11}{12}[\/latex] is equivalent to [latex]1 + \\frac{11}{12}[\/latex], which is read as \u201cone and 11 twelfths.\u201d<\/p>\n<p>Improper fractions can be rewritten as mixed numbers using division and remainders.<\/p>\n<section class=\"textbox questionHelp\">\n<p><b>How to: Convert Between Improper Fractions and Mixed Numbers<\/b><\/p>\n<p>To find the mixed number representation of an improper fraction, divide the numerator by the denominator. The quotient is the integer part, and the remainder becomes the numerator of the remaining fraction.<\/section>\n<section class=\"textbox example\">\n<p>Convert [latex]{\\Large\\frac{11}{6}}[\/latex] to a mixed number.<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><button class=\"show-answer show-answer-button collapsed\" data-target=\"q160921\">Show Solution<\/button> <\/p>\n<div id=\"q160921\" class=\"hidden-answer\" style=\"display: none\">\n<table id=\"eip-id1168469636042\" class=\"unnumbered unstyled\" style=\"width: 85%;\" summary=\"A division symbol is shown with an 11 on the inside. A 6 is on the outside and is labeled as the divisor. A 6 is below the 11. Below the 6 is a 5 that is labeled as the remainder. Above the division sign, a 1 is labeled as the quotient.\">\n<tbody>\n<tr>\n<td>&nbsp;<\/td>\n<td>[latex]{\\Large\\frac{11}{6}}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Divide the denominator into the numerator.<\/td>\n<td>Remember [latex]{\\Large\\frac{11}{6}}[\/latex] means [latex]11\\div 6[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>&nbsp;<\/td>\n<td><img decoding=\"async\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24220740\/CNX_BMath_Figure_04_01_031_img-01.png\" alt=\".\" \/><\/td>\n<\/tr>\n<tr>\n<td>Identify the quotient, remainder and divisor.<\/td>\n<td>&nbsp;<\/td>\n<\/tr>\n<tr>\n<td>Write the mixed number as [latex]\\text{quotient }({\\Large\\frac{\\text{remainder}}{\\text{divisor}}})[\/latex] .<\/td>\n<td>[latex]1{\\Large\\frac{5}{6}}[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>&nbsp;<\/p>\n<p>So, [latex]{\\Large\\frac{11}{6}}=1{\\Large\\frac{5}{6}}[\/latex].<\/p>\n<\/div>\n<\/div>\n<\/section>\n<section class=\"textbox example\">\n<p>Rewrite [latex]\\frac{48}{13}[\/latex] as a mixed number.<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><button class=\"show-answer show-answer-button collapsed\" data-target=\"q160936\">Show Solution<\/button> <\/p>\n<div id=\"q160936\" class=\"hidden-answer\" style=\"display: none\"> When [latex]48[\/latex] is divided by [latex]13[\/latex], the result is [latex]3[\/latex] with a remainder of [latex]9[\/latex]. So, we can rewrite [latex]\\frac{48}{13}[\/latex] as [latex]3\\frac{9}{13}[\/latex]. <\/div>\n<\/div>\n<\/section>\n<section class=\"textbox tryIt\">\n<iframe loading=\"lazy\" id=\"ohm12700\" class=\"resizable\" src=\"https:\/\/ohm.one.lumenlearning.com\/multiembedq.php?id=12700&theme=lumen&iframe_resize_id=ohm12700&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><br \/>\n<\/section>\n<p>Similarly, we can convert a mixed number into an improper fraction.<\/p>\n<section class=\"textbox questionHelp\">\n<p><b>How to: Convert Between Mixed Numbers and Improper Fractions<\/p>\n<p><\/b>To convert a mixed number to an improper fraction, first convert the whole number part to a fraction by writing the whole number as itself divided by [latex]1[\/latex], and then add the two fractions.<b><br \/>\n<\/b><\/p>\n<\/section>\n<p>Alternately, we can multiply the whole number part and the denominator of the fractional part. Next, add that product to the numerator. Finally, express the number as that product divided by the denominator.<\/p>\n<section class=\"textbox example\">\n<p>Convert the mixed number [latex]4{\\Large\\frac{2}{3}}[\/latex] to an improper fraction.<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><button class=\"show-answer show-answer-button collapsed\" data-target=\"q486918\">Show Solution<\/button> <\/p>\n<div id=\"q486918\" class=\"hidden-answer\" style=\"display: none\">\n<table id=\"eip-id1168466233262\" class=\"unnumbered unstyled\" style=\"width: 85%;\" summary=\"The mixed number 4 and 2 thirds is shown. The first step says,\">\n<tbody>\n<tr>\n<td>&nbsp;<\/td>\n<td>[latex]4{\\Large\\frac{2}{3}}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Multiply the whole number by the denominator.<\/td>\n<td>&nbsp;<\/td>\n<\/tr>\n<tr>\n<td>The whole number is [latex]4[\/latex] and the denominator is [latex]3[\/latex].<\/td>\n<td><img decoding=\"async\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24220743\/CNX_BMath_Figure_04_01_068_img-01.png\" alt=\".\" \/><\/td>\n<\/tr>\n<tr>\n<td>Simplify.<\/td>\n<td><img decoding=\"async\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24220744\/CNX_BMath_Figure_04_01_068_img-02.png\" alt=\".\" \/><\/td>\n<\/tr>\n<tr>\n<td>Add the numerator to the product.<\/td>\n<td>&nbsp;<\/td>\n<\/tr>\n<tr>\n<td>The numerator of the mixed number is [latex]2[\/latex].<\/td>\n<td><img decoding=\"async\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24220745\/CNX_BMath_Figure_04_01_068_img-03.png\" alt=\".\" \/><\/td>\n<\/tr>\n<tr>\n<td>Simplify.<\/td>\n<td><img decoding=\"async\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24220745\/CNX_BMath_Figure_04_01_068_img-04.png\" alt=\".\" \/><\/td>\n<\/tr>\n<tr>\n<td>Write the final sum over the original denominator. The denominator is [latex]3[\/latex].<\/td>\n<td>[latex]{\\Large\\frac{14}{3}}[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/section>\n<section class=\"textbox example\">\n<p>Rewrite [latex]5\\frac{4}{9}[\/latex] as an improper fraction.<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><button class=\"show-answer show-answer-button collapsed\" data-target=\"q160931\">Show Solution<\/button> <\/p>\n<div id=\"q160931\" class=\"hidden-answer\" style=\"display: none\">\n<ul>\n<li><strong>Step 1:<\/strong> Multiply the integer part, [latex]5[\/latex], by the denominator, [latex]9[\/latex], which gives [latex]5\u00d79=45[\/latex].<\/li>\n<li><strong>Step 2:<\/strong> Add that product to the numerator, which gives [latex]45+4=49[\/latex].<\/li>\n<li><strong>Step 3:<\/strong> Write the number as the sum, [latex]49[\/latex], divided by the denominator, [latex]9[\/latex], which gives [latex]\\frac{49}{9}[\/latex].<\/li>\n<\/ul>\n<\/div>\n<\/div>\n<\/section>\n<section class=\"textbox tryIt\">\n<iframe loading=\"lazy\" id=\"ohm12701\" class=\"resizable\" src=\"https:\/\/ohm.one.lumenlearning.com\/multiembedq.php?id=12701&theme=lumen&iframe_resize_id=ohm12701&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><br \/>\n<\/section>\n<section class=\"textbox proTip\">\n<p>Desmos can be used to convert from a mixed number to an improper fraction. To do so, we use the idea that a mixed number, such as [latex]5\\frac{6}{11}[\/latex], is another way to represent [latex]5+\\frac{6}{11}[\/latex].<\/p>\n<p>If [latex]5+\\frac{6}{11}[\/latex] is entered in Desmos, the result is the decimal form of the number. However, clicking the fraction button to the left will convert the decimal to an improper fraction, [latex]\\frac{61}{11}[\/latex]. <\/p>\n<p>As an added bonus, Desmos will automatically reduce the fraction to lowest terms. For more on how to use Desmos to convert an improper fraction to a mixed number, <a href=\"https:\/\/www.youtube.com\/watch?v=M21fk_LtryU\" target=\"_blank\" rel=\"noopener\">watch this video.<\/a><\/p>\n<p>You can view the <a href=\"https:\/\/course-building.s3.us-west-2.amazonaws.com\/Quantitative+Reasoning+-+2023+Build\/Transcriptions\/Converting+Improper+Fractions+to+Mixed+Number+on+the+Desmos+Scientific+Calculator.txt\" target=\"_blank\" rel=\"noopener\">transcript for \u201cConverting Improper Fractions to Mixed Number on the Desmos Scientific Calculator\u201d here (opens in new window).<\/a><\/p>\n<\/section>\n","protected":false},"author":15,"menu_order":15,"template":"","meta":{"_candela_citation":"[{\"type\":\"original\",\"description\":\"Revision and Adaptation\",\"author\":\"\",\"organization\":\"Lumen Learning\",\"url\":\"\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"\"},{\"type\":\"cc-attribution\",\"description\":\"Prealgebra\",\"author\":\"Lynn Marecek & MaryAnne Anthony-Smith\",\"organization\":\"OpenStax\",\"url\":\"\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"Access for free at https:\/\/openstax.org\/books\/prealgebra\/pages\/1-introduction\"},{\"type\":\"cc-attribution\",\"description\":\"Contemporary Mathematics\",\"author\":\"Donna Kirk\",\"organization\":\"OpenStax\",\"url\":\"https:\/\/openstax.org\/books\/contemporary-mathematics\/pages\/3-4-rational-numbers\",\"project\":\"3.4 Rational Numbers\",\"license\":\"cc-by\",\"license_terms\":\"Access for free at https:\/\/openstax.org\/books\/contemporary-mathematics\/pages\/1-introduction\"}]","pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"part":53,"module-header":"learn_it","content_attributions":[{"type":"original","description":"Revision and Adaptation","author":"","organization":"Lumen Learning","url":"","project":"","license":"cc-by","license_terms":""},{"type":"cc-attribution","description":"Prealgebra","author":"Lynn Marecek & MaryAnne Anthony-Smith","organization":"OpenStax","url":"","project":"","license":"cc-by","license_terms":"Access for free at https:\/\/openstax.org\/books\/prealgebra\/pages\/1-introduction"},{"type":"cc-attribution","description":"Contemporary Mathematics","author":"Donna Kirk","organization":"OpenStax","url":"https:\/\/openstax.org\/books\/contemporary-mathematics\/pages\/3-4-rational-numbers","project":"3.4 Rational Numbers","license":"cc-by","license_terms":"Access for free at https:\/\/openstax.org\/books\/contemporary-mathematics\/pages\/1-introduction"}],"internal_book_links":[],"video_content":null,"cc_video_embed_content":{"cc_scripts":"","media_targets":[]},"try_it_collection":null,"_links":{"self":[{"href":"https:\/\/content.one.lumenlearning.com\/quantitativereasoning\/wp-json\/pressbooks\/v2\/chapters\/8591"}],"collection":[{"href":"https:\/\/content.one.lumenlearning.com\/quantitativereasoning\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/content.one.lumenlearning.com\/quantitativereasoning\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/quantitativereasoning\/wp-json\/wp\/v2\/users\/15"}],"version-history":[{"count":34,"href":"https:\/\/content.one.lumenlearning.com\/quantitativereasoning\/wp-json\/pressbooks\/v2\/chapters\/8591\/revisions"}],"predecessor-version":[{"id":14732,"href":"https:\/\/content.one.lumenlearning.com\/quantitativereasoning\/wp-json\/pressbooks\/v2\/chapters\/8591\/revisions\/14732"}],"part":[{"href":"https:\/\/content.one.lumenlearning.com\/quantitativereasoning\/wp-json\/pressbooks\/v2\/parts\/53"}],"metadata":[{"href":"https:\/\/content.one.lumenlearning.com\/quantitativereasoning\/wp-json\/pressbooks\/v2\/chapters\/8591\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/content.one.lumenlearning.com\/quantitativereasoning\/wp-json\/wp\/v2\/media?parent=8591"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/quantitativereasoning\/wp-json\/pressbooks\/v2\/chapter-type?post=8591"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/quantitativereasoning\/wp-json\/wp\/v2\/contributor?post=8591"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/quantitativereasoning\/wp-json\/wp\/v2\/license?post=8591"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}