{"id":3684,"date":"2020-01-29T03:12:16","date_gmt":"2020-01-29T03:12:16","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/mathforlibscoreq\/?post_type=chapter&#038;p=3684"},"modified":"2021-02-05T23:51:09","modified_gmt":"2021-02-05T23:51:09","slug":"using-the-identity-and-inverse-properties-of-addition-and-subtraction","status":"web-only","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/slcc-mathforliberalartscorequisite\/chapter\/using-the-identity-and-inverse-properties-of-addition-and-subtraction\/","title":{"raw":"Using the Identity and Inverse Properties of Addition and Subtraction","rendered":"Using the Identity and Inverse Properties of Addition and Subtraction"},"content":{"raw":"<div class=\"textbox learning-objectives\">\r\n<h3>Learning Outcomes<\/h3>\r\n<ul>\r\n \t<li>Identify the identity properties of multiplication and addition<\/li>\r\n \t<li>Use the inverse property of addition and multiplication to simplify expressions<\/li>\r\n<\/ul>\r\n<\/div>\r\n<h2>Recognize the Identity Properties of Addition and Multiplication<\/h2>\r\nWhat happens when we add zero to any number? Adding zero doesn\u2019t change the value. For this reason, we call [latex]0[\/latex] the additive identity.\r\n\r\nFor example,\r\n<p style=\"text-align: center\">[latex]\\begin{array}{ccccc}\\hfill 13+0\\hfill &amp; &amp; \\hfill -14+0\\hfill &amp; &amp; \\hfill 0+\\left(-3x\\right)\\hfill \\\\ \\hfill 13\\hfill &amp; &amp; \\hfill -14\\hfill &amp; &amp; \\hfill -3x\\hfill \\end{array}[\/latex]<\/p>\r\nWhat happens when you multiply any number by one? Multiplying by one doesn\u2019t change the value. So we call [latex]1[\/latex] the multiplicative identity.\r\n\r\nFor example,\r\n<p style=\"text-align: center\">[latex]\\begin{array}{ccccc}\\hfill 43\\cdot 1\\hfill &amp; &amp; \\hfill -27\\cdot 1\\hfill &amp; &amp; \\hfill 1\\cdot \\frac{6y}{5}\\hfill \\\\ \\hfill 43\\hfill &amp; &amp; \\hfill -27\\hfill &amp; &amp; \\hfill \\frac{6y}{5}\\hfill \\end{array}[\/latex]<\/p>\r\n\r\n<div class=\"textbox shaded\">\r\n<h3>Identity Properties<\/h3>\r\nThe I<strong>dentity Property of Addition<\/strong>: for any real number [latex]a[\/latex],\r\n<p style=\"text-align: center\">[latex]\\begin{array}{}\\\\ \\hfill a+0=a(0)+a=a\\hfill \\\\ \\hfill \\text{0 is called the}\\mathbf{\\text{ additive identity}}\\hfill \\end{array}[\/latex]<\/p>\r\nThe I<strong>dentity Property of Multiplication<\/strong>: for any real number [latex]a[\/latex]\r\n<p style=\"text-align: center\">[latex]\\begin{array}{c}\\hfill a\\cdot 1=a(1)\\cdot a=a\\hfill \\\\ \\hfill \\text{1 is called the}\\mathbf{\\text{ multiplicative identity}}\\hfill \\end{array}[\/latex]<\/p>\r\n\r\n<\/div>\r\n<div class=\"textbox exercises\">\r\n<h3>example<\/h3>\r\nIdentify whether each equation demonstrates the identity property of addition or multiplication.\r\n\r\n1. [latex]7+0=7[\/latex]\r\n2. [latex]-16\\left(1\\right)=-16[\/latex]\r\n\r\nSolution:\r\n<table id=\"eip-id1168468511337\" class=\"unnumbered unstyled\" style=\"width: 85%\" summary=\".\">\r\n<tbody>\r\n<tr>\r\n<td>1.<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>[latex]7+0=7[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>We are adding 0.<\/td>\r\n<td>We are using the identity property of addition.<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<table id=\"eip-id1168466094843\" class=\"unnumbered unstyled\" style=\"width: 85%\" summary=\".\">\r\n<tbody>\r\n<tr>\r\n<td>2.<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>[latex]-16\\left(1\\right)=-16[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>We are multiplying by 1.<\/td>\r\n<td>We are using the identity property of multiplication.<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<\/div>\r\n<div class=\"textbox key-takeaways\">\r\n<h3>try it<\/h3>\r\n[ohm_question]146481[\/ohm_question]\r\n\r\n<\/div>\r\n<h2>\u00a0Use the Inverse Properties of Addition and Multiplication<\/h2>\r\n<table id=\"eip-id1168468695527\" class=\"unnumbered unstyled\" style=\"width: 85%\" summary=\"The image has the question \">\r\n<tbody>\r\n<tr>\r\n<td colspan=\"2\">What number added to 5 gives the additive identity, 0?<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>[latex]5 + =0[\/latex]<\/td>\r\n<td>We know [latex]5+(\\color {red}{--5})=0[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td colspan=\"2\">What number added to \u22126 gives the additive identity, 0?<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>[latex]-6 + =0[\/latex]<\/td>\r\n<td>We know [latex]--6+\\color {red}{6}=0[\/latex]<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\nNotice that in each case, the missing number was the opposite of the number.\r\n\r\nWe call [latex]-a[\/latex] the additive inverse of [latex]a[\/latex]. The opposite of a number is its additive inverse. A number and its opposite add to [latex]0[\/latex], which is the additive identity.\r\n\r\nWhat number multiplied by [latex]\\Large\\frac{2}{3}[\/latex] gives the multiplicative identity, [latex]1?[\/latex] In other words, two-thirds times what results in [latex]1?[\/latex]\r\n<table id=\"eip-id1168466750224\" class=\"unnumbered unstyled\" style=\"width: 85%\" summary=\"The image shows the equation 2 thirds times blank space equal to 1. We know 2 thirds times 3 halves is 1.\">\r\n<tbody>\r\n<tr>\r\n<td>[latex]\\Large\\frac{2}{3}\\normalsize\\cdot =1[\/latex]<\/td>\r\n<td>We know [latex]\\Large\\frac{2}{3}\\normalsize\\cdot\\color{red}{\\Large\\frac{3}{2}}\\normalsize=1[\/latex]<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\nWhat number multiplied by [latex]2[\/latex] gives the multiplicative identity, [latex]1?[\/latex] In other words two times what results in [latex]1?[\/latex]\r\n<table id=\"eip-id1168466030782\" class=\"unnumbered unstyled\" style=\"width: 85%\" summary=\"The image shows the equation 2 times blank space equal to 1. We know 2 times 1 half is 1.\">\r\n<tbody>\r\n<tr>\r\n<td>[latex]2\\cdot =1[\/latex]<\/td>\r\n<td>We know [latex]2\\cdot\\color{red}{\\Large\\frac{1}{2}}\\normalsize=1[\/latex]<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\nNotice that in each case, the missing number was the reciprocal of the number.\r\n\r\nWe call [latex]\\Large\\frac{1}{a}[\/latex] the multiplicative inverse of [latex]a\\left(a\\ne 0\\right)\\text{.}[\/latex] The reciprocal of a number is its multiplicative inverse. A number and its reciprocal multiply to [latex]1[\/latex], which is the multiplicative identity.\r\n\r\nWe\u2019ll formally state the Inverse Properties here:\r\n<div class=\"textbox shaded\">\r\n<h3>Inverse Properties<\/h3>\r\n<strong>Inverse Property of Addition<\/strong> for any real number [latex]a[\/latex],\r\n<p style=\"text-align: center\">[latex]\\begin{array}{}\\\\ \\hfill a+\\left(-a\\right)=0\\hfill \\\\ \\hfill -a\\text{ is the}\\mathbf{\\text{ additive inverse }}\\text{of }a.\\hfill \\end{array}[\/latex]<\/p>\r\n<p style=\"text-align: left\"><strong>Inverse Property of Multiplication<\/strong> for any real number [latex]a\\ne 0[\/latex],<\/p>\r\n<p style=\"text-align: center\">[latex]\\begin{array}{}\\\\ \\\\ \\hfill a\\cdot \\frac{1}{a}=1\\hfill \\\\ \\hfill \\frac{1}{a}\\text{is the}\\mathbf{\\text{ multiplicative inverse }}\\text{of }a.\\hfill \\end{array}[\/latex]<\/p>\r\n\r\n<\/div>\r\n<div class=\"textbox exercises\">\r\n<h3>example<\/h3>\r\nFind the additive inverse of each expression:\r\n1. [latex]13[\/latex]\r\n2. [latex]-\\Large\\frac{5}{8}[\/latex]\r\n3. [latex]0.6[\/latex]\r\n[reveal-answer q=\"219788\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"219788\"]\r\n\r\nSolution:\r\nTo find the additive inverse, we find the opposite.\r\n1. The additive inverse of [latex]13[\/latex] is its opposite, [latex]-13[\/latex]\r\n2. The additive inverse of [latex]-\\Large\\frac{5}{8}[\/latex] is its opposite, [latex]\\Large\\frac{5}{8}[\/latex]\r\n3. The additive inverse of [latex]0.6[\/latex] is its opposite, [latex]-0.6[\/latex]\r\n\r\n[\/hidden-answer]\r\n\r\n<\/div>\r\n<div class=\"textbox key-takeaways\">\r\n<h3>try it<\/h3>\r\n[ohm_question]146482[\/ohm_question]\r\n\r\n<\/div>\r\n<div class=\"textbox exercises\">\r\n<h3>example<\/h3>\r\nFind the multiplicative inverse:\r\n1. [latex]9[\/latex]\r\n2. [latex]-\\Large\\frac{1}{9}[\/latex]\r\n3. [latex]0.9[\/latex]\r\n[reveal-answer q=\"16229\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"16229\"]\r\n\r\nSolution:\r\nTo find the multiplicative inverse, we find the reciprocal.\r\n1. The multiplicative inverse of [latex]9[\/latex] is its reciprocal, [latex]\\Large\\frac{1}{9}[\/latex]\r\n2. The multiplicative inverse of [latex]-\\Large\\frac{1}{9}[\/latex] is its reciprocal, [latex]-9[\/latex]\r\n3. To find the multiplicative inverse of [latex]0.9[\/latex], we first convert [latex]0.9[\/latex] to a fraction, [latex]\\Large\\frac{9}{10}[\/latex]. Then we find the reciprocal, [latex]\\Large\\frac{10}{9}[\/latex]\r\n\r\n[\/hidden-answer]\r\n\r\n<\/div>\r\n<div class=\"textbox key-takeaways\">\r\n<h3>try it<\/h3>\r\n[ohm_question]146483[\/ohm_question]\r\n\r\n[ohm_question]146519[\/ohm_question]\r\n\r\n[ohm_question]146520[\/ohm_question]\r\n\r\n<\/div>","rendered":"<div class=\"textbox learning-objectives\">\n<h3>Learning Outcomes<\/h3>\n<ul>\n<li>Identify the identity properties of multiplication and addition<\/li>\n<li>Use the inverse property of addition and multiplication to simplify expressions<\/li>\n<\/ul>\n<\/div>\n<h2>Recognize the Identity Properties of Addition and Multiplication<\/h2>\n<p>What happens when we add zero to any number? Adding zero doesn\u2019t change the value. For this reason, we call [latex]0[\/latex] the additive identity.<\/p>\n<p>For example,<\/p>\n<p style=\"text-align: center\">[latex]\\begin{array}{ccccc}\\hfill 13+0\\hfill & & \\hfill -14+0\\hfill & & \\hfill 0+\\left(-3x\\right)\\hfill \\\\ \\hfill 13\\hfill & & \\hfill -14\\hfill & & \\hfill -3x\\hfill \\end{array}[\/latex]<\/p>\n<p>What happens when you multiply any number by one? Multiplying by one doesn\u2019t change the value. So we call [latex]1[\/latex] the multiplicative identity.<\/p>\n<p>For example,<\/p>\n<p style=\"text-align: center\">[latex]\\begin{array}{ccccc}\\hfill 43\\cdot 1\\hfill & & \\hfill -27\\cdot 1\\hfill & & \\hfill 1\\cdot \\frac{6y}{5}\\hfill \\\\ \\hfill 43\\hfill & & \\hfill -27\\hfill & & \\hfill \\frac{6y}{5}\\hfill \\end{array}[\/latex]<\/p>\n<div class=\"textbox shaded\">\n<h3>Identity Properties<\/h3>\n<p>The I<strong>dentity Property of Addition<\/strong>: for any real number [latex]a[\/latex],<\/p>\n<p style=\"text-align: center\">[latex]\\begin{array}{}\\\\ \\hfill a+0=a(0)+a=a\\hfill \\\\ \\hfill \\text{0 is called the}\\mathbf{\\text{ additive identity}}\\hfill \\end{array}[\/latex]<\/p>\n<p>The I<strong>dentity Property of Multiplication<\/strong>: for any real number [latex]a[\/latex]<\/p>\n<p style=\"text-align: center\">[latex]\\begin{array}{c}\\hfill a\\cdot 1=a(1)\\cdot a=a\\hfill \\\\ \\hfill \\text{1 is called the}\\mathbf{\\text{ multiplicative identity}}\\hfill \\end{array}[\/latex]<\/p>\n<\/div>\n<div class=\"textbox exercises\">\n<h3>example<\/h3>\n<p>Identify whether each equation demonstrates the identity property of addition or multiplication.<\/p>\n<p>1. [latex]7+0=7[\/latex]<br \/>\n2. [latex]-16\\left(1\\right)=-16[\/latex]<\/p>\n<p>Solution:<\/p>\n<table id=\"eip-id1168468511337\" class=\"unnumbered unstyled\" style=\"width: 85%\" summary=\".\">\n<tbody>\n<tr>\n<td>1.<\/td>\n<\/tr>\n<tr>\n<td>[latex]7+0=7[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>We are adding 0.<\/td>\n<td>We are using the identity property of addition.<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<table id=\"eip-id1168466094843\" class=\"unnumbered unstyled\" style=\"width: 85%\" summary=\".\">\n<tbody>\n<tr>\n<td>2.<\/td>\n<\/tr>\n<tr>\n<td>[latex]-16\\left(1\\right)=-16[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>We are multiplying by 1.<\/td>\n<td>We are using the identity property of multiplication.<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<div class=\"textbox key-takeaways\">\n<h3>try it<\/h3>\n<p><iframe loading=\"lazy\" id=\"ohm146481\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=146481&theme=oea&iframe_resize_id=ohm146481&show_question_numbers\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<\/div>\n<h2>\u00a0Use the Inverse Properties of Addition and Multiplication<\/h2>\n<table id=\"eip-id1168468695527\" class=\"unnumbered unstyled\" style=\"width: 85%\" summary=\"The image has the question\">\n<tbody>\n<tr>\n<td colspan=\"2\">What number added to 5 gives the additive identity, 0?<\/td>\n<\/tr>\n<tr>\n<td>[latex]5 + =0[\/latex]<\/td>\n<td>We know [latex]5+(\\color {red}{--5})=0[\/latex]<\/td>\n<\/tr>\n<tr>\n<td colspan=\"2\">What number added to \u22126 gives the additive identity, 0?<\/td>\n<\/tr>\n<tr>\n<td>[latex]-6 + =0[\/latex]<\/td>\n<td>We know [latex]--6+\\color {red}{6}=0[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>Notice that in each case, the missing number was the opposite of the number.<\/p>\n<p>We call [latex]-a[\/latex] the additive inverse of [latex]a[\/latex]. The opposite of a number is its additive inverse. A number and its opposite add to [latex]0[\/latex], which is the additive identity.<\/p>\n<p>What number multiplied by [latex]\\Large\\frac{2}{3}[\/latex] gives the multiplicative identity, [latex]1?[\/latex] In other words, two-thirds times what results in [latex]1?[\/latex]<\/p>\n<table id=\"eip-id1168466750224\" class=\"unnumbered unstyled\" style=\"width: 85%\" summary=\"The image shows the equation 2 thirds times blank space equal to 1. We know 2 thirds times 3 halves is 1.\">\n<tbody>\n<tr>\n<td>[latex]\\Large\\frac{2}{3}\\normalsize\\cdot =1[\/latex]<\/td>\n<td>We know [latex]\\Large\\frac{2}{3}\\normalsize\\cdot\\color{red}{\\Large\\frac{3}{2}}\\normalsize=1[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>What number multiplied by [latex]2[\/latex] gives the multiplicative identity, [latex]1?[\/latex] In other words two times what results in [latex]1?[\/latex]<\/p>\n<table id=\"eip-id1168466030782\" class=\"unnumbered unstyled\" style=\"width: 85%\" summary=\"The image shows the equation 2 times blank space equal to 1. We know 2 times 1 half is 1.\">\n<tbody>\n<tr>\n<td>[latex]2\\cdot =1[\/latex]<\/td>\n<td>We know [latex]2\\cdot\\color{red}{\\Large\\frac{1}{2}}\\normalsize=1[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>Notice that in each case, the missing number was the reciprocal of the number.<\/p>\n<p>We call [latex]\\Large\\frac{1}{a}[\/latex] the multiplicative inverse of [latex]a\\left(a\\ne 0\\right)\\text{.}[\/latex] The reciprocal of a number is its multiplicative inverse. A number and its reciprocal multiply to [latex]1[\/latex], which is the multiplicative identity.<\/p>\n<p>We\u2019ll formally state the Inverse Properties here:<\/p>\n<div class=\"textbox shaded\">\n<h3>Inverse Properties<\/h3>\n<p><strong>Inverse Property of Addition<\/strong> for any real number [latex]a[\/latex],<\/p>\n<p style=\"text-align: center\">[latex]\\begin{array}{}\\\\ \\hfill a+\\left(-a\\right)=0\\hfill \\\\ \\hfill -a\\text{ is the}\\mathbf{\\text{ additive inverse }}\\text{of }a.\\hfill \\end{array}[\/latex]<\/p>\n<p style=\"text-align: left\"><strong>Inverse Property of Multiplication<\/strong> for any real number [latex]a\\ne 0[\/latex],<\/p>\n<p style=\"text-align: center\">[latex]\\begin{array}{}\\\\ \\\\ \\hfill a\\cdot \\frac{1}{a}=1\\hfill \\\\ \\hfill \\frac{1}{a}\\text{is the}\\mathbf{\\text{ multiplicative inverse }}\\text{of }a.\\hfill \\end{array}[\/latex]<\/p>\n<\/div>\n<div class=\"textbox exercises\">\n<h3>example<\/h3>\n<p>Find the additive inverse of each expression:<br \/>\n1. [latex]13[\/latex]<br \/>\n2. [latex]-\\Large\\frac{5}{8}[\/latex]<br \/>\n3. [latex]0.6[\/latex]<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q219788\">Show Solution<\/span><\/p>\n<div id=\"q219788\" class=\"hidden-answer\" style=\"display: none\">\n<p>Solution:<br \/>\nTo find the additive inverse, we find the opposite.<br \/>\n1. The additive inverse of [latex]13[\/latex] is its opposite, [latex]-13[\/latex]<br \/>\n2. The additive inverse of [latex]-\\Large\\frac{5}{8}[\/latex] is its opposite, [latex]\\Large\\frac{5}{8}[\/latex]<br \/>\n3. The additive inverse of [latex]0.6[\/latex] is its opposite, [latex]-0.6[\/latex]<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox key-takeaways\">\n<h3>try it<\/h3>\n<p><iframe loading=\"lazy\" id=\"ohm146482\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=146482&theme=oea&iframe_resize_id=ohm146482&show_question_numbers\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<\/div>\n<div class=\"textbox exercises\">\n<h3>example<\/h3>\n<p>Find the multiplicative inverse:<br \/>\n1. [latex]9[\/latex]<br \/>\n2. [latex]-\\Large\\frac{1}{9}[\/latex]<br \/>\n3. [latex]0.9[\/latex]<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q16229\">Show Solution<\/span><\/p>\n<div id=\"q16229\" class=\"hidden-answer\" style=\"display: none\">\n<p>Solution:<br \/>\nTo find the multiplicative inverse, we find the reciprocal.<br \/>\n1. The multiplicative inverse of [latex]9[\/latex] is its reciprocal, [latex]\\Large\\frac{1}{9}[\/latex]<br \/>\n2. The multiplicative inverse of [latex]-\\Large\\frac{1}{9}[\/latex] is its reciprocal, [latex]-9[\/latex]<br \/>\n3. To find the multiplicative inverse of [latex]0.9[\/latex], we first convert [latex]0.9[\/latex] to a fraction, [latex]\\Large\\frac{9}{10}[\/latex]. Then we find the reciprocal, [latex]\\Large\\frac{10}{9}[\/latex]<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox key-takeaways\">\n<h3>try it<\/h3>\n<p><iframe loading=\"lazy\" id=\"ohm146483\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=146483&theme=oea&iframe_resize_id=ohm146483&show_question_numbers\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<p><iframe loading=\"lazy\" id=\"ohm146519\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=146519&theme=oea&iframe_resize_id=ohm146519&show_question_numbers\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<p><iframe loading=\"lazy\" id=\"ohm146520\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=146520&theme=oea&iframe_resize_id=ohm146520&show_question_numbers\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<\/div>\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-3684\">\n\t\t\t\t\t\t\t <div class=\"licensing\"><div class=\"license-attribution-dropdown-subheading\">CC licensed content, Original<\/div><ul class=\"citation-list\"><li>Question ID 146520, 146519, 146483, 146482, 146481. <strong>Authored by<\/strong>: Lumen Learning. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/licenses\/by\/4.0\/\">CC BY: Attribution<\/a><\/em><\/li><\/ul><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":25777,"menu_order":10,"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\"},{\"type\":\"original\",\"description\":\"Question ID 146520, 146519, 146483, 146482, 146481\",\"author\":\"Lumen Learning\",\"organization\":\"\",\"url\":\"\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"\"}]","CANDELA_OUTCOMES_GUID":"","pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"class_list":["post-3684","chapter","type-chapter","status-web-only","hentry"],"part":159,"_links":{"self":[{"href":"https:\/\/courses.lumenlearning.com\/slcc-mathforliberalartscorequisite\/wp-json\/pressbooks\/v2\/chapters\/3684","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/courses.lumenlearning.com\/slcc-mathforliberalartscorequisite\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/courses.lumenlearning.com\/slcc-mathforliberalartscorequisite\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/slcc-mathforliberalartscorequisite\/wp-json\/wp\/v2\/users\/25777"}],"version-history":[{"count":1,"href":"https:\/\/courses.lumenlearning.com\/slcc-mathforliberalartscorequisite\/wp-json\/pressbooks\/v2\/chapters\/3684\/revisions"}],"predecessor-version":[{"id":3685,"href":"https:\/\/courses.lumenlearning.com\/slcc-mathforliberalartscorequisite\/wp-json\/pressbooks\/v2\/chapters\/3684\/revisions\/3685"}],"part":[{"href":"https:\/\/courses.lumenlearning.com\/slcc-mathforliberalartscorequisite\/wp-json\/pressbooks\/v2\/parts\/159"}],"metadata":[{"href":"https:\/\/courses.lumenlearning.com\/slcc-mathforliberalartscorequisite\/wp-json\/pressbooks\/v2\/chapters\/3684\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/courses.lumenlearning.com\/slcc-mathforliberalartscorequisite\/wp-json\/wp\/v2\/media?parent=3684"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/slcc-mathforliberalartscorequisite\/wp-json\/pressbooks\/v2\/chapter-type?post=3684"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/slcc-mathforliberalartscorequisite\/wp-json\/wp\/v2\/contributor?post=3684"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/slcc-mathforliberalartscorequisite\/wp-json\/wp\/v2\/license?post=3684"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}