{"id":1652,"date":"2021-08-26T18:53:44","date_gmt":"2021-08-26T18:53:44","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/introstatscorequisite\/?post_type=chapter&#038;p=1652"},"modified":"2022-02-01T20:03:10","modified_gmt":"2022-02-01T20:03:10","slug":"properties-of-real-numbers","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/introstatscorequisite\/chapter\/properties-of-real-numbers\/","title":{"raw":"Properties of Real Numbers","rendered":"Properties of Real Numbers"},"content":{"raw":"<div class=\"textbox learning-objectives\">\r\n<h3>Learning Objectives<\/h3>\r\n<ul>\r\n \t<li>Use properties of real numbers to simplify expressions<\/li>\r\n<\/ul>\r\n<\/div>\r\n<div class=\"textbox\">\r\n<h3>A General Note: Properties of Real Numbers<\/h3>\r\nThe following properties hold for real numbers <em>a<\/em>, <em>b<\/em>, and <em>c<\/em>.\r\n<table style=\"width: 70%;\" summary=\"A table with six rows and three columns. The first entry of the first row is blank while the remaining columns read: Addition and Multiplication. The first entry of the second row reads: Commutative Property. The second column entry reads a plus b equals b plus a. The third column entry reads a times b equals b times a. The first entry of the third row reads Associative Property. The second column entry reads: a plus the quantity b plus c in parenthesis equals the quantity a plus b in parenthesis plus c. The third column entry reads: a times the quantity b times c in parenthesis equals the quantity a times b in parenthesis times c. The first entry of the fourth row reads: Distributive Property. The second and third column are combined on this row and read: a times the quantity b plus c in parenthesis equals a times b plus a times c. The first entry in the fifth row reads: Identity Property. The second column entry reads: There exists a unique real number called the additive identity, 0, such that for any real number a, a + 0 = a. The third column entry reads: There exists a unique real number called the multiplicative inverse, 1, such that for any real number a, a times 1 equals a. The first entry in the sixth row reads: Inverse Property. The second column entry reads: Every real number a has an additive inverse, or opposite, denoted negative a such that, a plus negative a equals zero. The third column entry reads: Every nonzero real\">\r\n<tbody>\r\n<tr>\r\n<th><\/th>\r\n<th>Addition<\/th>\r\n<th>Multiplication<\/th>\r\n<\/tr>\r\n<\/tbody>\r\n<tbody>\r\n<tr>\r\n<td><strong>Commutative Property<\/strong><\/td>\r\n<td>[latex]a+b=b+a[\/latex]<\/td>\r\n<td>[latex]a\\cdot b=b\\cdot a[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td><strong>Associative Property<\/strong><\/td>\r\n<td>[latex]a+\\left(b+c\\right)=\\left(a+b\\right)+c[\/latex]<\/td>\r\n<td>[latex]a\\left(bc\\right)=\\left(ab\\right)c[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td><strong>Distributive Property<\/strong><\/td>\r\n<td>[latex]a\\cdot \\left(b+c\\right)=a\\cdot b+a\\cdot c[\/latex]<\/td>\r\n<td><\/td>\r\n<\/tr>\r\n<tr>\r\n<td><strong>Identity Property<\/strong><\/td>\r\n<td>There exists a unique real number called the additive identity, 0, such that, for any real number <em>a<\/em>\r\n<div style=\"text-align: center;\">[latex]a+0=a[\/latex]<\/div><\/td>\r\n<td>There exists a unique real number called the multiplicative identity, 1, such that, for any real number <em>a<\/em>\r\n<div style=\"text-align: center;\">[latex]a\\cdot 1=a[\/latex]<\/div><\/td>\r\n<\/tr>\r\n<tr>\r\n<td><strong>Inverse Property<\/strong><\/td>\r\n<td>Every real number a has an additive inverse, or opposite, denoted [latex]\u2013a[\/latex], such that\r\n<div style=\"text-align: center;\">[latex]a+\\left(-a\\right)=0[\/latex]<\/div><\/td>\r\n<td>Every nonzero real number <em>a<\/em> has a multiplicative inverse, or reciprocal, denoted [latex]\\Large\\frac{1}{a}[\/latex], such that\r\n<div style=\"text-align: center;\">[latex]a\\cdot \\left(\\Large\\frac{1}{a}\\normalsize\\right)=1[\/latex]<\/div><\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<\/div>\r\nThese properties allow us to simplify expressions. We simplify an expression by removing grouping symbols and combining like terms. <strong>Like terms<\/strong> have exactly the same variable factors. For example, [latex]3x[\/latex] and [latex]5x[\/latex] are like terms, because they each have exactly one factor of [latex]x[\/latex]. On the other hand, [latex]3x^2[\/latex] and [latex]5x[\/latex] are not like terms because [latex]3x^2[\/latex] has two factors of [latex]x[\/latex] while [latex]5x[\/latex] has just one factor of [latex]x[\/latex]. The constant factor in a term is called its <strong>coefficient<\/strong>. The coefficient of [latex]3x[\/latex] is [latex]3[\/latex]. The coefficient of [latex]5x[\/latex] is [latex]5[\/latex]. The distributive property lets us combine like terms by adding their coefficients.\r\n<p style=\"text-align: center;\">[latex]3x+5x=(3+5)x=8x[\/latex]<\/p>\r\n\r\n<div class=\"textbox exercises\">\r\n<h3>Example<\/h3>\r\nSimplify each expression.\r\n<ol style=\"list-style-type: lower-alpha;\">\r\n \t<li>[latex]3x+5+4x-1[\/latex]<\/li>\r\n \t<li>[latex]2x+3(5x-2)[\/latex]<\/li>\r\n<\/ol>\r\n[reveal-answer q=\"75545\"]Show Answer[\/reveal-answer]\r\n[hidden-answer a=\"75545\"]\r\n<ol style=\"list-style-type: lower-alpha;\">\r\n \t<li>[latex]3x+5+4x-1[\/latex]\r\n<ul>\r\n \t<li>[latex]=3x+5+4x+(-1)[\/latex] (Subtracting [latex]1[\/latex] is the same as adding [latex]-1[\/latex])<\/li>\r\n \t<li>[latex]=3x+4x+5+(-1)[\/latex] (Commutative Property of Addition)<\/li>\r\n \t<li>[latex]=(3+4)x+4[\/latex] (Distributive Property; add [latex]5[\/latex] and [latex]-1[\/latex])<\/li>\r\n \t<li>[latex]=7x+4[\/latex]<\/li>\r\n<\/ul>\r\n<\/li>\r\n \t<li>To simplify the expression [latex]2x+3(5x-2)[\/latex] we first remove the grouping symbol using the distributive property.\r\n<ul>\r\n \t<li>[latex]2x+3(5x-2)[\/latex]<\/li>\r\n \t<li>[latex]=2x+15x-6[\/latex]<\/li>\r\n \t<li>[latex]=(2+15)x-6[\/latex]<\/li>\r\n \t<li>[latex]=17x-6[\/latex]<\/li>\r\n<\/ul>\r\n<\/li>\r\n<\/ol>\r\n[\/hidden-answer]\r\n\r\n<\/div>\r\nIn the following video you will be shown how to combine like terms using the idea of the distributive property.\r\n\r\nhttps:\/\/youtu.be\/JIleqbO8Tf0\r\n<div class=\"textbox exercises\">\r\n<h3>Example<\/h3>\r\nCombine like terns:\r\n<p style=\"text-align: center;\">[latex]3x^2-5x-2+x^2+7x-3[\/latex]<\/p>\r\n[reveal-answer q=\"356133\"]Show Answer[\/reveal-answer]\r\n[hidden-answer a=\"356133\"]\r\n\r\nThe like terms in this expression are:\r\n<p style=\"text-align: center;\">[latex]3x^2[\/latex] and [latex]x^2[\/latex]<\/p>\r\n<p style=\"text-align: center;\">[latex]-5x[\/latex] and [latex]7x[\/latex]<\/p>\r\n<p style=\"text-align: center;\">[latex]2[\/latex] and [latex]-3[\/latex]<\/p>\r\nWe can use the commutative property to rearrange the terms so that like terms are next to each other. Since subtraction is the same as adding a negative, we can move terms we are subtracting as long as we keep the sign with the term. If a term does not have a coefficient, the multiplication identity property tells us we can give it a coefficient [latex]1[\/latex].\r\n<p style=\"text-align: center;\">[latex]3x^2-5x+2+x^2+7x-3[\/latex]<\/p>\r\n<p style=\"text-align: center;\">[latex]=3x^2+1x^2-5x+7x+2-3[\/latex]<\/p>\r\nCombine like terms to obtain the simplified expression:\r\n<p style=\"text-align: center;\">[latex]4x^2+2x-1[\/latex]<\/p>\r\n[\/hidden-answer]\r\n\r\n<\/div>\r\nIn the video that follows, you will be shown another example of combining like terms.\r\n\r\nhttps:\/\/youtu.be\/b9-7eu29pNM","rendered":"<div class=\"textbox learning-objectives\">\n<h3>Learning Objectives<\/h3>\n<ul>\n<li>Use properties of real numbers to simplify expressions<\/li>\n<\/ul>\n<\/div>\n<div class=\"textbox\">\n<h3>A General Note: Properties of Real Numbers<\/h3>\n<p>The following properties hold for real numbers <em>a<\/em>, <em>b<\/em>, and <em>c<\/em>.<\/p>\n<table style=\"width: 70%;\" summary=\"A table with six rows and three columns. The first entry of the first row is blank while the remaining columns read: Addition and Multiplication. The first entry of the second row reads: Commutative Property. The second column entry reads a plus b equals b plus a. The third column entry reads a times b equals b times a. The first entry of the third row reads Associative Property. The second column entry reads: a plus the quantity b plus c in parenthesis equals the quantity a plus b in parenthesis plus c. The third column entry reads: a times the quantity b times c in parenthesis equals the quantity a times b in parenthesis times c. The first entry of the fourth row reads: Distributive Property. The second and third column are combined on this row and read: a times the quantity b plus c in parenthesis equals a times b plus a times c. The first entry in the fifth row reads: Identity Property. The second column entry reads: There exists a unique real number called the additive identity, 0, such that for any real number a, a + 0 = a. The third column entry reads: There exists a unique real number called the multiplicative inverse, 1, such that for any real number a, a times 1 equals a. The first entry in the sixth row reads: Inverse Property. The second column entry reads: Every real number a has an additive inverse, or opposite, denoted negative a such that, a plus negative a equals zero. The third column entry reads: Every nonzero real\">\n<tbody>\n<tr>\n<th><\/th>\n<th>Addition<\/th>\n<th>Multiplication<\/th>\n<\/tr>\n<\/tbody>\n<tbody>\n<tr>\n<td><strong>Commutative Property<\/strong><\/td>\n<td>[latex]a+b=b+a[\/latex]<\/td>\n<td>[latex]a\\cdot b=b\\cdot a[\/latex]<\/td>\n<\/tr>\n<tr>\n<td><strong>Associative Property<\/strong><\/td>\n<td>[latex]a+\\left(b+c\\right)=\\left(a+b\\right)+c[\/latex]<\/td>\n<td>[latex]a\\left(bc\\right)=\\left(ab\\right)c[\/latex]<\/td>\n<\/tr>\n<tr>\n<td><strong>Distributive Property<\/strong><\/td>\n<td>[latex]a\\cdot \\left(b+c\\right)=a\\cdot b+a\\cdot c[\/latex]<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td><strong>Identity Property<\/strong><\/td>\n<td>There exists a unique real number called the additive identity, 0, such that, for any real number <em>a<\/em><\/p>\n<div style=\"text-align: center;\">[latex]a+0=a[\/latex]<\/div>\n<\/td>\n<td>There exists a unique real number called the multiplicative identity, 1, such that, for any real number <em>a<\/em><\/p>\n<div style=\"text-align: center;\">[latex]a\\cdot 1=a[\/latex]<\/div>\n<\/td>\n<\/tr>\n<tr>\n<td><strong>Inverse Property<\/strong><\/td>\n<td>Every real number a has an additive inverse, or opposite, denoted [latex]\u2013a[\/latex], such that<\/p>\n<div style=\"text-align: center;\">[latex]a+\\left(-a\\right)=0[\/latex]<\/div>\n<\/td>\n<td>Every nonzero real number <em>a<\/em> has a multiplicative inverse, or reciprocal, denoted [latex]\\Large\\frac{1}{a}[\/latex], such that<\/p>\n<div style=\"text-align: center;\">[latex]a\\cdot \\left(\\Large\\frac{1}{a}\\normalsize\\right)=1[\/latex]<\/div>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<p>These properties allow us to simplify expressions. We simplify an expression by removing grouping symbols and combining like terms. <strong>Like terms<\/strong> have exactly the same variable factors. For example, [latex]3x[\/latex] and [latex]5x[\/latex] are like terms, because they each have exactly one factor of [latex]x[\/latex]. On the other hand, [latex]3x^2[\/latex] and [latex]5x[\/latex] are not like terms because [latex]3x^2[\/latex] has two factors of [latex]x[\/latex] while [latex]5x[\/latex] has just one factor of [latex]x[\/latex]. The constant factor in a term is called its <strong>coefficient<\/strong>. The coefficient of [latex]3x[\/latex] is [latex]3[\/latex]. The coefficient of [latex]5x[\/latex] is [latex]5[\/latex]. The distributive property lets us combine like terms by adding their coefficients.<\/p>\n<p style=\"text-align: center;\">[latex]3x+5x=(3+5)x=8x[\/latex]<\/p>\n<div class=\"textbox exercises\">\n<h3>Example<\/h3>\n<p>Simplify each expression.<\/p>\n<ol style=\"list-style-type: lower-alpha;\">\n<li>[latex]3x+5+4x-1[\/latex]<\/li>\n<li>[latex]2x+3(5x-2)[\/latex]<\/li>\n<\/ol>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q75545\">Show Answer<\/span><\/p>\n<div id=\"q75545\" class=\"hidden-answer\" style=\"display: none\">\n<ol style=\"list-style-type: lower-alpha;\">\n<li>[latex]3x+5+4x-1[\/latex]\n<ul>\n<li>[latex]=3x+5+4x+(-1)[\/latex] (Subtracting [latex]1[\/latex] is the same as adding [latex]-1[\/latex])<\/li>\n<li>[latex]=3x+4x+5+(-1)[\/latex] (Commutative Property of Addition)<\/li>\n<li>[latex]=(3+4)x+4[\/latex] (Distributive Property; add [latex]5[\/latex] and [latex]-1[\/latex])<\/li>\n<li>[latex]=7x+4[\/latex]<\/li>\n<\/ul>\n<\/li>\n<li>To simplify the expression [latex]2x+3(5x-2)[\/latex] we first remove the grouping symbol using the distributive property.\n<ul>\n<li>[latex]2x+3(5x-2)[\/latex]<\/li>\n<li>[latex]=2x+15x-6[\/latex]<\/li>\n<li>[latex]=(2+15)x-6[\/latex]<\/li>\n<li>[latex]=17x-6[\/latex]<\/li>\n<\/ul>\n<\/li>\n<\/ol>\n<\/div>\n<\/div>\n<\/div>\n<p>In the following video you will be shown how to combine like terms using the idea of the distributive property.<\/p>\n<p><iframe loading=\"lazy\" id=\"oembed-1\" title=\"Ex 1:  Combining Like Terms\" width=\"500\" height=\"281\" src=\"https:\/\/www.youtube.com\/embed\/JIleqbO8Tf0?feature=oembed&#38;rel=0\" frameborder=\"0\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/p>\n<div class=\"textbox exercises\">\n<h3>Example<\/h3>\n<p>Combine like terns:<\/p>\n<p style=\"text-align: center;\">[latex]3x^2-5x-2+x^2+7x-3[\/latex]<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q356133\">Show Answer<\/span><\/p>\n<div id=\"q356133\" class=\"hidden-answer\" style=\"display: none\">\n<p>The like terms in this expression are:<\/p>\n<p style=\"text-align: center;\">[latex]3x^2[\/latex] and [latex]x^2[\/latex]<\/p>\n<p style=\"text-align: center;\">[latex]-5x[\/latex] and [latex]7x[\/latex]<\/p>\n<p style=\"text-align: center;\">[latex]2[\/latex] and [latex]-3[\/latex]<\/p>\n<p>We can use the commutative property to rearrange the terms so that like terms are next to each other. Since subtraction is the same as adding a negative, we can move terms we are subtracting as long as we keep the sign with the term. If a term does not have a coefficient, the multiplication identity property tells us we can give it a coefficient [latex]1[\/latex].<\/p>\n<p style=\"text-align: center;\">[latex]3x^2-5x+2+x^2+7x-3[\/latex]<\/p>\n<p style=\"text-align: center;\">[latex]=3x^2+1x^2-5x+7x+2-3[\/latex]<\/p>\n<p>Combine like terms to obtain the simplified expression:<\/p>\n<p style=\"text-align: center;\">[latex]4x^2+2x-1[\/latex]<\/p>\n<\/div>\n<\/div>\n<\/div>\n<p>In the video that follows, you will be shown another example of combining like terms.<\/p>\n<p><iframe loading=\"lazy\" id=\"oembed-2\" title=\"Ex 2:  Combining Like Terms\" width=\"500\" height=\"281\" src=\"https:\/\/www.youtube.com\/embed\/b9-7eu29pNM?feature=oembed&#38;rel=0\" frameborder=\"0\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/p>\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-1652\">\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>Revision and Adaptation. <strong>Provided 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, Shared previously<\/div><ul class=\"citation-list\"><li>Ex 1: Combining Like Terms. <strong>Authored by<\/strong>: James Sousa (Mathispower4u.com). <strong>Located at<\/strong>: <a target=\"_blank\" href=\"https:\/\/youtu.be\/JIleqbO8Tf0\">https:\/\/youtu.be\/JIleqbO8Tf0<\/a>. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/licenses\/by\/4.0\/\">CC BY: Attribution<\/a><\/em><\/li><li>Ex 2: Combining Like Terms. <strong>Authored by<\/strong>: James Sousa (Mathispower4u.com). <strong>Located at<\/strong>: <a target=\"_blank\" href=\"https:\/\/youtu.be\/b9-7eu29pNM\">https:\/\/youtu.be\/b9-7eu29pNM<\/a>. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/licenses\/by\/4.0\/\">CC BY: Attribution<\/a><\/em><\/li><li>Unit 9: Real Numbers, from Developmental Math: An Open Program. <strong>Provided by<\/strong>: Monterey Institute of Technology and Education. <strong>Located at<\/strong>: <a target=\"_blank\" href=\"http:\/\/nrocnetwork.org\/dm-opentext\">http:\/\/nrocnetwork.org\/dm-opentext<\/a>. <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>College Algebra: Using Properties of Real Numbers. <strong>Located at<\/strong>: <a target=\"_blank\" href=\"https:\/\/courses.lumenlearning.com\/waymakerintermediatealgebra\/chapter\/read-use-properties-of-real-numbers\/\">https:\/\/courses.lumenlearning.com\/waymakerintermediatealgebra\/chapter\/read-use-properties-of-real-numbers\/<\/a>. <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>\n\t\t\t\t\t\t <\/div>\n\t\t\t\t\t <\/div>\n\t\t\t <\/section>","protected":false},"author":169134,"menu_order":3,"template":"","meta":{"_candela_citation":"[{\"type\":\"cc-attribution\",\"description\":\"College Algebra: Using Properties of Real Numbers\",\"author\":\"\",\"organization\":\"\",\"url\":\"https:\/\/courses.lumenlearning.com\/waymakerintermediatealgebra\/chapter\/read-use-properties-of-real-numbers\/\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"\"},{\"type\":\"original\",\"description\":\"Revision and Adaptation\",\"author\":\"\",\"organization\":\"Lumen Learning\",\"url\":\"\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"\"},{\"type\":\"cc\",\"description\":\"Ex 1: Combining Like Terms\",\"author\":\"James Sousa (Mathispower4u.com)\",\"organization\":\"\",\"url\":\"https:\/\/youtu.be\/JIleqbO8Tf0\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"\"},{\"type\":\"cc\",\"description\":\"Ex 2: Combining Like Terms\",\"author\":\"James Sousa (Mathispower4u.com)\",\"organization\":\"\",\"url\":\"https:\/\/youtu.be\/b9-7eu29pNM\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"\"},{\"type\":\"cc\",\"description\":\"Unit 9: Real Numbers, from Developmental Math: An Open Program\",\"author\":\"\",\"organization\":\"Monterey Institute of Technology and Education\",\"url\":\"http:\/\/nrocnetwork.org\/dm-opentext\",\"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-1652","chapter","type-chapter","status-publish","hentry"],"part":256,"_links":{"self":[{"href":"https:\/\/courses.lumenlearning.com\/introstatscorequisite\/wp-json\/pressbooks\/v2\/chapters\/1652","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/courses.lumenlearning.com\/introstatscorequisite\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/courses.lumenlearning.com\/introstatscorequisite\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/introstatscorequisite\/wp-json\/wp\/v2\/users\/169134"}],"version-history":[{"count":19,"href":"https:\/\/courses.lumenlearning.com\/introstatscorequisite\/wp-json\/pressbooks\/v2\/chapters\/1652\/revisions"}],"predecessor-version":[{"id":3646,"href":"https:\/\/courses.lumenlearning.com\/introstatscorequisite\/wp-json\/pressbooks\/v2\/chapters\/1652\/revisions\/3646"}],"part":[{"href":"https:\/\/courses.lumenlearning.com\/introstatscorequisite\/wp-json\/pressbooks\/v2\/parts\/256"}],"metadata":[{"href":"https:\/\/courses.lumenlearning.com\/introstatscorequisite\/wp-json\/pressbooks\/v2\/chapters\/1652\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/courses.lumenlearning.com\/introstatscorequisite\/wp-json\/wp\/v2\/media?parent=1652"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/introstatscorequisite\/wp-json\/pressbooks\/v2\/chapter-type?post=1652"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/introstatscorequisite\/wp-json\/wp\/v2\/contributor?post=1652"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/introstatscorequisite\/wp-json\/wp\/v2\/license?post=1652"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}