{"id":3086,"date":"2019-10-23T14:04:06","date_gmt":"2019-10-23T14:04:06","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/mathforlibscoreq\/?post_type=chapter&#038;p=3086"},"modified":"2021-02-05T23:51:12","modified_gmt":"2021-02-05T23:51:12","slug":"review-topics-for-success-12","status":"web-only","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/slcc-mathforliberalartscorequisite\/chapter\/review-topics-for-success-12\/","title":{"raw":"Summary: Review Topics","rendered":"Summary: Review Topics"},"content":{"raw":"<h2>Key Equations<\/h2>\r\n<ul>\r\n \t<li style=\"list-style-type: none\">\r\n<ul>\r\n \t<li>[latex]a+b=b+a[\/latex] describes the commutative property of addition.<\/li>\r\n \t<li>[latex]a \\cdot b = b \\cdot a[\/latex] describes the commutative property of multiplication.<\/li>\r\n \t<li>[latex]\\left(a+b\\right)+c=a+\\left(b+c\\right)[\/latex] describes the associative property of addition.<\/li>\r\n \t<li>[latex]\\left(a \\cdot b\\right)\\cdot c=a\\cdot \\left(b\\cdot c\\right)[\/latex] describes the associative property of multiplication.<\/li>\r\n \t<li>[latex]a\\left(b \\pm c\\right)=ab \\pm ac[\/latex] describes the distributive property of multiplication over addition or subtraction.<\/li>\r\n \t<li>[latex]\\left(b \\pm c\\right)a=ba+ca[\/latex] describes use of the distributive property from the right by the commutative property of multiplication.<\/li>\r\n \t<li>[latex]a \\cdot 0=0[\/latex]<\/li>\r\n \t<li>[latex]\\dfrac{0}{a}=0[\/latex] for all real [latex]a\\neq 0[\/latex]<\/li>\r\n \t<li>[latex]\\dfrac{a}{0}[\/latex] is undefined for all real [latex]a[\/latex].<\/li>\r\n \t<li>[latex]a+0=a\\left(0\\right)+a=a[\/latex] describes the identity property of addition. [latex]0[\/latex] is called the <em>additive identity<\/em>.<\/li>\r\n \t<li>[latex]a\\cdot1=a\\left(1\\right) \\cdot a=a[\/latex] describes the identity property of multiplication. [latex]1[\/latex] is called the <em>multiplicative identity<\/em>.<\/li>\r\n \t<li>[latex]a+\\left(-a\\right)=0[\/latex] describes the inverse property of addition. [latex]-a[\/latex] is call the <em>additive inverse<\/em> of [latex]a[\/latex].<\/li>\r\n \t<li>[latex]a \\cdot \\dfrac{1}{a}=1[\/latex] describes the inverse property of multiplication. [latex]\\dfrac{1}{a}[\/latex] is called the <em>multiplicative inverse<\/em> of [latex]a[\/latex].<\/li>\r\n<\/ul>\r\n<\/li>\r\n<\/ul>\r\n<h2>Glossary<\/h2>\r\n<dl>\r\n \t<dt><strong>irrational number<\/strong><\/dt>\r\n \t<dd>a number that cannot be written as the ratio of two integers and whose decimal form neither terminates nor repeats<\/dd>\r\n \t<dt><strong>real numbers<\/strong><\/dt>\r\n \t<dd>the set of real numbers includes all rational numbers and all irrational numbers<\/dd>\r\n \t<dt><strong>rational number<\/strong><\/dt>\r\n \t<dd>a rational number is a number that can be written in the form [latex]\\dfrac{p}{q}[\/latex], where [latex]p[\/latex] and [latex]q[\/latex] are integers and [latex]q \\neq 0[\/latex]<\/dd>\r\n<\/dl>","rendered":"<h2>Key Equations<\/h2>\n<ul>\n<li style=\"list-style-type: none\">\n<ul>\n<li>[latex]a+b=b+a[\/latex] describes the commutative property of addition.<\/li>\n<li>[latex]a \\cdot b = b \\cdot a[\/latex] describes the commutative property of multiplication.<\/li>\n<li>[latex]\\left(a+b\\right)+c=a+\\left(b+c\\right)[\/latex] describes the associative property of addition.<\/li>\n<li>[latex]\\left(a \\cdot b\\right)\\cdot c=a\\cdot \\left(b\\cdot c\\right)[\/latex] describes the associative property of multiplication.<\/li>\n<li>[latex]a\\left(b \\pm c\\right)=ab \\pm ac[\/latex] describes the distributive property of multiplication over addition or subtraction.<\/li>\n<li>[latex]\\left(b \\pm c\\right)a=ba+ca[\/latex] describes use of the distributive property from the right by the commutative property of multiplication.<\/li>\n<li>[latex]a \\cdot 0=0[\/latex]<\/li>\n<li>[latex]\\dfrac{0}{a}=0[\/latex] for all real [latex]a\\neq 0[\/latex]<\/li>\n<li>[latex]\\dfrac{a}{0}[\/latex] is undefined for all real [latex]a[\/latex].<\/li>\n<li>[latex]a+0=a\\left(0\\right)+a=a[\/latex] describes the identity property of addition. [latex]0[\/latex] is called the <em>additive identity<\/em>.<\/li>\n<li>[latex]a\\cdot1=a\\left(1\\right) \\cdot a=a[\/latex] describes the identity property of multiplication. [latex]1[\/latex] is called the <em>multiplicative identity<\/em>.<\/li>\n<li>[latex]a+\\left(-a\\right)=0[\/latex] describes the inverse property of addition. [latex]-a[\/latex] is call the <em>additive inverse<\/em> of [latex]a[\/latex].<\/li>\n<li>[latex]a \\cdot \\dfrac{1}{a}=1[\/latex] describes the inverse property of multiplication. [latex]\\dfrac{1}{a}[\/latex] is called the <em>multiplicative inverse<\/em> of [latex]a[\/latex].<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<h2>Glossary<\/h2>\n<dl>\n<dt><strong>irrational number<\/strong><\/dt>\n<dd>a number that cannot be written as the ratio of two integers and whose decimal form neither terminates nor repeats<\/dd>\n<dt><strong>real numbers<\/strong><\/dt>\n<dd>the set of real numbers includes all rational numbers and all irrational numbers<\/dd>\n<dt><strong>rational number<\/strong><\/dt>\n<dd>a rational number is a number that can be written in the form [latex]\\dfrac{p}{q}[\/latex], where [latex]p[\/latex] and [latex]q[\/latex] are integers and [latex]q \\neq 0[\/latex]<\/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-3086\">\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><strong>Authored by<\/strong>: Deborah Devlin. <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>\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":12,"template":"","meta":{"_candela_citation":"[{\"type\":\"original\",\"description\":\"\",\"author\":\"Deborah Devlin\",\"organization\":\"Lumen Learning\",\"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-3086","chapter","type-chapter","status-web-only","hentry"],"part":159,"_links":{"self":[{"href":"https:\/\/courses.lumenlearning.com\/slcc-mathforliberalartscorequisite\/wp-json\/pressbooks\/v2\/chapters\/3086","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":5,"href":"https:\/\/courses.lumenlearning.com\/slcc-mathforliberalartscorequisite\/wp-json\/pressbooks\/v2\/chapters\/3086\/revisions"}],"predecessor-version":[{"id":5313,"href":"https:\/\/courses.lumenlearning.com\/slcc-mathforliberalartscorequisite\/wp-json\/pressbooks\/v2\/chapters\/3086\/revisions\/5313"}],"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\/3086\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/courses.lumenlearning.com\/slcc-mathforliberalartscorequisite\/wp-json\/wp\/v2\/media?parent=3086"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/slcc-mathforliberalartscorequisite\/wp-json\/pressbooks\/v2\/chapter-type?post=3086"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/slcc-mathforliberalartscorequisite\/wp-json\/wp\/v2\/contributor?post=3086"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/slcc-mathforliberalartscorequisite\/wp-json\/wp\/v2\/license?post=3086"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}