{"id":4631,"date":"2020-04-21T00:19:12","date_gmt":"2020-04-21T00:19:12","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/mathforliberalartscorequisite\/chapter\/summary-review-topics-2\/"},"modified":"2023-03-23T00:02:15","modified_gmt":"2023-03-23T00:02:15","slug":"summary-review-topics-2","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/slcc-mathforliberalartscorequisite\/chapter\/summary-review-topics-2\/","title":{"raw":"Summary: Review Topics","rendered":"Summary: Review Topics"},"content":{"raw":"\n\n<h2>Key Concepts<\/h2>\n<ul>\n \t<li>Phrases such as <em>sum<\/em>,&nbsp;<em>increased by<\/em>, <em>difference<\/em>, <em>decreased by<\/em>, <em>of<\/em>, <em>an<\/em>d, etc. can be translated into mathematical operations and notation to help solve a problem.<\/li>\n \t<li>To add or subtract fractions, make sure they each have the same denominator first.<\/li>\n \t<li>When dividing fractions, use the phrase <em>keep-change-flip<\/em> to remind you to multiply the first fraction by the reciprocal of the second one.<\/li>\n \t<li>Just like the digits of a whole number increase to the left by powers of 10, the digits after the decimal on the right decrease by fractions of powers of ten.<\/li>\n \t<li>When using inequality symbols, the smaller side of the symbol faces the smaller number and the larger side faces the larger number.<\/li>\n \t<li>The product or quotient of two negative numbers or two positive numbers is always positive; the product or quotient of two differently signed numbers is always negative.<\/li>\n<\/ul>\n<h2>Key Expressions, Equations, and Inequalities<\/h2>\n<ul>\n \t<li>[latex]a=b[\/latex] is read as \"[latex]a[\/latex] is equal to [latex]b[\/latex].\"<\/li>\n \t<li>[latex]a\\neq b[\/latex] is read as \"[latex]a[\/latex] is not equal to [latex]b[\/latex].\"<\/li>\n \t<li>[latex]a\\gt b[\/latex] can be read \"[latex]a[\/latex] is greater than [latex]b[\/latex]\" or \"[latex]b[\/latex] is less than [latex]a[\/latex].\"<\/li>\n \t<li>A fraction is written [latex]\\dfrac{a}{b},[\/latex] where [latex]a[\/latex] and [latex]b[\/latex] are integers and [latex]b \\neq 0[\/latex]. In a fraction, [latex]a[\/latex] is called the numerator and [latex]b[\/latex] is called the denominator.<\/li>\n \t<li>The distributive property, [latex]a(b+c)=ab+ac[\/latex], represents the distribution of multiplication over addition or subtraction.<\/li>\n \t<li>The property of one states that any number, except zero, divided by itself is one. That is [latex]\\dfrac{a}{a}=1[\/latex], where [latex]a \\neq 0[\/latex].<\/li>\n \t<li>if [latex]a, \\text{ } b, \\text{ and } c[\/latex] are numbers such that [latex]b \\neq 0, \\text { } c \\neq 0,[\/latex] then [latex]\\dfrac{a}{b} = \\dfrac{a\\cdot c}{b\\cdot c}[\/latex].<\/li>\n \t<li>To multiply fractions,&nbsp;[latex] \\frac{a}{b}\\cdot \\frac{c}{d}=\\frac{a\\cdot c}{b\\cdot d}=\\frac{\\text{product of the numerators}}{\\text{product of the denominators}}[\/latex]<\/li>\n<\/ul>\n<h2>Glossary<\/h2>\n<dl>\n \t<dt><strong>absolute value<\/strong><\/dt>\n \t<dd>a number's distance from zero on the number line, which is always positive<\/dd>\n \t<dt><strong>constant<\/strong><\/dt>\n \t<dd>a number whose value always stays the same<\/dd>\n \t<dt><strong>distributive property<\/strong><\/dt>\n \t<dd>a number multiplying an expression inside of parentheses distributes to each term in the contained expression<\/dd>\n \t<dt><strong>equation<\/strong><\/dt>\n \t<dd>two expressions connected by an equal sign<\/dd>\n \t<dt><strong>equivalent fractions<\/strong><\/dt>\n \t<dd>fractions that have the same value<\/dd>\n \t<dt><strong>exponent<\/strong><\/dt>\n \t<dd>a number in a superscript position that tells how many times to multiply the base by itself<\/dd>\n \t<dt><strong>expression<\/strong><\/dt>\n \t<dd>a number, a variable, or a combination of numbers and variables and operation symbols<\/dd>\n \t<dt><strong>improper fraction<\/strong><\/dt>\n \t<dd>a fraction [latex]\\dfrac{a}{b}, \\text{ } b \\neq 0[\/latex] is proper if [latex]a \\lt b[\/latex], and is improper if [latex]a \\geq b.[\/latex]<\/dd>\n \t<dt><strong>inequality<\/strong><\/dt>\n \t<dd>two expressions connected by an inequality sign<\/dd>\n \t<dt><strong>integers<\/strong><\/dt>\n \t<dd>counting numbers like 1, 2, 3, ... including their opposites (negatives) and zero<\/dd>\n \t<dt><strong>like terms<\/strong><\/dt>\n \t<dd>terms where the variables match exactly (exponents included)<\/dd>\n \t<dt><strong>operators<\/strong><\/dt>\n \t<dd>symbols that represent arithmetic operations such as addition, subtraction, multiplication, and division<\/dd>\n<\/dl>\n<dl>\n \t<dt><strong>order of operations<\/strong><\/dt>\n \t<dd>the universally accepted order to perform operations when more than one is present in an expression, often represented by the acronym PEMDAS<\/dd>\n \t<dt><strong>real numbers<\/strong><\/dt>\n \t<dd>fractions, negative numbers, decimals, integers, square roots, and zero<\/dd>\n<dt><strong>reciprocal<\/strong><\/dt>\n \t<dd>two fractions are reciprocals if their product is [latex]1[\/latex]<\/dd>\n \t<dt><strong>simplified fraction<\/strong><\/dt>\n \t<dd>also called a reduced fraction, or a fraction in lowest terms, a fraction having no common factors in the numerator and denominator<\/dd>\n \t<dt><strong>term<\/strong><\/dt>\n \t<dd>a single number, variable, or a product or quotient of numbers and\/or variables<\/dd>\n \t<dt><strong>variable<\/strong><\/dt>\n \t<dd>a letter that represents a number or quantity whose value may change<\/dd>\n<\/dl>\n\n","rendered":"<h2>Key Concepts<\/h2>\n<ul>\n<li>Phrases such as <em>sum<\/em>,&nbsp;<em>increased by<\/em>, <em>difference<\/em>, <em>decreased by<\/em>, <em>of<\/em>, <em>an<\/em>d, etc. can be translated into mathematical operations and notation to help solve a problem.<\/li>\n<li>To add or subtract fractions, make sure they each have the same denominator first.<\/li>\n<li>When dividing fractions, use the phrase <em>keep-change-flip<\/em> to remind you to multiply the first fraction by the reciprocal of the second one.<\/li>\n<li>Just like the digits of a whole number increase to the left by powers of 10, the digits after the decimal on the right decrease by fractions of powers of ten.<\/li>\n<li>When using inequality symbols, the smaller side of the symbol faces the smaller number and the larger side faces the larger number.<\/li>\n<li>The product or quotient of two negative numbers or two positive numbers is always positive; the product or quotient of two differently signed numbers is always negative.<\/li>\n<\/ul>\n<h2>Key Expressions, Equations, and Inequalities<\/h2>\n<ul>\n<li>[latex]a=b[\/latex] is read as &#8220;[latex]a[\/latex] is equal to [latex]b[\/latex].&#8221;<\/li>\n<li>[latex]a\\neq b[\/latex] is read as &#8220;[latex]a[\/latex] is not equal to [latex]b[\/latex].&#8221;<\/li>\n<li>[latex]a\\gt b[\/latex] can be read &#8220;[latex]a[\/latex] is greater than [latex]b[\/latex]&#8221; or &#8220;[latex]b[\/latex] is less than [latex]a[\/latex].&#8221;<\/li>\n<li>A fraction is written [latex]\\dfrac{a}{b},[\/latex] where [latex]a[\/latex] and [latex]b[\/latex] are integers and [latex]b \\neq 0[\/latex]. In a fraction, [latex]a[\/latex] is called the numerator and [latex]b[\/latex] is called the denominator.<\/li>\n<li>The distributive property, [latex]a(b+c)=ab+ac[\/latex], represents the distribution of multiplication over addition or subtraction.<\/li>\n<li>The property of one states that any number, except zero, divided by itself is one. That is [latex]\\dfrac{a}{a}=1[\/latex], where [latex]a \\neq 0[\/latex].<\/li>\n<li>if [latex]a, \\text{ } b, \\text{ and } c[\/latex] are numbers such that [latex]b \\neq 0, \\text { } c \\neq 0,[\/latex] then [latex]\\dfrac{a}{b} = \\dfrac{a\\cdot c}{b\\cdot c}[\/latex].<\/li>\n<li>To multiply fractions,&nbsp;[latex]\\frac{a}{b}\\cdot \\frac{c}{d}=\\frac{a\\cdot c}{b\\cdot d}=\\frac{\\text{product of the numerators}}{\\text{product of the denominators}}[\/latex]<\/li>\n<\/ul>\n<h2>Glossary<\/h2>\n<dl>\n<dt><strong>absolute value<\/strong><\/dt>\n<dd>a number&#8217;s distance from zero on the number line, which is always positive<\/dd>\n<dt><strong>constant<\/strong><\/dt>\n<dd>a number whose value always stays the same<\/dd>\n<dt><strong>distributive property<\/strong><\/dt>\n<dd>a number multiplying an expression inside of parentheses distributes to each term in the contained expression<\/dd>\n<dt><strong>equation<\/strong><\/dt>\n<dd>two expressions connected by an equal sign<\/dd>\n<dt><strong>equivalent fractions<\/strong><\/dt>\n<dd>fractions that have the same value<\/dd>\n<dt><strong>exponent<\/strong><\/dt>\n<dd>a number in a superscript position that tells how many times to multiply the base by itself<\/dd>\n<dt><strong>expression<\/strong><\/dt>\n<dd>a number, a variable, or a combination of numbers and variables and operation symbols<\/dd>\n<dt><strong>improper fraction<\/strong><\/dt>\n<dd>a fraction [latex]\\dfrac{a}{b}, \\text{ } b \\neq 0[\/latex] is proper if [latex]a \\lt b[\/latex], and is improper if [latex]a \\geq b.[\/latex]<\/dd>\n<dt><strong>inequality<\/strong><\/dt>\n<dd>two expressions connected by an inequality sign<\/dd>\n<dt><strong>integers<\/strong><\/dt>\n<dd>counting numbers like 1, 2, 3, &#8230; including their opposites (negatives) and zero<\/dd>\n<dt><strong>like terms<\/strong><\/dt>\n<dd>terms where the variables match exactly (exponents included)<\/dd>\n<dt><strong>operators<\/strong><\/dt>\n<dd>symbols that represent arithmetic operations such as addition, subtraction, multiplication, and division<\/dd>\n<\/dl>\n<dl>\n<dt><strong>order of operations<\/strong><\/dt>\n<dd>the universally accepted order to perform operations when more than one is present in an expression, often represented by the acronym PEMDAS<\/dd>\n<dt><strong>real numbers<\/strong><\/dt>\n<dd>fractions, negative numbers, decimals, integers, square roots, and zero<\/dd>\n<dt><strong>reciprocal<\/strong><\/dt>\n<dd>two fractions are reciprocals if their product is [latex]1[\/latex]<\/dd>\n<dt><strong>simplified fraction<\/strong><\/dt>\n<dd>also called a reduced fraction, or a fraction in lowest terms, a fraction having no common factors in the numerator and denominator<\/dd>\n<dt><strong>term<\/strong><\/dt>\n<dd>a single number, variable, or a product or quotient of numbers and\/or variables<\/dd>\n<dt><strong>variable<\/strong><\/dt>\n<dd>a letter that represents a number or quantity whose value may change<\/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-4631\">\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>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":17533,"menu_order":11,"template":"","meta":{"_candela_citation":"[{\"type\":\"original\",\"description\":\"Revision and Adaptation\",\"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-4631","chapter","type-chapter","status-publish","hentry"],"part":4619,"_links":{"self":[{"href":"https:\/\/courses.lumenlearning.com\/slcc-mathforliberalartscorequisite\/wp-json\/pressbooks\/v2\/chapters\/4631","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\/17533"}],"version-history":[{"count":1,"href":"https:\/\/courses.lumenlearning.com\/slcc-mathforliberalartscorequisite\/wp-json\/pressbooks\/v2\/chapters\/4631\/revisions"}],"predecessor-version":[{"id":5397,"href":"https:\/\/courses.lumenlearning.com\/slcc-mathforliberalartscorequisite\/wp-json\/pressbooks\/v2\/chapters\/4631\/revisions\/5397"}],"part":[{"href":"https:\/\/courses.lumenlearning.com\/slcc-mathforliberalartscorequisite\/wp-json\/pressbooks\/v2\/parts\/4619"}],"metadata":[{"href":"https:\/\/courses.lumenlearning.com\/slcc-mathforliberalartscorequisite\/wp-json\/pressbooks\/v2\/chapters\/4631\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/courses.lumenlearning.com\/slcc-mathforliberalartscorequisite\/wp-json\/wp\/v2\/media?parent=4631"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/slcc-mathforliberalartscorequisite\/wp-json\/pressbooks\/v2\/chapter-type?post=4631"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/slcc-mathforliberalartscorequisite\/wp-json\/wp\/v2\/contributor?post=4631"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/slcc-mathforliberalartscorequisite\/wp-json\/wp\/v2\/license?post=4631"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}