{"id":62,"date":"2021-06-04T00:04:43","date_gmt":"2021-06-04T00:04:43","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/uvu-introductoryalgebra\/chapter\/use-the-language-of-algebra\/"},"modified":"2023-11-30T17:47:27","modified_gmt":"2023-11-30T17:47:27","slug":"use-the-language-of-algebra","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/uvu-introductoryalgebra\/chapter\/use-the-language-of-algebra\/","title":{"raw":"3.1: Constants and Variables","rendered":"3.1: Constants and Variables"},"content":{"raw":"<div class=\"textbox learning-objectives\">\r\n<h3>Learning Outcomes<\/h3>\r\n<ul>\r\n \t<li>Use variables to represent unknown quantities in algebraic expressions<\/li>\r\n \t<li>Identify the variables and constants in an algebraic expression<\/li>\r\n \t<li>Use symbols and words to represent algebraic operations on variables and constants<\/li>\r\n<\/ul>\r\n<\/div>\r\n<div class=\"textbox key-takeaways\">\r\n<h3>Key words<\/h3>\r\n<ul>\r\n \t<li><strong>Constant<\/strong>: a number that never changes<\/li>\r\n \t<li><strong>Variable<\/strong>: a letter used as a stand-in for a number that can change<\/li>\r\n<\/ul>\r\n<\/div>\r\n<h2 data-type=\"title\">Using Variables and Algebraic Symbols<\/h2>\r\nGreg and Alex have the same birthday, but they were born in different years. This year Greg is [latex]20[\/latex] years old and Alex is [latex]23[\/latex], so Alex is [latex]3[\/latex] years older than Greg. When Greg was [latex]12[\/latex], Alex was [latex]15[\/latex]. When Greg is [latex]35[\/latex], Alex will be [latex]38[\/latex]. No matter what Greg\u2019s age is, Alex\u2019s age will always be [latex]3[\/latex] years more, right?\r\n\r\nIn the language of algebra, we say that Greg\u2019s age and Alex\u2019s age are variable and the three is a constant. The ages change, or vary, so age is a <em><strong>variable<\/strong><\/em>. The [latex]3[\/latex] years between them always stays the same, so the age difference is the <em><strong>constant<\/strong><\/em>.\r\n\r\nIn algebra, letters of the alphabet are used to represent variables. Suppose we call Greg\u2019s age [latex]g[\/latex]. Then we could use [latex]g+3[\/latex] to represent Alex\u2019s age. See the table below.\r\n<table style=\"width: 40%;\" summary=\"This table has five rows and two columns. The first row is a header row and is labeled \">\r\n<thead>\r\n<tr valign=\"top\">\r\n<th data-align=\"center\">Greg\u2019s age<\/th>\r\n<th data-align=\"center\">Alex\u2019s age<\/th>\r\n<\/tr>\r\n<\/thead>\r\n<tbody>\r\n<tr valign=\"top\">\r\n<td data-align=\"center\">[latex]12[\/latex]<\/td>\r\n<td data-align=\"center\">[latex]15[\/latex]<\/td>\r\n<\/tr>\r\n<tr valign=\"top\">\r\n<td data-align=\"center\">[latex]20[\/latex]<\/td>\r\n<td data-align=\"center\">[latex]23[\/latex]<\/td>\r\n<\/tr>\r\n<tr valign=\"top\">\r\n<td data-align=\"center\">[latex]35[\/latex]<\/td>\r\n<td data-align=\"center\">[latex]38[\/latex]<\/td>\r\n<\/tr>\r\n<tr valign=\"top\">\r\n<td data-align=\"center\">[latex]g[\/latex]<\/td>\r\n<td data-align=\"center\">[latex]g+3[\/latex]<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<div class=\"textbox shaded\">\r\n<h3>Variables and Constants<\/h3>\r\nA variable is a letter that represents a number or quantity whose value may change.\r\nA constant is a number whose value always stays the same.\r\n\r\n<\/div>\r\nTo write algebraically, we need some symbols as well as numbers and variables. There are several types of symbols we will be using. Earlier, we introduced the symbols for the four basic arithmetic operations: addition, subtraction, multiplication, and division. We will summarize them here, along with words we use for the operations and the result.\r\n<table class=\"unnumbered\" style=\"width: 95.227%;\" summary=\"This table has five rows and four columns. The first row is a header row. Each column is labeled accordingly: the first is labeled \" data-label=\"\">\r\n<thead>\r\n<tr valign=\"top\">\r\n<th style=\"width: 15.0087%;\" data-align=\"left\"><strong>Operation<\/strong><\/th>\r\n<th style=\"width: 21.2178%;\" data-align=\"left\"><strong>Notation<\/strong><\/th>\r\n<th style=\"width: 29.9201%;\" data-align=\"left\"><strong>Say:<\/strong><\/th>\r\n<th style=\"width: 135.075%;\" data-align=\"left\"><strong>The result is\u2026<\/strong><\/th>\r\n<\/tr>\r\n<\/thead>\r\n<tbody>\r\n<tr valign=\"top\">\r\n<td style=\"width: 15.0087%;\" data-align=\"left\">Addition<\/td>\r\n<td style=\"width: 21.2178%;\" data-align=\"left\">[latex]a+b[\/latex]<\/td>\r\n<td style=\"width: 29.9201%;\" data-align=\"left\">[latex]a\\text{ plus }b[\/latex]<\/td>\r\n<td style=\"width: 135.075%;\" data-align=\"left\">the sum of [latex]a[\/latex] and [latex]b[\/latex]<\/td>\r\n<\/tr>\r\n<tr valign=\"top\">\r\n<td style=\"width: 15.0087%;\" data-align=\"left\">Subtraction<\/td>\r\n<td style=\"width: 21.2178%;\" data-align=\"left\">[latex]a-b[\/latex]<\/td>\r\n<td style=\"width: 29.9201%;\" data-align=\"left\">[latex]a\\text{ minus }b[\/latex]<\/td>\r\n<td style=\"width: 135.075%;\" data-align=\"left\">the difference of [latex]a[\/latex] and [latex]b[\/latex]<\/td>\r\n<\/tr>\r\n<tr valign=\"top\">\r\n<td style=\"width: 15.0087%;\" data-align=\"left\">Multiplication<\/td>\r\n<td style=\"width: 21.2178%;\" data-align=\"left\">[latex]a\\cdot b,\\left(a\\right)\\left(b\\right),\\left(a\\right)b,a\\left(b\\right)[\/latex]<\/td>\r\n<td style=\"width: 29.9201%;\" data-align=\"left\">[latex]a\\text{ times }b[\/latex]<\/td>\r\n<td style=\"width: 135.075%;\" data-align=\"left\">The product of [latex]a[\/latex] and [latex]b[\/latex]<\/td>\r\n<\/tr>\r\n<tr valign=\"top\">\r\n<td style=\"width: 15.0087%;\" data-align=\"left\">Division<\/td>\r\n<td style=\"width: 21.2178%;\" data-align=\"left\">[latex]a\\div b,a\/b,\\frac{a}{b},b\\overline{)a}[\/latex]<\/td>\r\n<td style=\"width: 29.9201%;\" data-align=\"left\">[latex]a[\/latex] divided by [latex]b[\/latex]<\/td>\r\n<td style=\"width: 135.075%;\" data-align=\"left\">The quotient of [latex]a[\/latex] and [latex]b[\/latex]<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\nIn algebra, the cross symbol, [latex]\\times [\/latex], is no longer used to show multiplication because that symbol may cause confusion with the letter x, or variable [latex]x[\/latex]. Does 3xy mean [latex]3\\times y[\/latex] (three times [latex]y[\/latex] ) or [latex]3\\cdot x\\cdot y[\/latex] (three times [latex]x\\text{ times }y[\/latex] )? To make it clear to everyone, we use a center dot \u2022 or parentheses ( ) to represent multiplication in algebra.\r\n\r\nTranslating from words to algebra or vice versa is an important skill. When translating from symbolic form to words, or from words to symbolic form, pay attention to the words <strong><em data-effect=\"italics\">of<\/em><\/strong> or <strong><em data-effect=\"italics\">and<\/em><\/strong> to help find the numbers.\r\n<ul id=\"fs-id1969800\" data-labeled-item=\"true\">\r\n \t<li>The <em data-effect=\"italics\">sum\u00a0<\/em><strong><em data-effect=\"italics\">of<\/em><\/strong> [latex]5[\/latex] <strong><em data-effect=\"italics\">and<\/em><\/strong> [latex]3[\/latex] means addition, \u00a0[latex]5[\/latex] plus [latex]3[\/latex], which we write as [latex]5+3[\/latex].<\/li>\r\n \t<li>The <em data-effect=\"italics\">difference\u00a0<\/em><strong><em data-effect=\"italics\">of<\/em><\/strong> [latex]9[\/latex] <strong><em data-effect=\"italics\">and<\/em><\/strong> [latex]2[\/latex] means subtraction, \u00a0[latex]9[\/latex] minus [latex]2[\/latex], which we write as [latex]9 - 2[\/latex].<\/li>\r\n \t<li>The <em data-effect=\"italics\">product\u00a0<\/em><strong><em data-effect=\"italics\">of<\/em><\/strong> [latex]4[\/latex] <strong><em data-effect=\"italics\">and<\/em><\/strong> [latex]8[\/latex] means multiplication, \u00a0[latex]4[\/latex] times [latex]8[\/latex], which we can write as [latex]4 \\times 8 [\/latex].<\/li>\r\n \t<li>The <em data-effect=\"italics\">quotient\u00a0<\/em><strong><em data-effect=\"italics\">of<\/em><\/strong> [latex]20[\/latex] <strong><em data-effect=\"italics\">and<\/em><\/strong> [latex]5[\/latex] means division, divide [latex]20[\/latex] by [latex]5[\/latex], which we can write as [latex]20\\div 5[\/latex].<\/li>\r\n<\/ul>\r\n<div class=\"textbox exercises\">\r\n<h3>Exercises<\/h3>\r\nTranslate from algebra to words:\r\n<ol>\r\n \t<li>[latex]12+14[\/latex]<\/li>\r\n \t<li>[latex]\\left(30\\right)\\left(5\\right)[\/latex]<\/li>\r\n \t<li>[latex]64\\div 8[\/latex]<\/li>\r\n \t<li>[latex]x-y[\/latex]<\/li>\r\n<\/ol>\r\nSolution:\r\n<table class=\"unnumbered unstyled\" style=\"width: 40%;\" summary=\".\" data-label=\"\">\r\n<tbody>\r\n<tr style=\"height: 15.7812px;\">\r\n<td style=\"height: 15.7812px;\">1.<\/td>\r\n<\/tr>\r\n<tr style=\"height: 15px;\">\r\n<td style=\"height: 15px;\" data-align=\"center\">[latex]12+14[\/latex]<\/td>\r\n<\/tr>\r\n<tr style=\"height: 15px;\">\r\n<td style=\"height: 15px;\" data-align=\"center\">[latex]12[\/latex] plus [latex]14[\/latex]<\/td>\r\n<\/tr>\r\n<tr style=\"height: 15px;\">\r\n<td style=\"height: 15px;\" data-align=\"center\">the sum of twelve and fourteen<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<table style=\"width: 40%;\">\r\n<tbody>\r\n<tr>\r\n<td>2.<\/td>\r\n<\/tr>\r\n<tr>\r\n<td data-align=\"center\">[latex]\\left(30\\right)\\left(5\\right)[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td data-align=\"center\">[latex]30[\/latex] times [latex]5[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td data-align=\"center\">the product of thirty and five<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<table class=\"unnumbered unstyled\" style=\"width: 40%;\" summary=\".\" data-label=\"\">\r\n<tbody>\r\n<tr>\r\n<td>3.<\/td>\r\n<\/tr>\r\n<tr>\r\n<td data-align=\"center\">[latex]64\\div 8[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td data-align=\"center\">[latex]64[\/latex] divided by [latex]8[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td data-align=\"center\">the quotient of sixty-four and eight<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<table class=\"unnumbered unstyled\" style=\"width: 40%;\" summary=\".\" data-label=\"\">\r\n<tbody>\r\n<tr style=\"height: 15.5625px;\">\r\n<td style=\"height: 15.5625px;\">4.<\/td>\r\n<\/tr>\r\n<tr style=\"height: 15px;\">\r\n<td style=\"height: 15px;\" data-align=\"center\">[latex]x-y[\/latex]<\/td>\r\n<\/tr>\r\n<tr style=\"height: 15px;\">\r\n<td style=\"height: 15px;\" data-align=\"center\">[latex]x[\/latex] minus [latex]y[\/latex]<\/td>\r\n<\/tr>\r\n<tr style=\"height: 15px;\">\r\n<td style=\"height: 15px;\" data-align=\"center\">the difference of [latex]x[\/latex] and [latex]y[\/latex]<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<\/div>\r\n<div class=\"textbox key-takeaways\">\r\n<h3>TRY\u00a0IT<\/h3>\r\n<iframe id=\"mom1\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=144651&amp;theme=oea&amp;iframe_resize_id=mom1\" width=\"100%\" height=\"330\"><\/iframe>\r\n\r\n<iframe id=\"mom2\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=144652&amp;theme=oea&amp;iframe_resize_id=mom2\" width=\"100%\" height=\"250\"><\/iframe>\r\n\r\n<\/div>\r\nWhen two quantities have the same value, we say they are equal and connect them with an <strong><em data-effect=\"italics\">equals sign<\/em><\/strong>.","rendered":"<div class=\"textbox learning-objectives\">\n<h3>Learning Outcomes<\/h3>\n<ul>\n<li>Use variables to represent unknown quantities in algebraic expressions<\/li>\n<li>Identify the variables and constants in an algebraic expression<\/li>\n<li>Use symbols and words to represent algebraic operations on variables and constants<\/li>\n<\/ul>\n<\/div>\n<div class=\"textbox key-takeaways\">\n<h3>Key words<\/h3>\n<ul>\n<li><strong>Constant<\/strong>: a number that never changes<\/li>\n<li><strong>Variable<\/strong>: a letter used as a stand-in for a number that can change<\/li>\n<\/ul>\n<\/div>\n<h2 data-type=\"title\">Using Variables and Algebraic Symbols<\/h2>\n<p>Greg and Alex have the same birthday, but they were born in different years. This year Greg is [latex]20[\/latex] years old and Alex is [latex]23[\/latex], so Alex is [latex]3[\/latex] years older than Greg. When Greg was [latex]12[\/latex], Alex was [latex]15[\/latex]. When Greg is [latex]35[\/latex], Alex will be [latex]38[\/latex]. No matter what Greg\u2019s age is, Alex\u2019s age will always be [latex]3[\/latex] years more, right?<\/p>\n<p>In the language of algebra, we say that Greg\u2019s age and Alex\u2019s age are variable and the three is a constant. The ages change, or vary, so age is a <em><strong>variable<\/strong><\/em>. The [latex]3[\/latex] years between them always stays the same, so the age difference is the <em><strong>constant<\/strong><\/em>.<\/p>\n<p>In algebra, letters of the alphabet are used to represent variables. Suppose we call Greg\u2019s age [latex]g[\/latex]. Then we could use [latex]g+3[\/latex] to represent Alex\u2019s age. See the table below.<\/p>\n<table style=\"width: 40%;\" summary=\"This table has five rows and two columns. The first row is a header row and is labeled\">\n<thead>\n<tr valign=\"top\">\n<th data-align=\"center\">Greg\u2019s age<\/th>\n<th data-align=\"center\">Alex\u2019s age<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr valign=\"top\">\n<td data-align=\"center\">[latex]12[\/latex]<\/td>\n<td data-align=\"center\">[latex]15[\/latex]<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-align=\"center\">[latex]20[\/latex]<\/td>\n<td data-align=\"center\">[latex]23[\/latex]<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-align=\"center\">[latex]35[\/latex]<\/td>\n<td data-align=\"center\">[latex]38[\/latex]<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-align=\"center\">[latex]g[\/latex]<\/td>\n<td data-align=\"center\">[latex]g+3[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<div class=\"textbox shaded\">\n<h3>Variables and Constants<\/h3>\n<p>A variable is a letter that represents a number or quantity whose value may change.<br \/>\nA constant is a number whose value always stays the same.<\/p>\n<\/div>\n<p>To write algebraically, we need some symbols as well as numbers and variables. There are several types of symbols we will be using. Earlier, we introduced the symbols for the four basic arithmetic operations: addition, subtraction, multiplication, and division. We will summarize them here, along with words we use for the operations and the result.<\/p>\n<table class=\"unnumbered\" style=\"width: 95.227%;\" summary=\"This table has five rows and four columns. The first row is a header row. Each column is labeled accordingly: the first is labeled\" data-label=\"\">\n<thead>\n<tr valign=\"top\">\n<th style=\"width: 15.0087%;\" data-align=\"left\"><strong>Operation<\/strong><\/th>\n<th style=\"width: 21.2178%;\" data-align=\"left\"><strong>Notation<\/strong><\/th>\n<th style=\"width: 29.9201%;\" data-align=\"left\"><strong>Say:<\/strong><\/th>\n<th style=\"width: 135.075%;\" data-align=\"left\"><strong>The result is\u2026<\/strong><\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr valign=\"top\">\n<td style=\"width: 15.0087%;\" data-align=\"left\">Addition<\/td>\n<td style=\"width: 21.2178%;\" data-align=\"left\">[latex]a+b[\/latex]<\/td>\n<td style=\"width: 29.9201%;\" data-align=\"left\">[latex]a\\text{ plus }b[\/latex]<\/td>\n<td style=\"width: 135.075%;\" data-align=\"left\">the sum of [latex]a[\/latex] and [latex]b[\/latex]<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td style=\"width: 15.0087%;\" data-align=\"left\">Subtraction<\/td>\n<td style=\"width: 21.2178%;\" data-align=\"left\">[latex]a-b[\/latex]<\/td>\n<td style=\"width: 29.9201%;\" data-align=\"left\">[latex]a\\text{ minus }b[\/latex]<\/td>\n<td style=\"width: 135.075%;\" data-align=\"left\">the difference of [latex]a[\/latex] and [latex]b[\/latex]<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td style=\"width: 15.0087%;\" data-align=\"left\">Multiplication<\/td>\n<td style=\"width: 21.2178%;\" data-align=\"left\">[latex]a\\cdot b,\\left(a\\right)\\left(b\\right),\\left(a\\right)b,a\\left(b\\right)[\/latex]<\/td>\n<td style=\"width: 29.9201%;\" data-align=\"left\">[latex]a\\text{ times }b[\/latex]<\/td>\n<td style=\"width: 135.075%;\" data-align=\"left\">The product of [latex]a[\/latex] and [latex]b[\/latex]<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td style=\"width: 15.0087%;\" data-align=\"left\">Division<\/td>\n<td style=\"width: 21.2178%;\" data-align=\"left\">[latex]a\\div b,a\/b,\\frac{a}{b},b\\overline{)a}[\/latex]<\/td>\n<td style=\"width: 29.9201%;\" data-align=\"left\">[latex]a[\/latex] divided by [latex]b[\/latex]<\/td>\n<td style=\"width: 135.075%;\" data-align=\"left\">The quotient of [latex]a[\/latex] and [latex]b[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>In algebra, the cross symbol, [latex]\\times[\/latex], is no longer used to show multiplication because that symbol may cause confusion with the letter x, or variable [latex]x[\/latex]. Does 3xy mean [latex]3\\times y[\/latex] (three times [latex]y[\/latex] ) or [latex]3\\cdot x\\cdot y[\/latex] (three times [latex]x\\text{ times }y[\/latex] )? To make it clear to everyone, we use a center dot \u2022 or parentheses ( ) to represent multiplication in algebra.<\/p>\n<p>Translating from words to algebra or vice versa is an important skill. When translating from symbolic form to words, or from words to symbolic form, pay attention to the words <strong><em data-effect=\"italics\">of<\/em><\/strong> or <strong><em data-effect=\"italics\">and<\/em><\/strong> to help find the numbers.<\/p>\n<ul id=\"fs-id1969800\" data-labeled-item=\"true\">\n<li>The <em data-effect=\"italics\">sum\u00a0<\/em><strong><em data-effect=\"italics\">of<\/em><\/strong> [latex]5[\/latex] <strong><em data-effect=\"italics\">and<\/em><\/strong> [latex]3[\/latex] means addition, \u00a0[latex]5[\/latex] plus [latex]3[\/latex], which we write as [latex]5+3[\/latex].<\/li>\n<li>The <em data-effect=\"italics\">difference\u00a0<\/em><strong><em data-effect=\"italics\">of<\/em><\/strong> [latex]9[\/latex] <strong><em data-effect=\"italics\">and<\/em><\/strong> [latex]2[\/latex] means subtraction, \u00a0[latex]9[\/latex] minus [latex]2[\/latex], which we write as [latex]9 - 2[\/latex].<\/li>\n<li>The <em data-effect=\"italics\">product\u00a0<\/em><strong><em data-effect=\"italics\">of<\/em><\/strong> [latex]4[\/latex] <strong><em data-effect=\"italics\">and<\/em><\/strong> [latex]8[\/latex] means multiplication, \u00a0[latex]4[\/latex] times [latex]8[\/latex], which we can write as [latex]4 \\times 8[\/latex].<\/li>\n<li>The <em data-effect=\"italics\">quotient\u00a0<\/em><strong><em data-effect=\"italics\">of<\/em><\/strong> [latex]20[\/latex] <strong><em data-effect=\"italics\">and<\/em><\/strong> [latex]5[\/latex] means division, divide [latex]20[\/latex] by [latex]5[\/latex], which we can write as [latex]20\\div 5[\/latex].<\/li>\n<\/ul>\n<div class=\"textbox exercises\">\n<h3>Exercises<\/h3>\n<p>Translate from algebra to words:<\/p>\n<ol>\n<li>[latex]12+14[\/latex]<\/li>\n<li>[latex]\\left(30\\right)\\left(5\\right)[\/latex]<\/li>\n<li>[latex]64\\div 8[\/latex]<\/li>\n<li>[latex]x-y[\/latex]<\/li>\n<\/ol>\n<p>Solution:<\/p>\n<table class=\"unnumbered unstyled\" style=\"width: 40%;\" summary=\".\" data-label=\"\">\n<tbody>\n<tr style=\"height: 15.7812px;\">\n<td style=\"height: 15.7812px;\">1.<\/td>\n<\/tr>\n<tr style=\"height: 15px;\">\n<td style=\"height: 15px;\" data-align=\"center\">[latex]12+14[\/latex]<\/td>\n<\/tr>\n<tr style=\"height: 15px;\">\n<td style=\"height: 15px;\" data-align=\"center\">[latex]12[\/latex] plus [latex]14[\/latex]<\/td>\n<\/tr>\n<tr style=\"height: 15px;\">\n<td style=\"height: 15px;\" data-align=\"center\">the sum of twelve and fourteen<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<table style=\"width: 40%;\">\n<tbody>\n<tr>\n<td>2.<\/td>\n<\/tr>\n<tr>\n<td data-align=\"center\">[latex]\\left(30\\right)\\left(5\\right)[\/latex]<\/td>\n<\/tr>\n<tr>\n<td data-align=\"center\">[latex]30[\/latex] times [latex]5[\/latex]<\/td>\n<\/tr>\n<tr>\n<td data-align=\"center\">the product of thirty and five<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<table class=\"unnumbered unstyled\" style=\"width: 40%;\" summary=\".\" data-label=\"\">\n<tbody>\n<tr>\n<td>3.<\/td>\n<\/tr>\n<tr>\n<td data-align=\"center\">[latex]64\\div 8[\/latex]<\/td>\n<\/tr>\n<tr>\n<td data-align=\"center\">[latex]64[\/latex] divided by [latex]8[\/latex]<\/td>\n<\/tr>\n<tr>\n<td data-align=\"center\">the quotient of sixty-four and eight<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<table class=\"unnumbered unstyled\" style=\"width: 40%;\" summary=\".\" data-label=\"\">\n<tbody>\n<tr style=\"height: 15.5625px;\">\n<td style=\"height: 15.5625px;\">4.<\/td>\n<\/tr>\n<tr style=\"height: 15px;\">\n<td style=\"height: 15px;\" data-align=\"center\">[latex]x-y[\/latex]<\/td>\n<\/tr>\n<tr style=\"height: 15px;\">\n<td style=\"height: 15px;\" data-align=\"center\">[latex]x[\/latex] minus [latex]y[\/latex]<\/td>\n<\/tr>\n<tr style=\"height: 15px;\">\n<td style=\"height: 15px;\" data-align=\"center\">the difference of [latex]x[\/latex] and [latex]y[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<div class=\"textbox key-takeaways\">\n<h3>TRY\u00a0IT<\/h3>\n<p><iframe loading=\"lazy\" id=\"mom1\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=144651&amp;theme=oea&amp;iframe_resize_id=mom1\" width=\"100%\" height=\"330\"><\/iframe><\/p>\n<p><iframe loading=\"lazy\" id=\"mom2\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=144652&amp;theme=oea&amp;iframe_resize_id=mom2\" width=\"100%\" height=\"250\"><\/iframe><\/p>\n<\/div>\n<p>When two quantities have the same value, we say they are equal and connect them with an <strong><em data-effect=\"italics\">equals sign<\/em><\/strong>.<\/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-62\">\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>Write Inequalities as Words. <strong>Authored by<\/strong>: James Sousa (Mathispower4u.com) for Lumen Learning. <strong>Located at<\/strong>: <a target=\"_blank\" href=\"https:\/\/youtu.be\/q2ciQBwkjbk\">https:\/\/youtu.be\/q2ciQBwkjbk<\/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, Shared previously<\/div><ul class=\"citation-list\"><li>Question ID: 144651, 144652, 144653, 144654, 144655, 144729. <strong>Authored by<\/strong>: Alyson Day. <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>: IMathAS Community License CC-BY + GPL<\/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":23485,"menu_order":2,"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\":\"Write Inequalities as Words\",\"author\":\"James Sousa (Mathispower4u.com) for Lumen 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