{"id":9243,"date":"2017-05-02T19:51:30","date_gmt":"2017-05-02T19:51:30","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/prealgebra\/?post_type=chapter&#038;p=9243"},"modified":"2019-01-22T19:55:22","modified_gmt":"2019-01-22T19:55:22","slug":"translating-algebraic-expressions-from-words","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/csn-prealgebra\/chapter\/translating-algebraic-expressions-from-words\/","title":{"raw":"Translating Algebraic Expressions From Words","rendered":"Translating Algebraic Expressions From Words"},"content":{"raw":"<div class=\"textbox learning-objectives\">\r\n<h3>Learning Outcomes<\/h3>\r\n<ul>\r\n \t<li>Translate word phrases into algebraic expressions<\/li>\r\n \t<li>Write an algebraic expression that represents the relationship between two measurements such as length and width or the amount of different types of coins<\/li>\r\n<\/ul>\r\n<\/div>\r\n<h2>Translate Words to Algebraic Expressions<\/h2>\r\nIn the previous section, we listed many operation symbols that are used in algebra, and then we translated expressions and equations into word phrases and sentences. Now we\u2019ll reverse the process and translate word phrases into algebraic expressions. The symbols and variables we\u2019ve talked about will help us do that. They are summarized below.\r\n<table id=\"eip-386\" summary=\".\">\r\n<thead>\r\n<tr valign=\"top\">\r\n<th>Operation<\/th>\r\n<th>Phrase<\/th>\r\n<th>Expression<\/th>\r\n<\/tr>\r\n<\/thead>\r\n<tbody>\r\n<tr valign=\"top\">\r\n<td><strong>Addition<\/strong><\/td>\r\n<td>[latex]a[\/latex] plus [latex]b[\/latex]\r\n\r\nthe sum of [latex]a[\/latex] and [latex]b[\/latex]\r\n\r\n[latex]a[\/latex] increased by [latex]b[\/latex]\r\n\r\n[latex]b[\/latex] more than [latex]a[\/latex]\r\n\r\nthe total of [latex]a[\/latex] and [latex]b[\/latex]\r\n\r\n[latex]b[\/latex] added to [latex]a[\/latex]<\/td>\r\n<td>[latex]a+b[\/latex]<\/td>\r\n<\/tr>\r\n<tr valign=\"top\">\r\n<td><strong>Subtraction<\/strong><\/td>\r\n<td>[latex]a[\/latex] minus [latex]b[\/latex]\r\n\r\nthe difference of [latex]a[\/latex] and [latex]b[\/latex]\r\n\r\n[latex]b[\/latex] subtracted from [latex]a[\/latex]\r\n\r\n[latex]a[\/latex] decreased by [latex]b[\/latex]\r\n\r\n[latex]b[\/latex] less than [latex]a[\/latex]<\/td>\r\n<td>[latex]a-b[\/latex]<\/td>\r\n<\/tr>\r\n<tr valign=\"top\">\r\n<td><strong>Multiplication<\/strong><\/td>\r\n<td>[latex]a[\/latex] times [latex]b[\/latex]\r\n\r\nthe product of [latex]a[\/latex] and [latex]b[\/latex]<\/td>\r\n<td>[latex]a\\cdot b[\/latex] , [latex]ab[\/latex] , [latex]a\\left(b\\right)[\/latex] , [latex]\\left(a\\right)\\left(b\\right)[\/latex]<\/td>\r\n<\/tr>\r\n<tr valign=\"top\">\r\n<td><strong>Division<\/strong><\/td>\r\n<td>[latex]a[\/latex] divided by [latex]b[\/latex]\r\n\r\nthe quotient of [latex]a[\/latex] and [latex]b[\/latex]\r\n\r\nthe ratio of [latex]a[\/latex] and [latex]b[\/latex]\r\n\r\n[latex]b[\/latex] divided into [latex]a[\/latex]<\/td>\r\n<td>[latex]a\\div b[\/latex] , [latex]a\/b[\/latex] , [latex]\\frac{a}{b}[\/latex] , [latex]b\\overline{)a}[\/latex]<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\nLook closely at these phrases using the four operations:\r\n<ul id=\"fs-id1171105561839\">\r\n \t<li>the sum <em>of<\/em> [latex]a[\/latex] <em>and<\/em> [latex]b[\/latex]<\/li>\r\n \t<li>the difference <em>of<\/em> [latex]a[\/latex] <em>and<\/em> [latex]b[\/latex]<\/li>\r\n \t<li>the product <em>of<\/em> [latex]a[\/latex] <em>and<\/em> [latex]b[\/latex]<\/li>\r\n \t<li>the quotient <em>of<\/em> [latex]a[\/latex] <em>and<\/em> [latex]b[\/latex]<\/li>\r\n<\/ul>\r\nEach phrase tells you to operate on two numbers. Look for the words <strong><em>of<\/em><\/strong> and <strong><em>and<\/em><\/strong> to find the numbers.\r\n<div class=\"textbox exercises\">\r\n<h3>example<\/h3>\r\nTranslate each word phrase into an algebraic expression:\r\n\r\n1. The difference of [latex]20[\/latex] and [latex]4[\/latex]\r\n2. The quotient of [latex]10x[\/latex] and [latex]3[\/latex]\r\n\r\nSolution\r\n1. The key word is <em>difference<\/em>, which tells us the operation is subtraction. Look for the words <em>of<\/em> and <em>and<\/em> to find the numbers to subtract.\r\n[latex]\\begin{array}{}\\\\ \\text{the difference of }20\\text{ and }4\\hfill \\\\ 20\\text{ minus }4\\hfill \\\\ 20 - 4\\hfill \\end{array}[\/latex]\r\n\r\n2. The key word is <em>quotient<\/em>, which tells us the operation is division.\r\n[latex]\\begin{array}{}\\\\ \\text{the quotient of }10x\\text{ and }3\\hfill \\\\ \\text{divide }10x\\text{ by }3\\hfill \\\\ 10x\\div 3\\hfill \\end{array}[\/latex]\r\nThis can also be written as [latex]\\begin{array}{l}10x\/3\\text{ or}\\frac{10x}{3}\\hfill \\end{array}[\/latex]\r\n\r\n<\/div>\r\n&nbsp;\r\n<div class=\"textbox key-takeaways\">\r\n<h3>try it<\/h3>\r\n[ohm_question]146541[\/ohm_question]\r\n\r\n[ohm_question]143240[\/ohm_question]\r\n\r\n[ohm_question]143207[\/ohm_question]\r\n\r\n[ohm_question]146542[\/ohm_question]\r\n\r\n<\/div>\r\n&nbsp;\r\n<div class=\"textbox exercises\">\r\n<h3>example<\/h3>\r\nTranslate each word phrase into an algebraic expression:\r\n<ol>\r\n \t<li>How old will you be in eight years? What age is eight more years than your age now? Did you add [latex]8[\/latex] to your present age? Eight <em>more than<\/em> means eight added to your present age.<\/li>\r\n \t<li>How old were you seven years ago? This is seven years less than your age now. You subtract [latex]7[\/latex] from your present age,<em>a<\/em>. Seven <em>less than<\/em> means seven subtracted from your present <em>age,a.<\/em><\/li>\r\n<\/ol>\r\n[reveal-answer q=\"879313\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"879313\"]\r\n\r\nSolution:\r\n\r\n1. Eight more than [latex]y[\/latex]\r\n2. Seven less than [latex]a[\/latex]\r\n\r\n1. The key words are <em>more than<\/em>. They tell us the operation is addition. <em>More than<\/em> means \"added to\".\r\n[latex]\\begin{array}{l}\\text{Eight more than }y\\\\ \\text{Eight added to }y\\\\ y+8\\end{array}[\/latex]\r\n\r\n2. The key words are <em>less than<\/em>. They tell us the operation is subtraction. <em>Less than<\/em> means \"subtracted from\".\r\n[latex]\\begin{array}{l}\\text{Seven less than }a\\\\ \\text{Seven subtracted from }a\\\\ a - 7\\end{array}[\/latex]\r\n\r\n[\/hidden-answer]\r\n\r\n<\/div>\r\n&nbsp;\r\n<div class=\"textbox key-takeaways\">\r\n<h3>try it<\/h3>\r\n[ohm_question]144907[\/ohm_question]\r\n\r\n<\/div>\r\n&nbsp;\r\n<div class=\"textbox exercises\">\r\n<h3>example<\/h3>\r\nTranslate each word phrase into an algebraic expression:\r\n\r\n1. five times the sum of [latex]m[\/latex] and [latex]n[\/latex]\r\n2. the sum of five times [latex]m[\/latex] and [latex]n[\/latex]\r\n[reveal-answer q=\"888823\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"888823\"]\r\n\r\nSolution\r\n1. There are two operation words: <em>times<\/em> tells us to multiply and <em>sum<\/em> tells us to add. Because we are multiplying [latex]5[\/latex] times the sum, we need parentheses around the sum of [latex]m[\/latex] and [latex]n[\/latex].\r\n<p style=\"padding-left: 60px\">five times the sum of [latex]m[\/latex] and [latex]n[\/latex]<\/p>\r\n<p style=\"padding-left: 60px\">[latex]5(m+n)[\/latex]<\/p>\r\n2. To take a sum, we look for the words <em>of<\/em> and <em>and<\/em> to see what is being added. Here we are taking the sum <em>of<\/em> five times [latex]m[\/latex] and [latex]n[\/latex].\r\n<p style=\"padding-left: 60px\">the sum of five times [latex]m[\/latex] and [latex]n[\/latex]<\/p>\r\n<p style=\"padding-left: 60px\">[latex]5m+n[\/latex]<\/p>\r\nNotice how the use of parentheses changes the result. In part 1, we add first and in part 2, we multiply first.\r\n\r\n[\/hidden-answer]\r\n\r\n<\/div>\r\n&nbsp;\r\n<div class=\"textbox key-takeaways\">\r\n<h3>try it<\/h3>\r\n[ohm_question]144916[\/ohm_question]\r\n\r\n<\/div>\r\nWatch the video below to better understand how to write algebraic expressions from statements.\r\n\r\nhttps:\/\/youtu.be\/Hub7ku7UHT4\r\n\r\nLater in this course, we\u2019ll apply our skills in algebra to solving equations. We\u2019ll usually start by translating a word phrase to an algebraic expression. We\u2019ll need to be clear about what the expression will represent. We\u2019ll see how to do this in the next two examples.\r\n\r\n&nbsp;\r\n<div class=\"textbox exercises\">\r\n<h3>example<\/h3>\r\nThe height of a rectangular window is [latex]6[\/latex] inches less than the width. Let [latex]w[\/latex] represent the width of the window. Write an expression for the height of the window.\r\n[reveal-answer q=\"704093\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"704093\"]\r\n\r\nSolution\r\n<table id=\"eip-id1168466033010\" class=\"unnumbered unstyled\" summary=\".\">\r\n<tbody>\r\n<tr>\r\n<td>Write a phrase about the height.<\/td>\r\n<td>[latex]6[\/latex] less than the width<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Substitute [latex]w[\/latex] for the width.<\/td>\r\n<td>[latex]6[\/latex] less than [latex]w[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Rewrite 'less than' as 'subtracted from'.<\/td>\r\n<td>[latex]6[\/latex] subtracted from [latex]w[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Translate the phrase into algebra.<\/td>\r\n<td>[latex]w - 6[\/latex]<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n[\/hidden-answer]\r\n\r\n<\/div>\r\n&nbsp;\r\n<div class=\"textbox key-takeaways\">\r\n<h3>try it<\/h3>\r\n[ohm_question]144917[\/ohm_question]\r\n\r\n<\/div>\r\n&nbsp;\r\n<div class=\"textbox exercises\">\r\n<h3>example<\/h3>\r\nBlanca has dimes and quarters in her purse. The number of dimes is [latex]2[\/latex] less than [latex]5[\/latex] times the number of quarters. Let [latex]q[\/latex] represent the number of quarters. Write an expression for the number of dimes.\r\n[reveal-answer q=\"365611\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"365611\"]\r\n\r\nSolution\r\n<table id=\"eip-id1168467234223\" class=\"unnumbered unstyled\" summary=\".\">\r\n<tbody>\r\n<tr>\r\n<td>Write a phrase about the number of dimes.<\/td>\r\n<td>two less than five times the number of quarters<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Substitute [latex]q[\/latex] for the number of quarters.<\/td>\r\n<td>[latex]2[\/latex] less than five times [latex]q[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Translate [latex]5[\/latex] <em>times<\/em> [latex]q[\/latex] .<\/td>\r\n<td>[latex]2[\/latex] less than [latex]5q[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Translate the phrase into algebra.<\/td>\r\n<td>[latex]5q - 2[\/latex]<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n[\/hidden-answer]\r\n\r\n<\/div>\r\n&nbsp;\r\n<div class=\"textbox key-takeaways\">\r\n<h3>try it<\/h3>\r\n[ohm_question]144918[\/ohm_question]\r\n\r\n<\/div>\r\nIn the following video we show more examples of how to write basic algebraic expressions from words, and simplify.\r\n\r\nhttps:\/\/youtu.be\/x6b-OIBKSks","rendered":"<div class=\"textbox learning-objectives\">\n<h3>Learning Outcomes<\/h3>\n<ul>\n<li>Translate word phrases into algebraic expressions<\/li>\n<li>Write an algebraic expression that represents the relationship between two measurements such as length and width or the amount of different types of coins<\/li>\n<\/ul>\n<\/div>\n<h2>Translate Words to Algebraic Expressions<\/h2>\n<p>In the previous section, we listed many operation symbols that are used in algebra, and then we translated expressions and equations into word phrases and sentences. Now we\u2019ll reverse the process and translate word phrases into algebraic expressions. The symbols and variables we\u2019ve talked about will help us do that. They are summarized below.<\/p>\n<table id=\"eip-386\" summary=\".\">\n<thead>\n<tr valign=\"top\">\n<th>Operation<\/th>\n<th>Phrase<\/th>\n<th>Expression<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr valign=\"top\">\n<td><strong>Addition<\/strong><\/td>\n<td>[latex]a[\/latex] plus [latex]b[\/latex]<\/p>\n<p>the sum of [latex]a[\/latex] and [latex]b[\/latex]<\/p>\n<p>[latex]a[\/latex] increased by [latex]b[\/latex]<\/p>\n<p>[latex]b[\/latex] more than [latex]a[\/latex]<\/p>\n<p>the total of [latex]a[\/latex] and [latex]b[\/latex]<\/p>\n<p>[latex]b[\/latex] added to [latex]a[\/latex]<\/td>\n<td>[latex]a+b[\/latex]<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td><strong>Subtraction<\/strong><\/td>\n<td>[latex]a[\/latex] minus [latex]b[\/latex]<\/p>\n<p>the difference of [latex]a[\/latex] and [latex]b[\/latex]<\/p>\n<p>[latex]b[\/latex] subtracted from [latex]a[\/latex]<\/p>\n<p>[latex]a[\/latex] decreased by [latex]b[\/latex]<\/p>\n<p>[latex]b[\/latex] less than [latex]a[\/latex]<\/td>\n<td>[latex]a-b[\/latex]<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td><strong>Multiplication<\/strong><\/td>\n<td>[latex]a[\/latex] times [latex]b[\/latex]<\/p>\n<p>the product of [latex]a[\/latex] and [latex]b[\/latex]<\/td>\n<td>[latex]a\\cdot b[\/latex] , [latex]ab[\/latex] , [latex]a\\left(b\\right)[\/latex] , [latex]\\left(a\\right)\\left(b\\right)[\/latex]<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td><strong>Division<\/strong><\/td>\n<td>[latex]a[\/latex] divided by [latex]b[\/latex]<\/p>\n<p>the quotient of [latex]a[\/latex] and [latex]b[\/latex]<\/p>\n<p>the ratio of [latex]a[\/latex] and [latex]b[\/latex]<\/p>\n<p>[latex]b[\/latex] divided into [latex]a[\/latex]<\/td>\n<td>[latex]a\\div b[\/latex] , [latex]a\/b[\/latex] , [latex]\\frac{a}{b}[\/latex] , [latex]b\\overline{)a}[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>Look closely at these phrases using the four operations:<\/p>\n<ul id=\"fs-id1171105561839\">\n<li>the sum <em>of<\/em> [latex]a[\/latex] <em>and<\/em> [latex]b[\/latex]<\/li>\n<li>the difference <em>of<\/em> [latex]a[\/latex] <em>and<\/em> [latex]b[\/latex]<\/li>\n<li>the product <em>of<\/em> [latex]a[\/latex] <em>and<\/em> [latex]b[\/latex]<\/li>\n<li>the quotient <em>of<\/em> [latex]a[\/latex] <em>and<\/em> [latex]b[\/latex]<\/li>\n<\/ul>\n<p>Each phrase tells you to operate on two numbers. Look for the words <strong><em>of<\/em><\/strong> and <strong><em>and<\/em><\/strong> to find the numbers.<\/p>\n<div class=\"textbox exercises\">\n<h3>example<\/h3>\n<p>Translate each word phrase into an algebraic expression:<\/p>\n<p>1. The difference of [latex]20[\/latex] and [latex]4[\/latex]<br \/>\n2. The quotient of [latex]10x[\/latex] and [latex]3[\/latex]<\/p>\n<p>Solution<br \/>\n1. The key word is <em>difference<\/em>, which tells us the operation is subtraction. Look for the words <em>of<\/em> and <em>and<\/em> to find the numbers to subtract.<br \/>\n[latex]\\begin{array}{}\\\\ \\text{the difference of }20\\text{ and }4\\hfill \\\\ 20\\text{ minus }4\\hfill \\\\ 20 - 4\\hfill \\end{array}[\/latex]<\/p>\n<p>2. The key word is <em>quotient<\/em>, which tells us the operation is division.<br \/>\n[latex]\\begin{array}{}\\\\ \\text{the quotient of }10x\\text{ and }3\\hfill \\\\ \\text{divide }10x\\text{ by }3\\hfill \\\\ 10x\\div 3\\hfill \\end{array}[\/latex]<br \/>\nThis can also be written as [latex]\\begin{array}{l}10x\/3\\text{ or}\\frac{10x}{3}\\hfill \\end{array}[\/latex]<\/p>\n<\/div>\n<p>&nbsp;<\/p>\n<div class=\"textbox key-takeaways\">\n<h3>try it<\/h3>\n<p><iframe loading=\"lazy\" id=\"ohm146541\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=146541&theme=oea&iframe_resize_id=ohm146541&show_question_numbers\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<p><iframe loading=\"lazy\" id=\"ohm143240\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=143240&theme=oea&iframe_resize_id=ohm143240&show_question_numbers\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<p><iframe loading=\"lazy\" id=\"ohm143207\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=143207&theme=oea&iframe_resize_id=ohm143207&show_question_numbers\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<p><iframe loading=\"lazy\" id=\"ohm146542\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=146542&theme=oea&iframe_resize_id=ohm146542&show_question_numbers\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<\/div>\n<p>&nbsp;<\/p>\n<div class=\"textbox exercises\">\n<h3>example<\/h3>\n<p>Translate each word phrase into an algebraic expression:<\/p>\n<ol>\n<li>How old will you be in eight years? What age is eight more years than your age now? Did you add [latex]8[\/latex] to your present age? Eight <em>more than<\/em> means eight added to your present age.<\/li>\n<li>How old were you seven years ago? This is seven years less than your age now. You subtract [latex]7[\/latex] from your present age,<em>a<\/em>. Seven <em>less than<\/em> means seven subtracted from your present <em>age,a.<\/em><\/li>\n<\/ol>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q879313\">Show Solution<\/span><\/p>\n<div id=\"q879313\" class=\"hidden-answer\" style=\"display: none\">\n<p>Solution:<\/p>\n<p>1. Eight more than [latex]y[\/latex]<br \/>\n2. Seven less than [latex]a[\/latex]<\/p>\n<p>1. The key words are <em>more than<\/em>. They tell us the operation is addition. <em>More than<\/em> means &#8220;added to&#8221;.<br \/>\n[latex]\\begin{array}{l}\\text{Eight more than }y\\\\ \\text{Eight added to }y\\\\ y+8\\end{array}[\/latex]<\/p>\n<p>2. The key words are <em>less than<\/em>. They tell us the operation is subtraction. <em>Less than<\/em> means &#8220;subtracted from&#8221;.<br \/>\n[latex]\\begin{array}{l}\\text{Seven less than }a\\\\ \\text{Seven subtracted from }a\\\\ a - 7\\end{array}[\/latex]<\/p>\n<\/div>\n<\/div>\n<\/div>\n<p>&nbsp;<\/p>\n<div class=\"textbox key-takeaways\">\n<h3>try it<\/h3>\n<p><iframe loading=\"lazy\" id=\"ohm144907\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=144907&theme=oea&iframe_resize_id=ohm144907&show_question_numbers\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<\/div>\n<p>&nbsp;<\/p>\n<div class=\"textbox exercises\">\n<h3>example<\/h3>\n<p>Translate each word phrase into an algebraic expression:<\/p>\n<p>1. five times the sum of [latex]m[\/latex] and [latex]n[\/latex]<br \/>\n2. the sum of five times [latex]m[\/latex] and [latex]n[\/latex]<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q888823\">Show Solution<\/span><\/p>\n<div id=\"q888823\" class=\"hidden-answer\" style=\"display: none\">\n<p>Solution<br \/>\n1. There are two operation words: <em>times<\/em> tells us to multiply and <em>sum<\/em> tells us to add. Because we are multiplying [latex]5[\/latex] times the sum, we need parentheses around the sum of [latex]m[\/latex] and [latex]n[\/latex].<\/p>\n<p style=\"padding-left: 60px\">five times the sum of [latex]m[\/latex] and [latex]n[\/latex]<\/p>\n<p style=\"padding-left: 60px\">[latex]5(m+n)[\/latex]<\/p>\n<p>2. To take a sum, we look for the words <em>of<\/em> and <em>and<\/em> to see what is being added. Here we are taking the sum <em>of<\/em> five times [latex]m[\/latex] and [latex]n[\/latex].<\/p>\n<p style=\"padding-left: 60px\">the sum of five times [latex]m[\/latex] and [latex]n[\/latex]<\/p>\n<p style=\"padding-left: 60px\">[latex]5m+n[\/latex]<\/p>\n<p>Notice how the use of parentheses changes the result. In part 1, we add first and in part 2, we multiply first.<\/p>\n<\/div>\n<\/div>\n<\/div>\n<p>&nbsp;<\/p>\n<div class=\"textbox key-takeaways\">\n<h3>try it<\/h3>\n<p><iframe loading=\"lazy\" id=\"ohm144916\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=144916&theme=oea&iframe_resize_id=ohm144916&show_question_numbers\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<\/div>\n<p>Watch the video below to better understand how to write algebraic expressions from statements.<\/p>\n<p><iframe loading=\"lazy\" id=\"oembed-1\" title=\"Write Algebraic Expressions from Statements: Form  ax+b and a(x+b)\" width=\"500\" height=\"281\" src=\"https:\/\/www.youtube.com\/embed\/Hub7ku7UHT4?feature=oembed&#38;rel=0\" frameborder=\"0\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/p>\n<p>Later in this course, we\u2019ll apply our skills in algebra to solving equations. We\u2019ll usually start by translating a word phrase to an algebraic expression. We\u2019ll need to be clear about what the expression will represent. We\u2019ll see how to do this in the next two examples.<\/p>\n<p>&nbsp;<\/p>\n<div class=\"textbox exercises\">\n<h3>example<\/h3>\n<p>The height of a rectangular window is [latex]6[\/latex] inches less than the width. Let [latex]w[\/latex] represent the width of the window. Write an expression for the height of the window.<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q704093\">Show Solution<\/span><\/p>\n<div id=\"q704093\" class=\"hidden-answer\" style=\"display: none\">\n<p>Solution<\/p>\n<table id=\"eip-id1168466033010\" class=\"unnumbered unstyled\" summary=\".\">\n<tbody>\n<tr>\n<td>Write a phrase about the height.<\/td>\n<td>[latex]6[\/latex] less than the width<\/td>\n<\/tr>\n<tr>\n<td>Substitute [latex]w[\/latex] for the width.<\/td>\n<td>[latex]6[\/latex] less than [latex]w[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Rewrite &#8216;less than&#8217; as &#8216;subtracted from&#8217;.<\/td>\n<td>[latex]6[\/latex] subtracted from [latex]w[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Translate the phrase into algebra.<\/td>\n<td>[latex]w - 6[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<p>&nbsp;<\/p>\n<div class=\"textbox key-takeaways\">\n<h3>try it<\/h3>\n<p><iframe loading=\"lazy\" id=\"ohm144917\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=144917&theme=oea&iframe_resize_id=ohm144917&show_question_numbers\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<\/div>\n<p>&nbsp;<\/p>\n<div class=\"textbox exercises\">\n<h3>example<\/h3>\n<p>Blanca has dimes and quarters in her purse. The number of dimes is [latex]2[\/latex] less than [latex]5[\/latex] times the number of quarters. Let [latex]q[\/latex] represent the number of quarters. Write an expression for the number of dimes.<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q365611\">Show Solution<\/span><\/p>\n<div id=\"q365611\" class=\"hidden-answer\" style=\"display: none\">\n<p>Solution<\/p>\n<table id=\"eip-id1168467234223\" class=\"unnumbered unstyled\" summary=\".\">\n<tbody>\n<tr>\n<td>Write a phrase about the number of dimes.<\/td>\n<td>two less than five times the number of quarters<\/td>\n<\/tr>\n<tr>\n<td>Substitute [latex]q[\/latex] for the number of quarters.<\/td>\n<td>[latex]2[\/latex] less than five times [latex]q[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Translate [latex]5[\/latex] <em>times<\/em> [latex]q[\/latex] .<\/td>\n<td>[latex]2[\/latex] less than [latex]5q[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Translate the phrase into algebra.<\/td>\n<td>[latex]5q - 2[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<p>&nbsp;<\/p>\n<div class=\"textbox key-takeaways\">\n<h3>try it<\/h3>\n<p><iframe loading=\"lazy\" id=\"ohm144918\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=144918&theme=oea&iframe_resize_id=ohm144918&show_question_numbers\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<\/div>\n<p>In the following video we show more examples of how to write basic algebraic expressions from words, and simplify.<\/p>\n<p><iframe loading=\"lazy\" id=\"oembed-2\" title=\"Write Basic Expressions from Words Modeling Situations\" width=\"500\" height=\"281\" src=\"https:\/\/www.youtube.com\/embed\/x6b-OIBKSks?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-9243\">\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 Algebraic Expressions from Statements: Form ax+b and a(x+b). <strong>Authored by<\/strong>: Sousa, James (mathispower4u.com) for Lumen Learning. <strong>Located at<\/strong>: <a target=\"_blank\" href=\"https:\/\/youtu.be\/Hub7ku7UHT4\">https:\/\/youtu.be\/Hub7ku7UHT4<\/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>Write Basic Expressions from Words Modeling Situations. <strong>Authored by<\/strong>: James Sousa (Mathispower4u.com) for Lumen Learning. <strong>Located at<\/strong>: <a target=\"_blank\" href=\"https:\/\/youtu.be\/x6b-OIBKSks\">https:\/\/youtu.be\/x6b-OIBKSks<\/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: 144907, 144916, 144917, 144918,146542,146541 . <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>. <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 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