{"id":15318,"date":"2021-10-11T23:05:29","date_gmt":"2021-10-11T23:05:29","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/ccbcmd-math-1\/chapter\/writing-proportions\/"},"modified":"2021-10-17T01:44:37","modified_gmt":"2021-10-17T01:44:37","slug":"writing-proportions","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/ccbcmd-math-1\/chapter\/writing-proportions\/","title":{"raw":"Writing Proportions","rendered":"Writing Proportions"},"content":{"raw":"<div class=\"textbox learning-objectives\">\r\n<h3>Learning Outcomes<\/h3>\r\n<ul>\r\n \t<li>Write the proportion<\/li>\r\n<\/ul>\r\n<\/div>\r\nIf you wanted to power the city of Lincoln, Nebraska using wind power, how many wind\u00a0turbines would you need to install? Questions like these can be answered using rates and proportions.\r\n\r\n<a href=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/1141\/2016\/11\/14205401\/wind-364996_1280.jpg\"><img class=\"aligncenter wp-image-497\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/3360\/2018\/06\/28163101\/wind-364996_1280-1024x685.jpg\" alt=\"two wind turbines in a field of flowers and low trees\" width=\"613\" height=\"410\" \/><\/a>\r\n<div class=\"textbox\">\r\n<h2 style=\"text-align: justify;\">Rates<\/h2>\r\nA rate is the ratio (fraction) of two quantities.\r\n\r\nA <strong>unit rate<\/strong> is a rate with a denominator of one.\r\n\r\n<\/div>\r\n<div class=\"textbox exercises\">\r\n<h3>Example<\/h3>\r\nYour car can drive 300 miles on a tank of 15 gallons. Express this as a rate.\r\n[reveal-answer q=\"378596\"]Show Answer[\/reveal-answer]\r\n[hidden-answer a=\"378596\"]Expressed as a rate, [latex]\\displaystyle\\frac{300\\text{ miles}}{15\\text{ gallons}}[\/latex]. We can divide to find a unit rate:[latex]\\displaystyle\\frac{20\\text{ miles}}{1\\text{ gallon}}[\/latex], which we could also write as [latex]\\displaystyle{20}\\frac{\\text{miles}}{\\text{gallon}}[\/latex], or just 20 miles per gallon.[\/hidden-answer]\r\n\r\n<\/div>\r\nIn <a href=\"https:\/\/courses.lumenlearning.com\/wm-developmentalemporium\/chapter\/ratios-and-rate\/\">the section on Ratios and Rates we saw some ways they are used in our daily lives<\/a>. When two ratios or rates are equal, the equation relating them is called a proportion.\r\n<div class=\"textbox shaded\">\r\n<h3>Proportion<\/h3>\r\nA proportion is an equation of the form [latex]{\\Large\\frac{a}{b}}={\\Large\\frac{c}{d}}[\/latex], where [latex]b\\ne 0,d\\ne 0[\/latex].\r\nThe proportion states two ratios or rates are equal. The proportion is read [latex]\\text{\"}a[\/latex] is to [latex]b[\/latex], as [latex]c[\/latex] is to [latex]d\\text{\".}[\/latex]\r\n\r\n<\/div>\r\nThe equation [latex]{\\Large\\frac{1}{2}}={\\Large\\frac{4}{8}}[\/latex] is a proportion because the two fractions are equal. The proportion [latex]{\\Large\\frac{1}{2}}={\\Large\\frac{4}{8}}[\/latex] is read \"[latex]1[\/latex] is to [latex]2[\/latex] as [latex]4[\/latex] is to [latex]8[\/latex]\".\r\n\r\nIf we compare quantities with units, we have to be sure we are comparing them in the right order. For example, in the proportion [latex]{\\Large\\frac{\\text{20 students}}{\\text{1 teacher}}}={\\Large\\frac{\\text{60 students}}{\\text{3 teachers}}}[\/latex] we compare the number of students to the number of teachers. We put students in the numerators and teachers in the denominators.\r\n<div class=\"textbox exercises\">\r\n<h3>example<\/h3>\r\nWrite each sentence as a proportion:\r\n\r\n1. [latex]3[\/latex] is to [latex]7[\/latex] as [latex]15[\/latex] is to [latex]35[\/latex].\r\n2. [latex]5[\/latex] hits in [latex]8[\/latex] at bats is the same as [latex]30[\/latex] hits in [latex]48[\/latex] at-bats.\r\n3. [latex]\\text{\\$1.50}[\/latex] for [latex]6[\/latex] ounces is equivalent to [latex]\\text{\\$2.25}[\/latex] for [latex]9[\/latex] ounces.\r\n\r\nSolution\r\n<table id=\"eip-id1168468496922\" class=\"unnumbered unstyled\" summary=\".\">\r\n<tbody>\r\n<tr>\r\n<td>1.<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>[latex]3[\/latex] is to [latex]7[\/latex] as [latex]15[\/latex] is to [latex]35[\/latex].<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Write as a proportion.<\/td>\r\n<td>[latex]{\\Large\\frac{3}{7}}={\\Large\\frac{15}{35}}[\/latex]<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<table id=\"eip-id1168047457950\" class=\"unnumbered unstyled\" summary=\".\">\r\n<tbody>\r\n<tr>\r\n<td>2.<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>[latex]5[\/latex] hits in [latex]8[\/latex] at-bats is the same as [latex]30[\/latex] hits in [latex]48[\/latex] at-bats.<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Write each fraction to compare hits to at-bats.<\/td>\r\n<td>[latex]{\\Large\\frac{\\text{hits}}{\\text{at-bats}}}={\\Large\\frac{\\text{hits}}{\\text{at-bats}}}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Write as a proportion.<\/td>\r\n<td>[latex]{\\Large\\frac{5}{8}}={\\Large\\frac{30}{48}}[\/latex]<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<table id=\"eip-id1168047661662\" class=\"unnumbered unstyled\" summary=\".\">\r\n<tbody>\r\n<tr>\r\n<td>3.<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>[latex]\\text{\\$1.50}[\/latex] for [latex]6[\/latex] ounces is equivalent to [latex]\\text{\\$2.25}[\/latex] for [latex]9[\/latex] ounces.<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Write each fraction to compare dollars to ounces.<\/td>\r\n<td>[latex]{\\Large\\frac{$}{\\text{ounces}}}={\\Large\\frac{$}{\\text{ounces}}}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Write as a proportion.<\/td>\r\n<td>[latex]{\\Large\\frac{1.50}{6}}={\\Large\\frac{2.25}{9}}[\/latex]<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<\/div>\r\n&nbsp;\r\n<div class=\"textbox key-takeaways\">\r\n<h3>try it<\/h3>\r\n&nbsp;\r\n\r\n[ohm_question]146798[\/ohm_question]\r\n\r\n[ohm_question]146799[\/ohm_question]\r\n\r\n<\/div>\r\nLook at the proportions [latex]{\\Large\\frac{1}{2}}={\\Large\\frac{4}{8}}[\/latex] and [latex]{\\Large\\frac{2}{3}}={\\Large\\frac{6}{9}}[\/latex]. From our work with equivalent fractions we know these equations are true. But how do we know if an equation is a proportion with equivalent fractions if it contains fractions with larger numbers?\r\n\r\nTo determine if a proportion is true, we find the <strong>cross products<\/strong> of each proportion. To find the cross products, we multiply each denominator with the opposite numerator (diagonally across the equal sign). The results are called a cross products because of the cross formed. The cross products of a proportion are equal.\r\n\r\n<img class=\"aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24222123\/CNX_BMath_Figure_06_05_028_img.png\" alt=\"The figure shows cross multiplication of two proportions. There is the proportion 1 is to 2 as 4 is to 8. Arrows are shown diagonally across the equal sign to show cross products. The equations formed by cross multiplying are 8 \u00b7 1 = 8 and 2 \u00b7 4 = 8. There is the proportion 2 is to 3 as 6 is to 9. Arrows are shown diagonally across the equal sign to show cross products. The equations formed by cross multiplying are 9 \u00b7 2 = 18 and 3 \u00b7 6 = 18.\" \/>\r\n\r\nCross Products of a Proportion\r\n\r\nFor any proportion of the form [latex]{\\Large\\frac{a}{b}}={\\Large\\frac{c}{d}}[\/latex], where [latex]b\\ne 0,d\\ne 0[\/latex], its cross products are equal.\r\n\r\n<img class=\"aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24222125\/CNX_BMath_Figure_06_05_003_img.png\" alt=\"No Alt Text\" \/>\r\n\r\nCross products can be used to test whether a proportion is true. To test whether an equation makes a proportion, we find the cross products. If they are the equal, we have a proportion.\r\n<div class=\"textbox exercises\">\r\n<h3>example<\/h3>\r\nDetermine whether each equation is a proportion:\r\n\r\n1.\u00a0 [latex]{\\Large\\frac{4}{9}}={\\Large\\frac{12}{28}}[\/latex]\r\n2.\u00a0 [latex]{\\Large\\frac{17.5}{37.5}}={\\Large\\frac{7}{15}}[\/latex]\r\n[reveal-answer q=\"586373\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"586373\"]\r\n\r\nSolution\r\nTo determine if the equation is a proportion, we find the cross products. If they are equal, the equation is a proportion.\r\n<table id=\"eip-id1168468703669\" class=\"unnumbered unstyled\" summary=\"The figure shows the steps to finding the cross products of the proportion 4 is to 9 as 12 is to 28. The cross multiplication shown is 28 times 4 = 112 and 9 times 12 = 28.\">\r\n<tbody>\r\n<tr>\r\n<td>1.<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>[latex]{\\Large\\frac{4}{9}}={\\Large\\frac{12}{28}}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Find the cross products.<\/td>\r\n<td>[latex]28\\cdot 4=1129\\cdot 12=108[\/latex]\r\n\r\n<img src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24222127\/CNX_BMath_Figure_06_05_020_img-02.png\" alt=\".\" \/><\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\nSince the cross products are not equal, [latex]28\\cdot 4\\ne 9\\cdot 12[\/latex], the equation is not a proportion.\r\n<table id=\"eip-id1168469699712\" class=\"unnumbered unstyled\" summary=\"The figure shows the steps to finding the cross products of the proportion 17.5 is to 37.5 as 7 is to 15. The cross multiplication shown is 15 times 17.5 = 262.5 and 37.5 times 7 = 262.5.\">\r\n<tbody>\r\n<tr>\r\n<td>2.<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>[latex]{\\Large\\frac{17.5}{37.5}}={\\Large\\frac{7}{15}}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Find the cross products.<\/td>\r\n<td>[latex]15\\cdot 17.5=262.5[\/latex]\r\n\r\n[latex]37.5\\cdot 7=262.5[\/latex]\r\n\r\n<img src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24222130\/CNX_BMath_Figure_06_05_021_img-02.png\" alt=\".\" \/><\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\nSince the cross products are equal, [latex]15\\cdot 17.5=37.5\\cdot 7[\/latex], the equation is a proportion.\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]146809[\/ohm_question]\r\n\r\n<\/div>\r\n<span style=\"color: #ff0000;\">\u00a0<\/span>\r\n<h2>Contribute!<\/h2>\r\n<div style=\"margin-bottom: 8px;\">Did you have an idea for improving this content? We\u2019d love your input.<\/div>\r\n<a style=\"font-size: 10pt; font-weight: 600; color: #077fab; text-decoration: none; border: 2px solid #077fab; border-radius: 7px; padding: 5px 25px; text-align: center; cursor: pointer; line-height: 1.5em;\" href=\"https:\/\/docs.google.com\/document\/d\/17N0yElNV8pRFOjWeU_kXmUQltWj7cwUwoeNwezoQk-k\" target=\"_blank\" rel=\"noopener\">Improve this page<\/a><a style=\"margin-left: 16px;\" href=\"https:\/\/docs.google.com\/document\/d\/1vy-T6DtTF-BbMfpVEI7VP_R7w2A4anzYZLXR8Pk4Fu4\" target=\"_blank\" rel=\"noopener\">Learn More<\/a>","rendered":"<div class=\"textbox learning-objectives\">\n<h3>Learning Outcomes<\/h3>\n<ul>\n<li>Write the proportion<\/li>\n<\/ul>\n<\/div>\n<p>If you wanted to power the city of Lincoln, Nebraska using wind power, how many wind\u00a0turbines would you need to install? Questions like these can be answered using rates and proportions.<\/p>\n<p><a href=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/1141\/2016\/11\/14205401\/wind-364996_1280.jpg\"><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-497\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/3360\/2018\/06\/28163101\/wind-364996_1280-1024x685.jpg\" alt=\"two wind turbines in a field of flowers and low trees\" width=\"613\" height=\"410\" \/><\/a><\/p>\n<div class=\"textbox\">\n<h2 style=\"text-align: justify;\">Rates<\/h2>\n<p>A rate is the ratio (fraction) of two quantities.<\/p>\n<p>A <strong>unit rate<\/strong> is a rate with a denominator of one.<\/p>\n<\/div>\n<div class=\"textbox exercises\">\n<h3>Example<\/h3>\n<p>Your car can drive 300 miles on a tank of 15 gallons. Express this as a rate.<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q378596\">Show Answer<\/span><\/p>\n<div id=\"q378596\" class=\"hidden-answer\" style=\"display: none\">Expressed as a rate, [latex]\\displaystyle\\frac{300\\text{ miles}}{15\\text{ gallons}}[\/latex]. We can divide to find a unit rate:[latex]\\displaystyle\\frac{20\\text{ miles}}{1\\text{ gallon}}[\/latex], which we could also write as [latex]\\displaystyle{20}\\frac{\\text{miles}}{\\text{gallon}}[\/latex], or just 20 miles per gallon.<\/div>\n<\/div>\n<\/div>\n<p>In <a href=\"https:\/\/courses.lumenlearning.com\/wm-developmentalemporium\/chapter\/ratios-and-rate\/\">the section on Ratios and Rates we saw some ways they are used in our daily lives<\/a>. When two ratios or rates are equal, the equation relating them is called a proportion.<\/p>\n<div class=\"textbox shaded\">\n<h3>Proportion<\/h3>\n<p>A proportion is an equation of the form [latex]{\\Large\\frac{a}{b}}={\\Large\\frac{c}{d}}[\/latex], where [latex]b\\ne 0,d\\ne 0[\/latex].<br \/>\nThe proportion states two ratios or rates are equal. The proportion is read [latex]\\text{\"}a[\/latex] is to [latex]b[\/latex], as [latex]c[\/latex] is to [latex]d\\text{\".}[\/latex]<\/p>\n<\/div>\n<p>The equation [latex]{\\Large\\frac{1}{2}}={\\Large\\frac{4}{8}}[\/latex] is a proportion because the two fractions are equal. The proportion [latex]{\\Large\\frac{1}{2}}={\\Large\\frac{4}{8}}[\/latex] is read &#8220;[latex]1[\/latex] is to [latex]2[\/latex] as [latex]4[\/latex] is to [latex]8[\/latex]&#8220;.<\/p>\n<p>If we compare quantities with units, we have to be sure we are comparing them in the right order. For example, in the proportion [latex]{\\Large\\frac{\\text{20 students}}{\\text{1 teacher}}}={\\Large\\frac{\\text{60 students}}{\\text{3 teachers}}}[\/latex] we compare the number of students to the number of teachers. We put students in the numerators and teachers in the denominators.<\/p>\n<div class=\"textbox exercises\">\n<h3>example<\/h3>\n<p>Write each sentence as a proportion:<\/p>\n<p>1. [latex]3[\/latex] is to [latex]7[\/latex] as [latex]15[\/latex] is to [latex]35[\/latex].<br \/>\n2. [latex]5[\/latex] hits in [latex]8[\/latex] at bats is the same as [latex]30[\/latex] hits in [latex]48[\/latex] at-bats.<br \/>\n3. [latex]\\text{\\$1.50}[\/latex] for [latex]6[\/latex] ounces is equivalent to [latex]\\text{\\$2.25}[\/latex] for [latex]9[\/latex] ounces.<\/p>\n<p>Solution<\/p>\n<table id=\"eip-id1168468496922\" class=\"unnumbered unstyled\" summary=\".\">\n<tbody>\n<tr>\n<td>1.<\/td>\n<\/tr>\n<tr>\n<td>[latex]3[\/latex] is to [latex]7[\/latex] as [latex]15[\/latex] is to [latex]35[\/latex].<\/td>\n<\/tr>\n<tr>\n<td>Write as a proportion.<\/td>\n<td>[latex]{\\Large\\frac{3}{7}}={\\Large\\frac{15}{35}}[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<table id=\"eip-id1168047457950\" class=\"unnumbered unstyled\" summary=\".\">\n<tbody>\n<tr>\n<td>2.<\/td>\n<\/tr>\n<tr>\n<td>[latex]5[\/latex] hits in [latex]8[\/latex] at-bats is the same as [latex]30[\/latex] hits in [latex]48[\/latex] at-bats.<\/td>\n<\/tr>\n<tr>\n<td>Write each fraction to compare hits to at-bats.<\/td>\n<td>[latex]{\\Large\\frac{\\text{hits}}{\\text{at-bats}}}={\\Large\\frac{\\text{hits}}{\\text{at-bats}}}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Write as a proportion.<\/td>\n<td>[latex]{\\Large\\frac{5}{8}}={\\Large\\frac{30}{48}}[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<table id=\"eip-id1168047661662\" class=\"unnumbered unstyled\" summary=\".\">\n<tbody>\n<tr>\n<td>3.<\/td>\n<\/tr>\n<tr>\n<td>[latex]\\text{\\$1.50}[\/latex] for [latex]6[\/latex] ounces is equivalent to [latex]\\text{\\$2.25}[\/latex] for [latex]9[\/latex] ounces.<\/td>\n<\/tr>\n<tr>\n<td>Write each fraction to compare dollars to ounces.<\/td>\n<td>[latex]{\\Large\\frac{$}{\\text{ounces}}}={\\Large\\frac{$}{\\text{ounces}}}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Write as a proportion.<\/td>\n<td>[latex]{\\Large\\frac{1.50}{6}}={\\Large\\frac{2.25}{9}}[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<p>&nbsp;<\/p>\n<div class=\"textbox key-takeaways\">\n<h3>try it<\/h3>\n<p>&nbsp;<\/p>\n<p><iframe loading=\"lazy\" id=\"ohm146798\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=146798&theme=oea&iframe_resize_id=ohm146798&show_question_numbers\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<p><iframe loading=\"lazy\" id=\"ohm146799\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=146799&theme=oea&iframe_resize_id=ohm146799&show_question_numbers\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<\/div>\n<p>Look at the proportions [latex]{\\Large\\frac{1}{2}}={\\Large\\frac{4}{8}}[\/latex] and [latex]{\\Large\\frac{2}{3}}={\\Large\\frac{6}{9}}[\/latex]. From our work with equivalent fractions we know these equations are true. But how do we know if an equation is a proportion with equivalent fractions if it contains fractions with larger numbers?<\/p>\n<p>To determine if a proportion is true, we find the <strong>cross products<\/strong> of each proportion. To find the cross products, we multiply each denominator with the opposite numerator (diagonally across the equal sign). The results are called a cross products because of the cross formed. The cross products of a proportion are equal.<\/p>\n<p><img decoding=\"async\" class=\"aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24222123\/CNX_BMath_Figure_06_05_028_img.png\" alt=\"The figure shows cross multiplication of two proportions. There is the proportion 1 is to 2 as 4 is to 8. Arrows are shown diagonally across the equal sign to show cross products. The equations formed by cross multiplying are 8 \u00b7 1 = 8 and 2 \u00b7 4 = 8. There is the proportion 2 is to 3 as 6 is to 9. Arrows are shown diagonally across the equal sign to show cross products. The equations formed by cross multiplying are 9 \u00b7 2 = 18 and 3 \u00b7 6 = 18.\" \/><\/p>\n<p>Cross Products of a Proportion<\/p>\n<p>For any proportion of the form [latex]{\\Large\\frac{a}{b}}={\\Large\\frac{c}{d}}[\/latex], where [latex]b\\ne 0,d\\ne 0[\/latex], its cross products are equal.<\/p>\n<p><img decoding=\"async\" class=\"aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24222125\/CNX_BMath_Figure_06_05_003_img.png\" alt=\"No Alt Text\" \/><\/p>\n<p>Cross products can be used to test whether a proportion is true. To test whether an equation makes a proportion, we find the cross products. If they are the equal, we have a proportion.<\/p>\n<div class=\"textbox exercises\">\n<h3>example<\/h3>\n<p>Determine whether each equation is a proportion:<\/p>\n<p>1.\u00a0 [latex]{\\Large\\frac{4}{9}}={\\Large\\frac{12}{28}}[\/latex]<br \/>\n2.\u00a0 [latex]{\\Large\\frac{17.5}{37.5}}={\\Large\\frac{7}{15}}[\/latex]<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q586373\">Show Solution<\/span><\/p>\n<div id=\"q586373\" class=\"hidden-answer\" style=\"display: none\">\n<p>Solution<br \/>\nTo determine if the equation is a proportion, we find the cross products. If they are equal, the equation is a proportion.<\/p>\n<table id=\"eip-id1168468703669\" class=\"unnumbered unstyled\" summary=\"The figure shows the steps to finding the cross products of the proportion 4 is to 9 as 12 is to 28. The cross multiplication shown is 28 times 4 = 112 and 9 times 12 = 28.\">\n<tbody>\n<tr>\n<td>1.<\/td>\n<\/tr>\n<tr>\n<td>[latex]{\\Large\\frac{4}{9}}={\\Large\\frac{12}{28}}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Find the cross products.<\/td>\n<td>[latex]28\\cdot 4=1129\\cdot 12=108[\/latex]<\/p>\n<p><img decoding=\"async\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24222127\/CNX_BMath_Figure_06_05_020_img-02.png\" alt=\".\" \/><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>Since the cross products are not equal, [latex]28\\cdot 4\\ne 9\\cdot 12[\/latex], the equation is not a proportion.<\/p>\n<table id=\"eip-id1168469699712\" class=\"unnumbered unstyled\" summary=\"The figure shows the steps to finding the cross products of the proportion 17.5 is to 37.5 as 7 is to 15. The cross multiplication shown is 15 times 17.5 = 262.5 and 37.5 times 7 = 262.5.\">\n<tbody>\n<tr>\n<td>2.<\/td>\n<\/tr>\n<tr>\n<td>[latex]{\\Large\\frac{17.5}{37.5}}={\\Large\\frac{7}{15}}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Find the cross products.<\/td>\n<td>[latex]15\\cdot 17.5=262.5[\/latex]<\/p>\n<p>[latex]37.5\\cdot 7=262.5[\/latex]<\/p>\n<p><img decoding=\"async\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24222130\/CNX_BMath_Figure_06_05_021_img-02.png\" alt=\".\" \/><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>Since the cross products are equal, [latex]15\\cdot 17.5=37.5\\cdot 7[\/latex], the equation is a proportion.<\/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=\"ohm146809\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=146809&theme=oea&iframe_resize_id=ohm146809&show_question_numbers\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<\/div>\n<p><span style=\"color: #ff0000;\">\u00a0<\/span><\/p>\n<h2>Contribute!<\/h2>\n<div style=\"margin-bottom: 8px;\">Did you have an idea for improving this content? 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