{"id":10381,"date":"2017-05-26T18:56:12","date_gmt":"2017-05-26T18:56:12","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/prealgebra\/?post_type=chapter&#038;p=10381"},"modified":"2024-04-30T16:36:35","modified_gmt":"2024-04-30T16:36:35","slug":"writing-ratios-as-fractions-or-decimals","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/wm-developmentalemporium\/chapter\/writing-ratios-as-fractions-or-decimals\/","title":{"raw":"Writing Ratios as Fractions","rendered":"Writing Ratios as Fractions"},"content":{"raw":"<div class=\"textbox learning-objectives\">\r\n<h3>Learning Outcomes<\/h3>\r\n<ul>\r\n \t<li>Write a ratio as a fraction<\/li>\r\n<\/ul>\r\n<\/div>\r\nWhen you apply for a mortgage, the loan officer will compare your total debt to your total income to decide if you qualify for the loan. This comparison is called the debt-to-income ratio. A ratio compares two quantities that are measured with the same unit. If we compare [latex]a[\/latex] and [latex]b[\/latex] , the ratio is written as [latex]a\\text{ to }b,{\\Large\\frac{a}{b}},\\text{ or }\\mathit{\\text{a}}\\text{:}\\mathit{\\text{b}}\\text{.}[\/latex]\r\n<div class=\"textbox shaded\">\r\n<h3>Ratios<\/h3>\r\nA ratio compares two numbers or two quantities that are measured with the same unit. The ratio of [latex]a[\/latex] to [latex]b[\/latex] is written [latex]a\\text{ to }b,{\\Large\\frac{a}{b}},\\text{or}\\mathit{\\text{a}}\\text{:}\\mathit{\\text{b}}\\text{.}[\/latex]\r\n\r\n<\/div>\r\nIn this section, we will use the fraction notation. When a ratio is written in fraction form, the fraction should be simplified. If it is an improper fraction, we do not change it to a mixed number. Because a ratio compares two quantities, we would leave a ratio as [latex]{\\Large\\frac{4}{1}}[\/latex] instead of simplifying it to [latex]4[\/latex] so that we can see the two parts of the ratio.\r\n<div class=\"textbox exercises\">\r\n<h3>example<\/h3>\r\nWrite each ratio as a fraction:\r\n<ol>\r\n \t<li>\u00a0[latex]15\\text{ to }27[\/latex]<\/li>\r\n \t<li>\u00a0 [latex]45\\text{ to }18[\/latex]<\/li>\r\n<\/ol>\r\nSolution\r\n<table id=\"eip-id1168466052931\" class=\"unnumbered unstyled\" summary=\".\">\r\n<tbody>\r\n<tr>\r\n<td>1.<\/td>\r\n<td><\/td>\r\n<\/tr>\r\n<tr>\r\n<td><\/td>\r\n<td>[latex]\\text{15 to 27}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Write as a fraction with the first number in the numerator and the second in the denominator.<\/td>\r\n<td>[latex]{\\Large\\frac{15}{27}}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Simplify the fraction.<\/td>\r\n<td>[latex]{\\Large\\frac{5}{9}}[\/latex]<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<table id=\"eip-id1168464946214\" class=\"unnumbered unstyled\" summary=\".\">\r\n<tbody>\r\n<tr>\r\n<td>2.<\/td>\r\n<td><\/td>\r\n<\/tr>\r\n<tr>\r\n<td><\/td>\r\n<td>[latex]\\text{45 to 18}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Write as a fraction with the first number in the numerator and the second in the denominator.<\/td>\r\n<td>[latex]{\\Large\\frac{45}{18}}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Simplify.<\/td>\r\n<td>[latex]{\\Large\\frac{5}{2}}[\/latex]<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\nWe leave the ratio in (2) as an improper fraction.\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]146453[\/ohm_question]\r\n\r\n<\/div>\r\nIn the following video you will see more examples of how to express a ratio as a fraction.\r\n\r\nhttps:\/\/youtu.be\/zUGLLvymVag\r\n<h2>Ratios Involving Decimals<\/h2>\r\nWe will often work with ratios of decimals, especially when we have ratios involving money. In these cases, we can eliminate the decimals by using the Equivalent Fractions Property to convert the ratio to a fraction with whole numbers in the numerator and denominator.\r\n\r\nFor example, consider the ratio [latex]0.8\\text{ to }0.05[\/latex]. We can write it as a fraction with decimals and then multiply the numerator and denominator by [latex]100[\/latex] to eliminate the decimals.\r\n\r\n<img class=\"aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24221828\/CNX_BMath_Figure_05_06_003_img.png\" alt=\"A fraction is shown with 0.8 in the numerator and 0.05 in the denominator. Below it is the same fraction with both the numerator and denominator multiplied by 100. Below that is a fraction with 80 in the numerator and 5 in the denominator.\" \/>\r\nDo you see a shortcut to find the equivalent fraction? Notice that [latex]0.8={\\Large\\frac{8}{10}}[\/latex] and [latex]0.05={\\Large\\frac{5}{100}}[\/latex]. The least common denominator of [latex]{\\Large\\frac{8}{10}}[\/latex] and [latex]{\\Large\\frac{5}{100}}[\/latex] is [latex]100[\/latex]. By multiplying the numerator and denominator of [latex]{\\Large\\frac{0.8}{0.05}}[\/latex] by [latex]100[\/latex], we \u2018moved\u2019 the decimal two places to the right to get the equivalent fraction with no decimals. Now that we understand the math behind the process, we can find the fraction with no decimals like this:\r\n<table id=\"eip-726\" class=\"unnumbered unstyled\" summary=\".\">\r\n<tbody>\r\n<tr>\r\n<td><\/td>\r\n<td><img src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24221829\/CNX_BMath_Figure_05_06_001_img.png\" alt=\"The top line says 0.80 over 0.05. There are blue arrows moving the decimal points over 2 places to the right.\" \/><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>\"Move\" the decimal 2 places.<\/td>\r\n<td>[latex]{\\Large\\frac{80}{5}}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Simplify.<\/td>\r\n<td>[latex]{\\Large\\frac{16}{1}}[\/latex]<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\nYou do not have to write out every step when you multiply the numerator and denominator by powers of ten. As long as you move both decimal places the same number of places, the ratio will remain the same.\r\n<div class=\"textbox exercises\">\r\n<h3>example<\/h3>\r\nWrite each ratio as a fraction of whole numbers:\r\n1.\u00a0 [latex]4.8\\text{ to }11.2[\/latex]\r\n2.\u00a0 [latex]2.7\\text{ to }0.54[\/latex]\r\n[reveal-answer q=\"432704\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"432704\"]\r\n\r\nSolution\r\n<table id=\"eip-id1168467212146\" class=\"unnumbered unstyled\" summary=\".\">\r\n<tbody>\r\n<tr>\r\n<td>1. \u00a0 [latex]\\text{4.8 to 11.2}[\/latex]<\/td>\r\n<td><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Write as a fraction.<\/td>\r\n<td>[latex]{\\Large\\frac{4.8}{11.2}}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Rewrite as an equivalent fraction without decimals, by moving both decimal points [latex]1[\/latex] place to the right.<\/td>\r\n<td>[latex]{\\Large\\frac{48}{112}}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Simplify.<\/td>\r\n<td>[latex]{\\Large\\frac{3}{7}}[\/latex]<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\nSo [latex]4.8\\text{ to }11.2[\/latex] is equivalent to [latex]{\\Large\\frac{3}{7}}[\/latex].\r\n<table id=\"eip-id1168468703868\" class=\"unnumbered unstyled\" summary=\".\">\r\n<tbody>\r\n<tr>\r\n<td>2.\r\n\r\nThe numerator has one decimal place and the denominator has [latex]2[\/latex]. To clear both decimals we need to move the decimal [latex]2[\/latex] places to the right.\r\n\r\n[latex]2.7\\text{ to }0.54[\/latex]<\/td>\r\n<td><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Write as a fraction.<\/td>\r\n<td>[latex]{\\Large\\frac{2.7}{0.54}}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Move both decimals right two places.<\/td>\r\n<td>[latex]{\\Large\\frac{270}{54}}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Simplify.<\/td>\r\n<td>[latex]{\\Large\\frac{5}{1}}[\/latex]<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\nSo [latex]2.7\\text{ to }0.54[\/latex] is equivalent to [latex]{\\Large\\frac{5}{1}}[\/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]146454[\/ohm_question]\r\n\r\n<\/div>\r\nThe following video shows more examples of how to express a ratio given as a decimal as a fraction.\r\n\r\nhttps:\/\/youtu.be\/xX-qtSw0hek\r\n\r\nSome ratios compare two mixed numbers. Remember that to divide mixed numbers, you first rewrite them as improper fractions.\r\n<div class=\"textbox exercises\">\r\n<h3>example<\/h3>\r\nWrite the ratio of [latex]1\\Large\\frac{1}{4}\\normalsize\\text{ to }2\\Large\\frac{3}{8}[\/latex] as a fraction.\r\n[reveal-answer q=\"485526\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"485526\"]\r\n\r\nSolution\r\n<table id=\"eip-id1168466269627\" class=\"unnumbered unstyled\" summary=\".\">\r\n<tbody>\r\n<tr>\r\n<td><\/td>\r\n<td>[latex]1{\\Large\\frac{1}{4}}\\text{ to }2{\\Large\\frac{3}{8}}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Write as a fraction.<\/td>\r\n<td>[latex]{\\Large\\frac{1\\LARGE\\frac{1}{4}}{\\normalsize 2\\LARGE\\frac{3}{8}}}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Convert the numerator and denominator to improper fractions.<\/td>\r\n<td>[latex]{\\Large\\frac{\\LARGE\\frac{5}{4}}{\\LARGE\\frac{19}{8}}}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Rewrite as a division of fractions.<\/td>\r\n<td>[latex]{\\Large\\frac{5}{4}}\\div {\\Large\\frac{19}{8}}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Invert the divisor and multiply.<\/td>\r\n<td>[latex]{\\Large\\frac{5}{4}}\\cdot {\\Large\\frac{8}{19}}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Simplify.<\/td>\r\n<td>[latex]{\\Large\\frac{10}{19}}[\/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]146469[\/ohm_question]\r\n\r\n<\/div>","rendered":"<div class=\"textbox learning-objectives\">\n<h3>Learning Outcomes<\/h3>\n<ul>\n<li>Write a ratio as a fraction<\/li>\n<\/ul>\n<\/div>\n<p>When you apply for a mortgage, the loan officer will compare your total debt to your total income to decide if you qualify for the loan. This comparison is called the debt-to-income ratio. A ratio compares two quantities that are measured with the same unit. If we compare [latex]a[\/latex] and [latex]b[\/latex] , the ratio is written as [latex]a\\text{ to }b,{\\Large\\frac{a}{b}},\\text{ or }\\mathit{\\text{a}}\\text{:}\\mathit{\\text{b}}\\text{.}[\/latex]<\/p>\n<div class=\"textbox shaded\">\n<h3>Ratios<\/h3>\n<p>A ratio compares two numbers or two quantities that are measured with the same unit. The ratio of [latex]a[\/latex] to [latex]b[\/latex] is written [latex]a\\text{ to }b,{\\Large\\frac{a}{b}},\\text{or}\\mathit{\\text{a}}\\text{:}\\mathit{\\text{b}}\\text{.}[\/latex]<\/p>\n<\/div>\n<p>In this section, we will use the fraction notation. When a ratio is written in fraction form, the fraction should be simplified. If it is an improper fraction, we do not change it to a mixed number. Because a ratio compares two quantities, we would leave a ratio as [latex]{\\Large\\frac{4}{1}}[\/latex] instead of simplifying it to [latex]4[\/latex] so that we can see the two parts of the ratio.<\/p>\n<div class=\"textbox exercises\">\n<h3>example<\/h3>\n<p>Write each ratio as a fraction:<\/p>\n<ol>\n<li>\u00a0[latex]15\\text{ to }27[\/latex]<\/li>\n<li>\u00a0 [latex]45\\text{ to }18[\/latex]<\/li>\n<\/ol>\n<p>Solution<\/p>\n<table id=\"eip-id1168466052931\" class=\"unnumbered unstyled\" summary=\".\">\n<tbody>\n<tr>\n<td>1.<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td>[latex]\\text{15 to 27}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Write as a fraction with the first number in the numerator and the second in the denominator.<\/td>\n<td>[latex]{\\Large\\frac{15}{27}}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Simplify the fraction.<\/td>\n<td>[latex]{\\Large\\frac{5}{9}}[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<table id=\"eip-id1168464946214\" class=\"unnumbered unstyled\" summary=\".\">\n<tbody>\n<tr>\n<td>2.<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td>[latex]\\text{45 to 18}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Write as a fraction with the first number in the numerator and the second in the denominator.<\/td>\n<td>[latex]{\\Large\\frac{45}{18}}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Simplify.<\/td>\n<td>[latex]{\\Large\\frac{5}{2}}[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>We leave the ratio in (2) as an improper fraction.<\/p>\n<\/div>\n<p>&nbsp;<\/p>\n<div class=\"textbox key-takeaways\">\n<h3>try it<\/h3>\n<p><iframe loading=\"lazy\" id=\"ohm146453\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=146453&theme=oea&iframe_resize_id=ohm146453&show_question_numbers\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<\/div>\n<p>In the following video you will see more examples of how to express a ratio as a fraction.<\/p>\n<p><iframe loading=\"lazy\" id=\"oembed-1\" title=\"Examples:  Write a Ratio as a Simplified Fraction\" width=\"500\" height=\"281\" src=\"https:\/\/www.youtube.com\/embed\/zUGLLvymVag?feature=oembed&#38;rel=0\" frameborder=\"0\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/p>\n<h2>Ratios Involving Decimals<\/h2>\n<p>We will often work with ratios of decimals, especially when we have ratios involving money. In these cases, we can eliminate the decimals by using the Equivalent Fractions Property to convert the ratio to a fraction with whole numbers in the numerator and denominator.<\/p>\n<p>For example, consider the ratio [latex]0.8\\text{ to }0.05[\/latex]. We can write it as a fraction with decimals and then multiply the numerator and denominator by [latex]100[\/latex] to eliminate the decimals.<\/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\/24221828\/CNX_BMath_Figure_05_06_003_img.png\" alt=\"A fraction is shown with 0.8 in the numerator and 0.05 in the denominator. Below it is the same fraction with both the numerator and denominator multiplied by 100. Below that is a fraction with 80 in the numerator and 5 in the denominator.\" \/><br \/>\nDo you see a shortcut to find the equivalent fraction? Notice that [latex]0.8={\\Large\\frac{8}{10}}[\/latex] and [latex]0.05={\\Large\\frac{5}{100}}[\/latex]. The least common denominator of [latex]{\\Large\\frac{8}{10}}[\/latex] and [latex]{\\Large\\frac{5}{100}}[\/latex] is [latex]100[\/latex]. By multiplying the numerator and denominator of [latex]{\\Large\\frac{0.8}{0.05}}[\/latex] by [latex]100[\/latex], we \u2018moved\u2019 the decimal two places to the right to get the equivalent fraction with no decimals. Now that we understand the math behind the process, we can find the fraction with no decimals like this:<\/p>\n<table id=\"eip-726\" class=\"unnumbered unstyled\" summary=\".\">\n<tbody>\n<tr>\n<td><\/td>\n<td><img decoding=\"async\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24221829\/CNX_BMath_Figure_05_06_001_img.png\" alt=\"The top line says 0.80 over 0.05. There are blue arrows moving the decimal points over 2 places to the right.\" \/><\/td>\n<\/tr>\n<tr>\n<td>&#8220;Move&#8221; the decimal 2 places.<\/td>\n<td>[latex]{\\Large\\frac{80}{5}}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Simplify.<\/td>\n<td>[latex]{\\Large\\frac{16}{1}}[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>You do not have to write out every step when you multiply the numerator and denominator by powers of ten. As long as you move both decimal places the same number of places, the ratio will remain the same.<\/p>\n<div class=\"textbox exercises\">\n<h3>example<\/h3>\n<p>Write each ratio as a fraction of whole numbers:<br \/>\n1.\u00a0 [latex]4.8\\text{ to }11.2[\/latex]<br \/>\n2.\u00a0 [latex]2.7\\text{ to }0.54[\/latex]<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q432704\">Show Solution<\/span><\/p>\n<div id=\"q432704\" class=\"hidden-answer\" style=\"display: none\">\n<p>Solution<\/p>\n<table id=\"eip-id1168467212146\" class=\"unnumbered unstyled\" summary=\".\">\n<tbody>\n<tr>\n<td>1. \u00a0 [latex]\\text{4.8 to 11.2}[\/latex]<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>Write as a fraction.<\/td>\n<td>[latex]{\\Large\\frac{4.8}{11.2}}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Rewrite as an equivalent fraction without decimals, by moving both decimal points [latex]1[\/latex] place to the right.<\/td>\n<td>[latex]{\\Large\\frac{48}{112}}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Simplify.<\/td>\n<td>[latex]{\\Large\\frac{3}{7}}[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>So [latex]4.8\\text{ to }11.2[\/latex] is equivalent to [latex]{\\Large\\frac{3}{7}}[\/latex].<\/p>\n<table id=\"eip-id1168468703868\" class=\"unnumbered unstyled\" summary=\".\">\n<tbody>\n<tr>\n<td>2.<\/p>\n<p>The numerator has one decimal place and the denominator has [latex]2[\/latex]. To clear both decimals we need to move the decimal [latex]2[\/latex] places to the right.<\/p>\n<p>[latex]2.7\\text{ to }0.54[\/latex]<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>Write as a fraction.<\/td>\n<td>[latex]{\\Large\\frac{2.7}{0.54}}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Move both decimals right two places.<\/td>\n<td>[latex]{\\Large\\frac{270}{54}}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Simplify.<\/td>\n<td>[latex]{\\Large\\frac{5}{1}}[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>So [latex]2.7\\text{ to }0.54[\/latex] is equivalent to [latex]{\\Large\\frac{5}{1}}[\/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=\"ohm146454\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=146454&theme=oea&iframe_resize_id=ohm146454&show_question_numbers\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<\/div>\n<p>The following video shows more examples of how to express a ratio given as a decimal as a fraction.<\/p>\n<p><iframe loading=\"lazy\" id=\"oembed-2\" title=\"Examples:  Write a Ratio as a Simplified Fractions Involving Decimals and Fractions\" width=\"500\" height=\"281\" src=\"https:\/\/www.youtube.com\/embed\/xX-qtSw0hek?feature=oembed&#38;rel=0\" frameborder=\"0\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/p>\n<p>Some ratios compare two mixed numbers. Remember that to divide mixed numbers, you first rewrite them as improper fractions.<\/p>\n<div class=\"textbox exercises\">\n<h3>example<\/h3>\n<p>Write the ratio of [latex]1\\Large\\frac{1}{4}\\normalsize\\text{ to }2\\Large\\frac{3}{8}[\/latex] as a fraction.<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q485526\">Show Solution<\/span><\/p>\n<div id=\"q485526\" class=\"hidden-answer\" style=\"display: none\">\n<p>Solution<\/p>\n<table id=\"eip-id1168466269627\" class=\"unnumbered unstyled\" summary=\".\">\n<tbody>\n<tr>\n<td><\/td>\n<td>[latex]1{\\Large\\frac{1}{4}}\\text{ to }2{\\Large\\frac{3}{8}}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Write as a fraction.<\/td>\n<td>[latex]{\\Large\\frac{1\\LARGE\\frac{1}{4}}{\\normalsize 2\\LARGE\\frac{3}{8}}}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Convert the numerator and denominator to improper fractions.<\/td>\n<td>[latex]{\\Large\\frac{\\LARGE\\frac{5}{4}}{\\LARGE\\frac{19}{8}}}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Rewrite as a division of fractions.<\/td>\n<td>[latex]{\\Large\\frac{5}{4}}\\div {\\Large\\frac{19}{8}}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Invert the divisor and multiply.<\/td>\n<td>[latex]{\\Large\\frac{5}{4}}\\cdot {\\Large\\frac{8}{19}}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Simplify.<\/td>\n<td>[latex]{\\Large\\frac{10}{19}}[\/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=\"ohm146469\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=146469&theme=oea&iframe_resize_id=ohm146469&show_question_numbers\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<\/div>\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-10381\">\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>Question ID 146469, 146454, 146453. <strong>Authored by<\/strong>: Lumen Learningq. <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><strong>Located at<\/strong>: <a target=\"_blank\" href=\"https:\/\/youtu.be\/zUGLLvymVag\">https:\/\/youtu.be\/zUGLLvymVag<\/a>. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/about\/pdm\">Public Domain: No Known Copyright<\/a><\/em><\/li><li>Examples: Write a Ratio as a Simplified Fractions Involving Decimals and Fractions. <strong>Authored by<\/strong>: James Sousa (Mathispower4u.com). <strong>Located at<\/strong>: <a target=\"_blank\" href=\"https:\/\/youtu.be\/xX-qtSw0hek\">https:\/\/youtu.be\/xX-qtSw0hek<\/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, 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":17533,"menu_order":9,"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\":\"cc\",\"description\":\"\",\"author\":\"\",\"organization\":\"\",\"url\":\"https:\/\/youtu.be\/zUGLLvymVag\",\"project\":\"\",\"license\":\"pd\",\"license_terms\":\"\"},{\"type\":\"cc\",\"description\":\"Examples: Write a Ratio as a Simplified Fractions Involving Decimals and Fractions\",\"author\":\"James Sousa (Mathispower4u.com)\",\"organization\":\"\",\"url\":\"https:\/\/youtu.be\/xX-qtSw0hek\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"\"},{\"type\":\"original\",\"description\":\"Question ID 146469, 146454, 146453\",\"author\":\"Lumen 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