{"id":4086,"date":"2020-04-05T20:59:06","date_gmt":"2020-04-05T20:59:06","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/mathforlibscoreq\/?post_type=chapter&#038;p=4086"},"modified":"2024-06-26T18:03:33","modified_gmt":"2024-06-26T18:03:33","slug":"writing-percents-as-ratios","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/slcc-mathforliberalartscorequisite\/chapter\/writing-percents-as-ratios\/","title":{"raw":"Writing Percents as Ratios","rendered":"Writing Percents as Ratios"},"content":{"raw":"<div class=\"textbox learning-objectives\">\r\n<h3>Learning Outcomes<\/h3>\r\n<ul>\r\n \t<li>Use the definition of percent<\/li>\r\n \t<li>Write a percent as a ratio<\/li>\r\n \t<li>Given a ratio, write as a percent and a fraction<\/li>\r\n<\/ul>\r\n<\/div>\r\nHow many cents are in one dollar? There are [latex]100[\/latex] cents in a dollar. How many years are in a century? There are [latex]100[\/latex] years in a century. Does this give you a clue about what the word \"percent\" means? It is really two words, \"per cent,\" and means per one hundred. A percent is a ratio whose denominator is [latex]100[\/latex]. We use the percent symbol [latex]\\text{%,}[\/latex] to show percent.\r\n<div class=\"textbox shaded\">\r\n<h3>Percent<\/h3>\r\nA percent is a ratio whose denominator is [latex]100[\/latex].\r\n\r\n<\/div>\r\nAccording to data from the American Association of Community Colleges [latex]\\left(2015\\right)[\/latex], about [latex]\\text{57%}[\/latex] of community college students are female. This means [latex]57[\/latex] out of every [latex]100[\/latex] community college students are female, as the image below\u00a0<span style=\"font-size: 16px;\">shows. Out of the [latex]100[\/latex] squares on the grid, [latex]57[\/latex] are shaded, which we write as the ratio [latex]\\Large\\frac{57}{100}[\/latex].<\/span>\r\n\r\nAmong every [latex]100[\/latex] community college students, [latex]57[\/latex] are female.\r\n\r\n<img class=\"aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24221858\/CNX_BMath_Figure_06_01_001.png\" alt=\"The figure shows a hundred flat with 57 units shaded.\" \/>\r\nSimilarly, [latex]\\text{25%}[\/latex] means a ratio of [latex]\\Large\\frac{25}{100}\\normalsize ,\\text{3%}[\/latex] means a ratio of [latex]\\Large\\frac{3}{100}[\/latex] and [latex]\\text{100%}[\/latex] means a ratio of [latex]\\Large\\frac{100}{100}[\/latex]. In words, \"one hundred percent\" means the total [latex]\\text{100%}[\/latex] is [latex]\\Large\\frac{100}{100}[\/latex], and since [latex]\\Large\\frac{100}{100}\\normalsize =1[\/latex], we see that [latex]\\text{100%}[\/latex] means [latex]1[\/latex] whole.\r\n<div class=\"textbox exercises\">\r\n<h3>example<\/h3>\r\nAccording to the Public Policy Institute of California [latex]\\left(2010\\right)\\text{, }\\text{44%}[\/latex] of parents of public school children would like their youngest child to earn a graduate degree. Write this percent as a ratio.\r\n\r\nSolution\r\n<table id=\"eip-id1168468695064\" class=\"unnumbered unstyled\" summary=\".\">\r\n<tbody>\r\n<tr>\r\n<td>The amount we want to convert is [latex]44%[\/latex].<\/td>\r\n<td>[latex]44%[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Write the percent as a ratio. Remember that <em>percent<\/em> means per [latex]100[\/latex].<\/td>\r\n<td>[latex]\\Large\\frac{44}{100}[\/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[ohm_question]146655[\/ohm_question]\r\n\r\n<\/div>\r\n&nbsp;\r\n<div class=\"textbox exercises\">\r\n<h3>example<\/h3>\r\nIn [latex]2007[\/latex], according to a U.S. Department of Education report, [latex]21[\/latex] out of every [latex]100[\/latex] first-time freshmen college students at [latex]\\text{4-year}[\/latex] public institutions took at least one remedial course. Write this as a ratio and then as a percent.\r\n[reveal-answer q=\"469361\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"469361\"]\r\n\r\nSolution\r\n<table id=\"eip-id1168467356132\" class=\"unnumbered unstyled\" summary=\".\">\r\n<tbody>\r\n<tr>\r\n<td>The amount we want to convert is [latex]21[\/latex] out of [latex]100[\/latex] .<\/td>\r\n<td>[latex]21[\/latex] out of [latex]100[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Write as a ratio.<\/td>\r\n<td>[latex]\\Large\\frac{21}{100}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Convert the [latex]21[\/latex] per [latex]100[\/latex] to percent.<\/td>\r\n<td>[latex]21[\/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\u00a0it<\/h3>\r\n[ohm_question]146656[\/ohm_question]\r\n\r\n<\/div>","rendered":"<div class=\"textbox learning-objectives\">\n<h3>Learning Outcomes<\/h3>\n<ul>\n<li>Use the definition of percent<\/li>\n<li>Write a percent as a ratio<\/li>\n<li>Given a ratio, write as a percent and a fraction<\/li>\n<\/ul>\n<\/div>\n<p>How many cents are in one dollar? There are [latex]100[\/latex] cents in a dollar. How many years are in a century? There are [latex]100[\/latex] years in a century. Does this give you a clue about what the word &#8220;percent&#8221; means? It is really two words, &#8220;per cent,&#8221; and means per one hundred. A percent is a ratio whose denominator is [latex]100[\/latex]. We use the percent symbol [latex]\\text{%,}[\/latex] to show percent.<\/p>\n<div class=\"textbox shaded\">\n<h3>Percent<\/h3>\n<p>A percent is a ratio whose denominator is [latex]100[\/latex].<\/p>\n<\/div>\n<p>According to data from the American Association of Community Colleges [latex]\\left(2015\\right)[\/latex], about [latex]\\text{57%}[\/latex] of community college students are female. This means [latex]57[\/latex] out of every [latex]100[\/latex] community college students are female, as the image below\u00a0<span style=\"font-size: 16px;\">shows. Out of the [latex]100[\/latex] squares on the grid, [latex]57[\/latex] are shaded, which we write as the ratio [latex]\\Large\\frac{57}{100}[\/latex].<\/span><\/p>\n<p>Among every [latex]100[\/latex] community college students, [latex]57[\/latex] are female.<\/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\/24221858\/CNX_BMath_Figure_06_01_001.png\" alt=\"The figure shows a hundred flat with 57 units shaded.\" \/><br \/>\nSimilarly, [latex]\\text{25%}[\/latex] means a ratio of [latex]\\Large\\frac{25}{100}\\normalsize ,\\text{3%}[\/latex] means a ratio of [latex]\\Large\\frac{3}{100}[\/latex] and [latex]\\text{100%}[\/latex] means a ratio of [latex]\\Large\\frac{100}{100}[\/latex]. In words, &#8220;one hundred percent&#8221; means the total [latex]\\text{100%}[\/latex] is [latex]\\Large\\frac{100}{100}[\/latex], and since [latex]\\Large\\frac{100}{100}\\normalsize =1[\/latex], we see that [latex]\\text{100%}[\/latex] means [latex]1[\/latex] whole.<\/p>\n<div class=\"textbox exercises\">\n<h3>example<\/h3>\n<p>According to the Public Policy Institute of California [latex]\\left(2010\\right)\\text{, }\\text{44%}[\/latex] of parents of public school children would like their youngest child to earn a graduate degree. Write this percent as a ratio.<\/p>\n<p>Solution<\/p>\n<table id=\"eip-id1168468695064\" class=\"unnumbered unstyled\" summary=\".\">\n<tbody>\n<tr>\n<td>The amount we want to convert is [latex]44%[\/latex].<\/td>\n<td>[latex]44%[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Write the percent as a ratio. Remember that <em>percent<\/em> means per [latex]100[\/latex].<\/td>\n<td>[latex]\\Large\\frac{44}{100}[\/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><iframe loading=\"lazy\" id=\"ohm146655\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=146655&theme=oea&iframe_resize_id=ohm146655&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>In [latex]2007[\/latex], according to a U.S. Department of Education report, [latex]21[\/latex] out of every [latex]100[\/latex] first-time freshmen college students at [latex]\\text{4-year}[\/latex] public institutions took at least one remedial course. Write this as a ratio and then as a percent.<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q469361\">Show Solution<\/span><\/p>\n<div id=\"q469361\" class=\"hidden-answer\" style=\"display: none\">\n<p>Solution<\/p>\n<table id=\"eip-id1168467356132\" class=\"unnumbered unstyled\" summary=\".\">\n<tbody>\n<tr>\n<td>The amount we want to convert is [latex]21[\/latex] out of [latex]100[\/latex] .<\/td>\n<td>[latex]21[\/latex] out of [latex]100[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Write as a ratio.<\/td>\n<td>[latex]\\Large\\frac{21}{100}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Convert the [latex]21[\/latex] per [latex]100[\/latex] to percent.<\/td>\n<td>[latex]21[\/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\u00a0it<\/h3>\n<p><iframe loading=\"lazy\" id=\"ohm146656\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=146656&theme=oea&iframe_resize_id=ohm146656&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-4086\">\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: 146656, 146655. <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 <\/section>","protected":false},"author":25777,"menu_order":6,"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\":\"Question ID: 146656, 146655\",\"author\":\"Lumen Learning\",\"organization\":\"\",\"url\":\"\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"IMathAS Community License CC-BY + GPL\"}]","CANDELA_OUTCOMES_GUID":"","pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"class_list":["post-4086","chapter","type-chapter","status-publish","hentry"],"part":5569,"_links":{"self":[{"href":"https:\/\/courses.lumenlearning.com\/slcc-mathforliberalartscorequisite\/wp-json\/pressbooks\/v2\/chapters\/4086","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/courses.lumenlearning.com\/slcc-mathforliberalartscorequisite\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/courses.lumenlearning.com\/slcc-mathforliberalartscorequisite\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/slcc-mathforliberalartscorequisite\/wp-json\/wp\/v2\/users\/25777"}],"version-history":[{"count":2,"href":"https:\/\/courses.lumenlearning.com\/slcc-mathforliberalartscorequisite\/wp-json\/pressbooks\/v2\/chapters\/4086\/revisions"}],"predecessor-version":[{"id":5580,"href":"https:\/\/courses.lumenlearning.com\/slcc-mathforliberalartscorequisite\/wp-json\/pressbooks\/v2\/chapters\/4086\/revisions\/5580"}],"part":[{"href":"https:\/\/courses.lumenlearning.com\/slcc-mathforliberalartscorequisite\/wp-json\/pressbooks\/v2\/parts\/5569"}],"metadata":[{"href":"https:\/\/courses.lumenlearning.com\/slcc-mathforliberalartscorequisite\/wp-json\/pressbooks\/v2\/chapters\/4086\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/courses.lumenlearning.com\/slcc-mathforliberalartscorequisite\/wp-json\/wp\/v2\/media?parent=4086"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/slcc-mathforliberalartscorequisite\/wp-json\/pressbooks\/v2\/chapter-type?post=4086"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/slcc-mathforliberalartscorequisite\/wp-json\/wp\/v2\/contributor?post=4086"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/slcc-mathforliberalartscorequisite\/wp-json\/wp\/v2\/license?post=4086"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}