{"id":1114,"date":"2023-03-30T16:51:39","date_gmt":"2023-03-30T16:51:39","guid":{"rendered":"https:\/\/content.one.lumenlearning.com\/quantitativereasoning\/?post_type=chapter&#038;p=1114"},"modified":"2025-08-24T04:06:53","modified_gmt":"2025-08-24T04:06:53","slug":"percents-learn-it-1","status":"web-only","type":"chapter","link":"https:\/\/content.one.lumenlearning.com\/quantitativereasoning\/chapter\/percents-learn-it-1\/","title":{"raw":"Percents: Learn It 1","rendered":"Percents: Learn It 1"},"content":{"raw":"<section class=\"textbox learningGoals\">\r\n<ul>\r\n\t<li>Write percents<\/li>\r\n\t<li>Determine unit rate using percentages<\/li>\r\n\t<li>Find both the relative and absolute change<\/li>\r\n<\/ul>\r\n<\/section>\r\n<h2>Percents<\/h2>\r\n<section class=\"textbox recall\">Recall that a fraction is written [latex]\\dfrac{a}{b},[\/latex] where [latex]a[\/latex] and [latex]b[\/latex] are integers and [latex]b \\neq 0[\/latex]. In a fraction, [latex]a[\/latex] is called the numerator and [latex]b[\/latex] is called the denominator.<\/section>\r\n<p>A\u00a0<strong>percent<\/strong> can be expressed as a fraction, that is a\u00a0<strong>ratio,\u00a0<\/strong>of some part of a quantity out of the whole quantity,\u00a0 [latex]\\dfrac{\\text{part}}{\\text{whole}}[\/latex]. <strong>Percent <\/strong>literally means \u201cper [latex]100[\/latex],\u201d or \u201cparts per hundred.\u201d When we write [latex]40\\%[\/latex], this is equivalent to the fraction [latex]\\displaystyle\\frac{40}{100}[\/latex] or the decimal [latex]0.40[\/latex]. Notice that [latex]80[\/latex] out of [latex]200[\/latex] and [latex]10[\/latex] out of [latex]25[\/latex] are also [latex]40\\%[\/latex], since [latex]\\displaystyle\\frac{80}{200}=\\frac{10}{25}=\\frac{40}{100}[\/latex].<\/p>\r\n<center><a href=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/1141\/2016\/11\/14203900\/percent-40844_1280.png\"><img class=\"wp-image-494\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/1141\/2016\/11\/14203900\/percent-40844_1280.png\" alt=\"Rounded rectangle divided into ten vertical sections. The left four are shaded yellow, while the right 6 are empty.\" width=\"500\" height=\"282\" \/><\/a><\/center><center><strong><span style=\"font-size: 10pt;\">Figure 1. A visual depiction of [latex]40\\%[\/latex]<\/span><\/strong><\/center>\r\n<section class=\"textbox keyTakeaway\">\r\n<div>\r\n<h3>percent<\/h3>\r\n\r\nA <strong>ratio<\/strong> is a comparison of two numbers by division. If we have a <em>part<\/em> that is some <em>percent<\/em> of a <em>whole<\/em>, then [latex]\\displaystyle\\text{percent}=\\frac{\\text{part}}{\\text{whole}}[\/latex], or equivalently, [latex]\\text{percent}\\cdot\\text{whole}=\\text{part}[\/latex].\u00a0<\/div>\r\n<\/section>\r\n<p>To do calculations using percentages, we write the percent as a decimal or fraction.<\/p>\r\n<h2>Convert a Percent to a\u00a0Decimal or Fraction<\/h2>\r\n<p>To do mathematical calculations with a given percent, we must first write it in numerical form. A percent may be represented as a percent, a fraction, or a decimal.<\/p>\r\n<section class=\"textbox questionHelp\">\r\n<p><strong>How to: Convert a Percent to a Fraction<\/strong><\/p>\r\n<ol>\r\n\t<li>Write the percent over a denominator of [latex]100[\/latex] and drop the percent symbol [latex]\\%[\/latex].<\/li>\r\n\t<li>Reduce the resulting fraction as needed.<\/li>\r\n<\/ol>\r\n<p style=\"padding-left: 60px;\">Ex. [latex]80 \\% =\\dfrac{80}{100}=\\dfrac{4\\cdot 20}{5\\cdot 20}=\\dfrac{4}{5}[\/latex]<\/p>\r\n<\/section>\r\n<section class=\"textbox questionHelp\">\r\n<p><strong>How to: Convert a Percent to a Decimal<\/strong><\/p>\r\n<p>There are three methods for writing a percent as a decimal.<\/p>\r\n<ul>\r\n\t<li>You can write the percent as a fraction, simply fully, then divide the numerator by the denominator.\r\n\r\n<ul>\r\n\t<li>[latex]80 \\% =\\dfrac{80}{100}=\\dfrac{4\\cdot 20}{5\\cdot 20}=\\dfrac{4}{5}=0.8[\/latex]<\/li>\r\n<\/ul>\r\n<\/li>\r\n\t<li>You can write the percent as a fraction, simplify to a denominator of [latex]10[\/latex], [latex]100[\/latex], [latex]1000[\/latex], etc., then rewrite as a decimal.\r\n\r\n<ul>\r\n\t<li>[latex]80 \\% =\\dfrac{80}{100}=\\dfrac{8\\cdot 10}{10\\cdot 10}=\\dfrac{8}{10}=\\text{ eight tenths }=0.8[\/latex]<\/li>\r\n<\/ul>\r\n<\/li>\r\n\t<li>Write the percent without the percent symbol [latex]\\%[\/latex], then place a decimal after the ones place and move it two places to the left.\r\n\r\n<ul>\r\n\t<li>[latex]80 \\% =80.0=0.80=0.8[\/latex]<\/li>\r\n<\/ul>\r\n<\/li>\r\n<\/ul>\r\n<\/section>\r\n<section class=\"textbox example\">Write each as a percent:\r\n\r\n<ol>\r\n\t<li>[latex]\\displaystyle\\frac{1}{4}[\/latex]<\/li>\r\n\t<li>[latex]0.02[\/latex]<\/li>\r\n\t<li>[latex]2.35[\/latex]<\/li>\r\n<\/ol>\r\n\r\n[reveal-answer q=\"660805\"]Show Solution[\/reveal-answer] [hidden-answer a=\"660805\"]\r\n\r\n<ol>\r\n\t<li>[latex]\\displaystyle\\frac{1}{4}=0.25 = 25\\%[\/latex]<\/li>\r\n\t<li>[latex]0.02 = 2\\%[\/latex]<\/li>\r\n\t<li>[latex]2.35 = 235\\%[\/latex]<\/li>\r\n<\/ol>\r\n\r\n[\/hidden-answer]<\/section>\r\n<section class=\"textbox tryIt\">[ohm2_question hide_question_numbers=1]6751[\/ohm2_question]<\/section>","rendered":"<section class=\"textbox learningGoals\">\n<ul>\n<li>Write percents<\/li>\n<li>Determine unit rate using percentages<\/li>\n<li>Find both the relative and absolute change<\/li>\n<\/ul>\n<\/section>\n<h2>Percents<\/h2>\n<section class=\"textbox recall\">Recall that a fraction is written [latex]\\dfrac{a}{b},[\/latex] where [latex]a[\/latex] and [latex]b[\/latex] are integers and [latex]b \\neq 0[\/latex]. In a fraction, [latex]a[\/latex] is called the numerator and [latex]b[\/latex] is called the denominator.<\/section>\n<p>A\u00a0<strong>percent<\/strong> can be expressed as a fraction, that is a\u00a0<strong>ratio,\u00a0<\/strong>of some part of a quantity out of the whole quantity,\u00a0 [latex]\\dfrac{\\text{part}}{\\text{whole}}[\/latex]. <strong>Percent <\/strong>literally means \u201cper [latex]100[\/latex],\u201d or \u201cparts per hundred.\u201d When we write [latex]40\\%[\/latex], this is equivalent to the fraction [latex]\\displaystyle\\frac{40}{100}[\/latex] or the decimal [latex]0.40[\/latex]. Notice that [latex]80[\/latex] out of [latex]200[\/latex] and [latex]10[\/latex] out of [latex]25[\/latex] are also [latex]40\\%[\/latex], since [latex]\\displaystyle\\frac{80}{200}=\\frac{10}{25}=\\frac{40}{100}[\/latex].<\/p>\n<div style=\"text-align: center;\"><a href=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/1141\/2016\/11\/14203900\/percent-40844_1280.png\"><img loading=\"lazy\" decoding=\"async\" class=\"wp-image-494\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/1141\/2016\/11\/14203900\/percent-40844_1280.png\" alt=\"Rounded rectangle divided into ten vertical sections. The left four are shaded yellow, while the right 6 are empty.\" width=\"500\" height=\"282\" \/><\/a><\/div>\n<div style=\"text-align: center;\"><strong><span style=\"font-size: 10pt;\">Figure 1. A visual depiction of [latex]40\\%[\/latex]<\/span><\/strong><\/div>\n<section class=\"textbox keyTakeaway\">\n<div>\n<h3>percent<\/h3>\n<p>A <strong>ratio<\/strong> is a comparison of two numbers by division. If we have a <em>part<\/em> that is some <em>percent<\/em> of a <em>whole<\/em>, then [latex]\\displaystyle\\text{percent}=\\frac{\\text{part}}{\\text{whole}}[\/latex], or equivalently, [latex]\\text{percent}\\cdot\\text{whole}=\\text{part}[\/latex].\u00a0<\/div>\n<\/section>\n<p>To do calculations using percentages, we write the percent as a decimal or fraction.<\/p>\n<h2>Convert a Percent to a\u00a0Decimal or Fraction<\/h2>\n<p>To do mathematical calculations with a given percent, we must first write it in numerical form. A percent may be represented as a percent, a fraction, or a decimal.<\/p>\n<section class=\"textbox questionHelp\">\n<p><strong>How to: Convert a Percent to a Fraction<\/strong><\/p>\n<ol>\n<li>Write the percent over a denominator of [latex]100[\/latex] and drop the percent symbol [latex]\\%[\/latex].<\/li>\n<li>Reduce the resulting fraction as needed.<\/li>\n<\/ol>\n<p style=\"padding-left: 60px;\">Ex. [latex]80 \\% =\\dfrac{80}{100}=\\dfrac{4\\cdot 20}{5\\cdot 20}=\\dfrac{4}{5}[\/latex]<\/p>\n<\/section>\n<section class=\"textbox questionHelp\">\n<p><strong>How to: Convert a Percent to a Decimal<\/strong><\/p>\n<p>There are three methods for writing a percent as a decimal.<\/p>\n<ul>\n<li>You can write the percent as a fraction, simply fully, then divide the numerator by the denominator.\n<ul>\n<li>[latex]80 \\% =\\dfrac{80}{100}=\\dfrac{4\\cdot 20}{5\\cdot 20}=\\dfrac{4}{5}=0.8[\/latex]<\/li>\n<\/ul>\n<\/li>\n<li>You can write the percent as a fraction, simplify to a denominator of [latex]10[\/latex], [latex]100[\/latex], [latex]1000[\/latex], etc., then rewrite as a decimal.\n<ul>\n<li>[latex]80 \\% =\\dfrac{80}{100}=\\dfrac{8\\cdot 10}{10\\cdot 10}=\\dfrac{8}{10}=\\text{ eight tenths }=0.8[\/latex]<\/li>\n<\/ul>\n<\/li>\n<li>Write the percent without the percent symbol [latex]\\%[\/latex], then place a decimal after the ones place and move it two places to the left.\n<ul>\n<li>[latex]80 \\% =80.0=0.80=0.8[\/latex]<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<\/section>\n<section class=\"textbox example\">Write each as a percent:<\/p>\n<ol>\n<li>[latex]\\displaystyle\\frac{1}{4}[\/latex]<\/li>\n<li>[latex]0.02[\/latex]<\/li>\n<li>[latex]2.35[\/latex]<\/li>\n<\/ol>\n<div class=\"qa-wrapper\" style=\"display: block\"><button class=\"show-answer show-answer-button collapsed\" data-target=\"q660805\">Show Solution<\/button> <\/p>\n<div id=\"q660805\" class=\"hidden-answer\" style=\"display: none\">\n<ol>\n<li>[latex]\\displaystyle\\frac{1}{4}=0.25 = 25\\%[\/latex]<\/li>\n<li>[latex]0.02 = 2\\%[\/latex]<\/li>\n<li>[latex]2.35 = 235\\%[\/latex]<\/li>\n<\/ol>\n<\/div>\n<\/div>\n<\/section>\n<section class=\"textbox tryIt\"><iframe loading=\"lazy\" id=\"ohm6751\" class=\"resizable\" src=\"https:\/\/ohm.one.lumenlearning.com\/multiembedq.php?id=6751&theme=lumen&iframe_resize_id=ohm6751&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/section>\n","protected":false},"author":15,"menu_order":11,"template":"","meta":{"_candela_citation":"[{\"type\":\"original\",\"description\":\"Revision and Adaptation\",\"author\":\"\",\"organization\":\"Lumen Learning\",\"url\":\"\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"\"},{\"type\":\"cc\",\"description\":\"Problem Solving\",\"author\":\"David Lippman\",\"organization\":\"\",\"url\":\"http:\/\/www.opentextbookstore.com\/mathinsociety\/\",\"project\":\"Math in Society\",\"license\":\"cc-by-sa\",\"license_terms\":\"\"},{\"type\":\"cc\",\"description\":\"40% shaded 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