{"id":4514,"date":"2017-06-07T18:50:14","date_gmt":"2017-06-07T18:50:14","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/aacc-collegealgebrafoundations\/chapter\/read-percent-basics\/"},"modified":"2017-08-15T11:54:25","modified_gmt":"2017-08-15T11:54:25","slug":"read-percent-basics","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/aacc-collegealgebrafoundations\/chapter\/read-percent-basics\/","title":{"raw":"Finding a Percent of a Whole","rendered":"Finding a Percent of a Whole"},"content":{"raw":"<div class=\"bcc-box bcc-highlight\">\r\n<h3>Learning Objectives<\/h3>\r\n<ul>\r\n \t<li>Explain the basics of percents\r\n<ul>\r\n \t<li>Find a percent of a whole<\/li>\r\n \t<li>Identify the amount, the base, and the percent in a percent problem<\/li>\r\n \t<li>Find the unknown in a percent problem<\/li>\r\n<\/ul>\r\n<\/li>\r\n<\/ul>\r\n<\/div>\r\n<h2>Percent of a Whole<\/h2>\r\nPercents are the ratio of a number and 100. Percents are used in many different applications. Percents are used widely to describe how something changed. For example, you may have heard that the amount of rainfall this month had decreased by 12% from last year, or that the number of jobless claims has increase by 5% this quarter over last quarter.\r\n\r\n[caption id=\"attachment_3014\" align=\"aligncenter\" width=\"300\"]<img class=\"wp-image-3014 size-medium\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/2011\/2017\/06\/07185013\/Screen-Shot-2016-04-20-at-12.44.43-PM-300x209.png\" alt=\"A graph showing the unemployment rate, with the y-axis representing percent and the x-axis representing time.\" width=\"300\" height=\"209\" \/> Unemployment rate as percent by year between 2004 and 2014.[\/caption]\r\n\r\nWe regularly use this kind of language to quickly describe how much something increased or decreased over time or between significant events.\r\n\r\nBefore we dissect the methods for finding percent change of a quantity, let's learn the basics of finding percent of a whole.\r\n\r\nFor example, if we knew a gas tank held 14 gallons, and wanted to know how many gallons were in [latex]\\frac{1}{4}[\/latex]\u00a0of a tank, we would find [latex]\\frac{1}{4}[\/latex]\u00a0of 14 gallons by multiplying:\r\n<p style=\"text-align: center\">[latex] \\frac{1}{4}\\,\\cdot \\,14=\\frac{1}{4}\\,\\cdot \\,\\frac{14}{1}=\\frac{14}{4}=3\\frac{2}{4}=3\\frac{1}{2}\\,\\,\\,\\text{gallons}[\/latex]<\/p>\r\nLikewise, if we wanted to find 25% of 14 gallons, we could find this by multiplying, but first we would need to convert the 25% to a decimal:\r\n<p style=\"text-align: center\">[latex]25\\%\\,\\,\\text{of}\\,\\,14\\,\\,\\,\\text{gallons}=0.25\\,\\cdot \\,14=3.5\\,\\,\\,\\text{gallons}[\/latex]<\/p>\r\n\r\n<div class=\"textbox shaded\">\r\n<h3>Finding a Percent of a Whole<\/h3>\r\nTo find a percent of a whole,\r\n<ul>\r\n \t<li>Write the percent as a decimal by moving the decimal two places to the left<\/li>\r\n \t<li>Then multiply the percent by the whole amount<\/li>\r\n<\/ul>\r\n<\/div>\r\n<div class=\"bcc-box bcc-info\">\r\n<h3>Example<\/h3>\r\nWhat is 15% of $200?\r\n\r\n[reveal-answer q=\"834578\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"834578\"]Write as a decimal.\u00a0Move the decimal point two places to the left.\r\n<p style=\"text-align: center\">[latex]15\\%=0.15[\/latex]<\/p>\r\nMultiply the decimal form of the percent by the whole number.\r\n<p style=\"text-align: center\">[latex]\\begin{array}{c}0.15\\cdot200\\\\30\\end{array}[\/latex]<\/p>\r\n\r\n<h4>Answer<\/h4>\r\n15% of $200 is $30\r\n\r\n[\/hidden-answer]\r\n\r\n<\/div>\r\nThe following video contains an example that is similar to the one above.\r\n\r\nhttps:\/\/youtu.be\/jTM7ZMvAzsc\r\n\r\nFrom the previous example, we can identify\u00a0three important parts to finding the percent of a whole:\r\n<ul>\r\n \t<li>the <b>percent<\/b>,\u00a0<b> <\/b>has the percent symbol (%) or the word \u201cpercent\u201d<\/li>\r\n \t<li>the <b>amount<\/b>, the amount is\u00a0part of the whole<\/li>\r\n \t<li>and the <b>base, <\/b>the base is the whole amount<\/li>\r\n<\/ul>\r\nThe following examples show how to identify the three parts: the percent, the base, and the amount.\r\n<div class=\"bcc-box bcc-info\">\r\n<h3>Example<\/h3>\r\nIdentify the percent, amount, and base in this problem.\r\n\r\n30 is 20% of what number?\r\n\r\n[reveal-answer q=\"204160\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"204160\"]\r\n\r\n<b>Percent:<\/b> The percent is the number with the % symbol: <b>20%<\/b>.\r\n\r\n<b>Base:<\/b> The base is the whole amount, which in this case is unknown.\r\n\r\n<b>Amount:<\/b> The amount based on the percent is <b>30<\/b>.\r\n<h4>Answer<\/h4>\r\nPercent = 20%\r\nAmount = 30\r\nBase = unknown\r\n\r\n[\/hidden-answer]\r\n\r\n<\/div>\r\nThe previous problem states that 30 is a portion of another number. That means 30 is the amount. Note that this problem could be rewritten: 20% of what number is 30?\r\n<div class=\"bcc-box bcc-info\">\r\n<h3>Example<\/h3>\r\nIdentify the percent, amount, and base in this problem.\r\n\r\nWhat percent of 30 is 3?\r\n\r\n[reveal-answer q=\"318375\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"318375\"]\r\n\r\n<b>Percent:<\/b> The percent is unknown, because the problem states \u201cwhat percent?\u201d.\r\n\r\n<b>Base:<\/b> The base is the whole amount, so the base is 30.\r\n\r\n<b>Amount:<\/b> The amount is a portion of the whole, which is 3 in this case.\r\n<h4>Answer<\/h4>\r\nPercent = unknown\r\nAmount = 3\r\nBase = 30\r\n\r\n[\/hidden-answer]\r\n\r\n<\/div>\r\n<div class=\"bcc-box bcc-info\">\r\n<h3>Example<\/h3>\r\nIdentify the percent, amount, and base in this problem.\r\n\r\nWhat is 60% of 45?\r\n\r\n[reveal-answer q=\"102763\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"102763\"]\r\n\r\n<b>Percent:<\/b> The percent is known\r\n\r\n<b>Base:\u00a0<\/b>The base is the whole amount, so the base is 45.\r\n\r\n<b>Amount:<\/b> The amount is a portion of the whole, which is what we want to identify.\r\n<h4>Answer<\/h4>\r\nPercent =\u00a060%\r\nAmount = unknown\r\nBase = 45\r\n\r\n[\/hidden-answer]\r\n\r\n<\/div>\r\nThe following video provides more examples that describe how to identify the percent, amount, and base in a percent problem.\r\n\r\nhttps:\/\/youtu.be\/zwT58-LJCvs\r\n\r\nIn the next section, you will use the parts of a percent problem to find the percent increase or decrease of a quantity by writing and solving equations.","rendered":"<div class=\"bcc-box bcc-highlight\">\n<h3>Learning Objectives<\/h3>\n<ul>\n<li>Explain the basics of percents\n<ul>\n<li>Find a percent of a whole<\/li>\n<li>Identify the amount, the base, and the percent in a percent problem<\/li>\n<li>Find the unknown in a percent problem<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<\/div>\n<h2>Percent of a Whole<\/h2>\n<p>Percents are the ratio of a number and 100. Percents are used in many different applications. Percents are used widely to describe how something changed. For example, you may have heard that the amount of rainfall this month had decreased by 12% from last year, or that the number of jobless claims has increase by 5% this quarter over last quarter.<\/p>\n<div id=\"attachment_3014\" style=\"width: 310px\" class=\"wp-caption aligncenter\"><img loading=\"lazy\" decoding=\"async\" aria-describedby=\"caption-attachment-3014\" class=\"wp-image-3014 size-medium\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/2011\/2017\/06\/07185013\/Screen-Shot-2016-04-20-at-12.44.43-PM-300x209.png\" alt=\"A graph showing the unemployment rate, with the y-axis representing percent and the x-axis representing time.\" width=\"300\" height=\"209\" \/><\/p>\n<p id=\"caption-attachment-3014\" class=\"wp-caption-text\">Unemployment rate as percent by year between 2004 and 2014.<\/p>\n<\/div>\n<p>We regularly use this kind of language to quickly describe how much something increased or decreased over time or between significant events.<\/p>\n<p>Before we dissect the methods for finding percent change of a quantity, let&#8217;s learn the basics of finding percent of a whole.<\/p>\n<p>For example, if we knew a gas tank held 14 gallons, and wanted to know how many gallons were in [latex]\\frac{1}{4}[\/latex]\u00a0of a tank, we would find [latex]\\frac{1}{4}[\/latex]\u00a0of 14 gallons by multiplying:<\/p>\n<p style=\"text-align: center\">[latex]\\frac{1}{4}\\,\\cdot \\,14=\\frac{1}{4}\\,\\cdot \\,\\frac{14}{1}=\\frac{14}{4}=3\\frac{2}{4}=3\\frac{1}{2}\\,\\,\\,\\text{gallons}[\/latex]<\/p>\n<p>Likewise, if we wanted to find 25% of 14 gallons, we could find this by multiplying, but first we would need to convert the 25% to a decimal:<\/p>\n<p style=\"text-align: center\">[latex]25\\%\\,\\,\\text{of}\\,\\,14\\,\\,\\,\\text{gallons}=0.25\\,\\cdot \\,14=3.5\\,\\,\\,\\text{gallons}[\/latex]<\/p>\n<div class=\"textbox shaded\">\n<h3>Finding a Percent of a Whole<\/h3>\n<p>To find a percent of a whole,<\/p>\n<ul>\n<li>Write the percent as a decimal by moving the decimal two places to the left<\/li>\n<li>Then multiply the percent by the whole amount<\/li>\n<\/ul>\n<\/div>\n<div class=\"bcc-box bcc-info\">\n<h3>Example<\/h3>\n<p>What is 15% of $200?<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q834578\">Show Solution<\/span><\/p>\n<div id=\"q834578\" class=\"hidden-answer\" style=\"display: none\">Write as a decimal.\u00a0Move the decimal point two places to the left.<\/p>\n<p style=\"text-align: center\">[latex]15\\%=0.15[\/latex]<\/p>\n<p>Multiply the decimal form of the percent by the whole number.<\/p>\n<p style=\"text-align: center\">[latex]\\begin{array}{c}0.15\\cdot200\\\\30\\end{array}[\/latex]<\/p>\n<h4>Answer<\/h4>\n<p>15% of $200 is $30<\/p>\n<\/div>\n<\/div>\n<\/div>\n<p>The following video contains an example that is similar to the one above.<\/p>\n<p><iframe loading=\"lazy\" id=\"oembed-1\" title=\"Find the Percent of a Number\" width=\"500\" height=\"281\" src=\"https:\/\/www.youtube.com\/embed\/jTM7ZMvAzsc?feature=oembed&#38;rel=0\" frameborder=\"0\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/p>\n<p>From the previous example, we can identify\u00a0three important parts to finding the percent of a whole:<\/p>\n<ul>\n<li>the <b>percent<\/b>,\u00a0<b> <\/b>has the percent symbol (%) or the word \u201cpercent\u201d<\/li>\n<li>the <b>amount<\/b>, the amount is\u00a0part of the whole<\/li>\n<li>and the <b>base, <\/b>the base is the whole amount<\/li>\n<\/ul>\n<p>The following examples show how to identify the three parts: the percent, the base, and the amount.<\/p>\n<div class=\"bcc-box bcc-info\">\n<h3>Example<\/h3>\n<p>Identify the percent, amount, and base in this problem.<\/p>\n<p>30 is 20% of what number?<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q204160\">Show Solution<\/span><\/p>\n<div id=\"q204160\" class=\"hidden-answer\" style=\"display: none\">\n<p><b>Percent:<\/b> The percent is the number with the % symbol: <b>20%<\/b>.<\/p>\n<p><b>Base:<\/b> The base is the whole amount, which in this case is unknown.<\/p>\n<p><b>Amount:<\/b> The amount based on the percent is <b>30<\/b>.<\/p>\n<h4>Answer<\/h4>\n<p>Percent = 20%<br \/>\nAmount = 30<br \/>\nBase = unknown<\/p>\n<\/div>\n<\/div>\n<\/div>\n<p>The previous problem states that 30 is a portion of another number. That means 30 is the amount. Note that this problem could be rewritten: 20% of what number is 30?<\/p>\n<div class=\"bcc-box bcc-info\">\n<h3>Example<\/h3>\n<p>Identify the percent, amount, and base in this problem.<\/p>\n<p>What percent of 30 is 3?<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q318375\">Show Solution<\/span><\/p>\n<div id=\"q318375\" class=\"hidden-answer\" style=\"display: none\">\n<p><b>Percent:<\/b> The percent is unknown, because the problem states \u201cwhat percent?\u201d.<\/p>\n<p><b>Base:<\/b> The base is the whole amount, so the base is 30.<\/p>\n<p><b>Amount:<\/b> The amount is a portion of the whole, which is 3 in this case.<\/p>\n<h4>Answer<\/h4>\n<p>Percent = unknown<br \/>\nAmount = 3<br \/>\nBase = 30<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"bcc-box bcc-info\">\n<h3>Example<\/h3>\n<p>Identify the percent, amount, and base in this problem.<\/p>\n<p>What is 60% of 45?<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q102763\">Show Solution<\/span><\/p>\n<div id=\"q102763\" class=\"hidden-answer\" style=\"display: none\">\n<p><b>Percent:<\/b> The percent is known<\/p>\n<p><b>Base:\u00a0<\/b>The base is the whole amount, so the base is 45.<\/p>\n<p><b>Amount:<\/b> The amount is a portion of the whole, which is what we want to identify.<\/p>\n<h4>Answer<\/h4>\n<p>Percent =\u00a060%<br \/>\nAmount = unknown<br \/>\nBase = 45<\/p>\n<\/div>\n<\/div>\n<\/div>\n<p>The following video provides more examples that describe how to identify the percent, amount, and base in a percent problem.<\/p>\n<p><iframe loading=\"lazy\" id=\"oembed-2\" title=\"Identify the Percent, Base, and Amount of a Percent Question\" width=\"500\" height=\"281\" src=\"https:\/\/www.youtube.com\/embed\/zwT58-LJCvs?feature=oembed&#38;rel=0\" frameborder=\"0\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/p>\n<p>In the next section, you will use the parts of a percent problem to find the percent increase or decrease of a quantity by writing and solving equations.<\/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-4514\">\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>Revision and Adaptation. <strong>Provided 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><\/li><li>Screenshot: Unemployment Graph. <strong>Provided 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><\/li><\/ul><div class=\"license-attribution-dropdown-subheading\">CC licensed content, Shared previously<\/div><ul class=\"citation-list\"><li>Find the Percent of a Number. <strong>Authored by<\/strong>: James Sousa (Mathispower4u.com) for Lumen Learning. <strong>Located at<\/strong>: <a target=\"_blank\" href=\"https:\/\/youtu.be\/jTM7ZMvAzsc\">https:\/\/youtu.be\/jTM7ZMvAzsc<\/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>Identify the Percent, Base, and Amount of a Percent Question. <strong>Authored by<\/strong>: James Sousa (Mathispower4u.com) for Lumen Learning. <strong>Located at<\/strong>: <a target=\"_blank\" href=\"https:\/\/youtu.be\/zwT58-LJCvs\">https:\/\/youtu.be\/zwT58-LJCvs<\/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>Unit 5: Percents, from Developmental Math: An Open Program. <strong>Provided by<\/strong>: Monterey Institute of Technology and Education. <strong>Located at<\/strong>: <a target=\"_blank\" href=\"http:\/\/nrocnetwork.org\/dm-opentext\">http:\/\/nrocnetwork.org\/dm-opentext<\/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>\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":4,"template":"","meta":{"_candela_citation":"[{\"type\":\"cc\",\"description\":\"Find the Percent of a Number\",\"author\":\"James Sousa (Mathispower4u.com) for Lumen Learning\",\"organization\":\"\",\"url\":\"https:\/\/youtu.be\/jTM7ZMvAzsc\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"\"},{\"type\":\"cc\",\"description\":\"Identify the Percent, Base, and Amount of a Percent 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