{"id":4435,"date":"2013-06-29T06:06:45","date_gmt":"2013-06-29T06:06:45","guid":{"rendered":"http:\/\/www.mometrix.com\/academy\/?page_id=4435"},"modified":"2026-03-25T11:55:29","modified_gmt":"2026-03-25T16:55:29","slug":"computation-with-percentages","status":"publish","type":"page","link":"https:\/\/www.mometrix.com\/academy\/computation-with-percentages\/","title":{"rendered":"Computation with Percentages"},"content":{"rendered":"\n\t\t\t<div id=\"mmDeferVideoEncompass_suUjYUf1OJs\" style=\"position: relative;\">\n\t\t\t<picture>\n\t\t\t\t<source srcset=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2023\/01\/circle-play-duotone.webp\" type=\"image\/webp\">\n\t\t\t\t<source srcset=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2023\/01\/circle-play-duotone.png\" type=\"image\/jpeg\"> \n\t\t\t\t<img fetchpriority=\"high\" decoding=\"async\" loading=\"eager\" id=\"videoThumbnailImage_suUjYUf1OJs\" data-source-videoID=\"suUjYUf1OJs\" src=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2023\/01\/circle-play-duotone.png\" alt=\"Computation with Percentages Video\" height=\"464\" width=\"825\" class=\"size-full\" data-matomo-title = \"Computation with Percentages\">\n\t\t\t<\/picture>\n\t\t\t<\/div>\n\t\t\t<style>img#videoThumbnailImage_suUjYUf1OJs:hover {cursor:pointer;} img#videoThumbnailImage_suUjYUf1OJs {background-size:contain;background-image:url(\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2023\/02\/1863-thumb-final-2.webp\");}<\/style>\n\t\t\t<script defer>\n\t\t\t  jQuery(\"img#videoThumbnailImage_suUjYUf1OJs\").click(function() {\n\t\t\t\tlet videoId = jQuery(this).attr(\"data-source-videoID\");\n\t\t\t\tlet helpTag = '<div id=\"mmDeferVideoYTMessage_suUjYUf1OJs\" style=\"display: none;position: absolute;top: -24px;width: 100%;text-align: center;\"><span style=\"font-style: italic;font-size: small;border-top: 1px solid #fc0;\">Having trouble? <a href=\"https:\/\/www.youtube.com\/watch?v='+videoId+'\" target=\"_blank\">Click here to watch on YouTube.<\/a><\/span><\/div>';\n\t\t\t\tlet tag = document.createElement(\"iframe\");\n\t\t\t\ttag.id = \"yt\" + videoId;\n\t\t\t\ttag.src = \"https:\/\/www.youtube-nocookie.com\/embed\/\" + videoId + \"?autoplay=1&controls=1&wmode=opaque&rel=0&egm=0&iv_load_policy=3&hd=0&enablejsapi=1\";\n\t\t\t\ttag.frameborder = 0;\n\t\t\t\ttag.allow = \"autoplay; fullscreen\";\n\t\t\t\ttag.width = this.width;\n\t\t\t\ttag.height = this.height;\n\t\t\t\ttag.setAttribute(\"data-matomo-title\",\"Computation with Percentages\");\n\t\t\t\tjQuery(\"div#mmDeferVideoEncompass_suUjYUf1OJs\").html(tag);\n\t\t\t\tjQuery(\"div#mmDeferVideoEncompass_suUjYUf1OJs\").prepend(helpTag);\n\t\t\t\tsetTimeout(function(){jQuery(\"div#mmDeferVideoYTMessage_suUjYUf1OJs\").css(\"display\", \"block\");}, 2000);\n\t\t\t  });\n\t\t\t  \n\t\t\t<\/script>\n\t\t\n<p><script>\nfunction LcW_Function() {\n  var x = document.getElementById(\"LcW\");\n  if (x.style.display === \"none\") {\n    x.style.display = \"block\";\n  } else {\n    x.style.display = \"none\";\n  }\n}\n<\/script><\/p>\n<div class=\"moc-toc hide-on-desktop hide-on-tablet\">\n<div><button onclick=\"LcW_Function()\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2024\/12\/toc2.svg\" width=\"16\" height=\"16\" alt=\"show or hide table of contents\"><\/button><\/p>\n<p>On this page<\/p>\n<\/div>\n<nav id=\"LcW\" style=\"display:none;\">\n<ul>\n<li class=\"toc-h2\"><a href=\"#Finding_the_Part\" class=\"smooth-scroll\">Finding the Part<\/a><\/li>\n<li class=\"toc-h2\"><a href=\"#Finding_the_Whole\" class=\"smooth-scroll\">Finding the Whole<\/a><\/li>\n<li class=\"toc-h2\"><a href=\"#How_to_Figure_out_Percentage\" class=\"smooth-scroll\">How to Figure out Percentage<\/a><\/li>\n<li class=\"toc-h2\"><a href=\"#Frequently_Asked_Questions\" class=\"smooth-scroll\">Frequently Asked Questions<\/a><\/li>\n<li class=\"toc-h2\"><a href=\"#Computation_with_Percentages_Practice_Questions\" class=\"smooth-scroll\">Computation with Percentages Practice Questions<\/a><\/li>\n<\/ul>\n<\/nav>\n<\/div>\n<div class=\"accordion\"><input id=\"transcript\" type=\"checkbox\" class=\"spoiler_button\" \/><label for=\"transcript\">Transcript<\/label><input id=\"FAQs\" type=\"checkbox\" class=\"spoiler_button\" \/><label for=\"FAQs\">FAQs<\/label><input id=\"PQs\" type=\"checkbox\" class=\"spoiler_button\" \/><label for=\"PQs\">Practice<\/label><a href=\"https:\/\/www.mometrix.com\/academy\/percentage-calculator\" target=\"none\" style=\"margin: 0 auto;\"><span class=\"accordion_calculator_button\">Calculator<\/span><\/a><\/p>\n<div class=\"spoiler\" id=\"transcript-spoiler\">\n<p>Hello, and welcome to this video about computation with percentages! Today we\u2019ll learn how to solve different types of problems involving percentages and how this skill can help you in the real world. <\/p>\n<p>Before we get started, let\u2019s review a few things. First, a <strong>ratio<\/strong> is a comparison of two or more numbers. Some ratios are <strong>part-to-whole ratios<\/strong>, comparing a part of something to the whole group. A <strong>percentage<\/strong> is a part-to-whole ratio that\u2019s expressed as a fraction of \\(100\\). For example, the percentage \\(80%\\) means \\(80\\) out of \\(100\\): \\(\\frac{80}{100}\\). In this case, \\(80\\) is the part and \\(100\\) is the whole. <\/p>\n<p>Solving problems with percentages involves translating a word problem into a mathematical equation. There are three types of problems with percentages: <\/p>\n<ol>\n<li>Finding the part<\/li>\n<li>Finding the whole<\/li>\n<li>Finding the percent<\/li>\n<\/ol>\n<p>We\u2019ll discuss these three problem types together and work on some examples to help you understand how to solve them. <\/p>\n<hr>\n<p>\nLet\u2019s start with the first problem type, finding the part.<\/p>\n<h2><span id=\"Finding_the_Part\" class=\"m-toc-anchor\"><\/span>Finding the Part<\/h2>\n<p>\nThe first problem type involves finding part of a given number that\u2019s equal to a given percent. <\/p>\n<p>Consider the following percentage problem: <em>What is 60% of 5<\/em>? To answer this question, we need to understand the information we are given in the problem. Let\u2019s look at each part of the word problem and translate it into an algebraic equation. The first part of the sentence, \u201cWhat is,\u201d means \u201cWhat number is equal to.\u201d Since we don\u2019t know the number in question, we use the variable \\(n\\) to represent this portion of the equation:<\/p>\n<div class=\"examplesentence\">\\(n=\\)<\/div>\n<p>\n&nbsp;<br \/>\nThe next portion of the question is \u201c\\(60%\\).\u201d Since \\(60%\\) equals \\(0.60\\), write \\(0.60\\) in the equation after the equal sign: <\/p>\n<div class=\"examplesentence\">\\(n=0.60\\)<\/div>\n<p>\n&nbsp;<br \/>\nThe next part of the question is \u201cof.\u201d When translating written equations into numerical equations, the word \u201cof\u201d indicates multiplication. Therefore, write a multiplication sign after \\(0.60\\) in the equation: <\/p>\n<div class=\"examplesentence\">\\(n=0.60 \\times\\)<\/div>\n<p>\n&nbsp;<br \/>\nThe last portion of the question is 5. Write 5 after the multiplication sign in the equation: <\/p>\n<div class=\"examplesentence\">\\(n=0.60 \\times 5\\)<\/div>\n<p>\n&nbsp;<br \/>\nFrom here, solve the equation for \\(n. 0.60\\times 5=3\\), so \\(n=3\\). Therefore, \\(60%\\) of \\(5\\) is \\(3\\). <\/p>\n<p>Now it\u2019s your turn. Consider the following percentage problem: <em>40% of 20 is what number<\/em>? <\/p>\n<p>Pause the video here, convert the written equation into an algebraic equation, and solve. <\/p>\n<p>Now that you\u2019ve tried this one on your own, let\u2019s take a look at it together. The algebraic equation that represents this question is: <\/p>\n<div class=\"examplesentence\">\\(0.40\\times 20=n\\)<\/div>\n<p>\n&nbsp;<br \/>\nFrom here, solve the equation for \\(n\\). \\(0.40\\times20=8\\), so \\(n=8\\). Therefore, 40% of \\(20\\) is \\(8\\). <\/p>\n<p>Great job!<\/p>\n<hr>\n<h2><span id=\"Finding_the_Whole\" class=\"m-toc-anchor\"><\/span>Finding the Whole<\/h2>\n<p>\nThe next percentage problem type is finding the whole. In these problems, we are given the percent and its equivalent part. We need to identify the whole. <\/p>\n<p>Consider the following percentage problem: <em>3 is 60% of what number?<\/em> To answer this question, we need to understand the information we are given in the problem. Let\u2019s look at each part of the word problem and translate it into an algebraic equation. The question starts with \u201c\\(3\\) is,\u201d which means \u201c\\(3\\) is equal to.\u201d Start the equation with \\(3\\) and an equal sign: <\/p>\n<div class=\"examplesentence\">\\(3=\\)<\/div>\n<p>\n&nbsp;<br \/>\nThe next part of the question is <em>60%<\/em>. Since <em>60%<\/em> equals \\(0.60\\), write \\(0.60\\) in the equation after the equal sign: <\/p>\n<div class=\"examplesentence\">\\(3=0.60\\)<\/div>\n<p>\n&nbsp;<br \/>\nThe next word in the question is \u201cof.\u201d When translating written equations to algebraic equations, the word \u201cof\u201d indicates multiplication. Therefore, write a multiplication sign after \\(0.60\\) in the equation: <\/p>\n<div class=\"examplesentence\">\\(3=0.60\\times\\)<\/div>\n<p>\n&nbsp;<br \/>\nThe next part of the question is \u201cwhat number.\u201d Since we don\u2019t know what number is being referred to, use the variable \\(n\\) to represent this number: <\/p>\n<div class=\"examplesentence\">\\(3=0.60\\times n\\)<\/div>\n<p>\n&nbsp;<br \/>\nWhen multiplying a number by a variable, remember that no multiplication sign is needed. We can write the equation with the coefficient \\(0.60\\) next to the variable \\(n\\):<\/p>\n<div class=\"examplesentence\">\\(3=0.60n\\)<\/div>\n<p>\n&nbsp;<br \/>\nFrom here, solve the equation for \\(n\\).<\/p>\n<p>To solve for \\(n\\), isolate the variable by doing inverse operations. The opposite of multiplying by \\(0.60\\) is dividing by \\(0.60\\), so divide both sides of the equation by \\(0.60\\). <\/p>\n<div class=\"examplesentence\">\\(\\frac{3}{0.60}=\\frac{0.60n}{0.60}\\)<\/div>\n<p>\n&nbsp;<br \/>\n\\(3\\div 0.60-5\\), so write \\(5\\) on the left side of the equation. And \\(0.60\\div 0.60=1\\), so write \\(1n\\), or just \\(n\\), on the right side of the equation.<\/p>\n<div class=\"examplesentence\">\\(5=n\\)<\/div>\n<p>\n&nbsp;<br \/>\nTherefore, \\(3\\) is 60% of \\(5\\).<\/p>\n<p>Now it\u2019s your turn. Consider the following percentage problem: <em>50<\/em> is 20% of what number? <\/p>\n<p>Pause the video here, translate the written equation into an algebraic equation, and solve.<\/p>\n<p>Now that you\u2019ve tried this one on your own, let\u2019s take a look at it together. The algebraic equation that represents this question is: <\/p>\n<div class=\"examplesentence\">\\(50=0.20n\\)<\/div>\n<p>\n&nbsp;<br \/>\nFrom here, solve the equation for \\(n\\).<\/p>\n<p>To solve for \\(n\\), isolate the variable by doing inverse operations. The opposite of multiplying by \\(0.20\\) is dividing by \\(0.20\\), so divide both sides of the equation by \\(0.20\\). <\/p>\n<div class=\"examplesentence\">\\(\\frac{50}{0.20}=\\frac{0.20n}{0.20}\\)<\/div>\n<p>\n&nbsp;<br \/>\n\\(50\\div 0.20=250\\), so write \\(250\\) on the left side of the equation. Then, if we divide the right side of the equation, we\u2019ll get \\(1\\), so we\u2019re left with \\(1n\\) on the right side of the equation. Since \\(1n\\) is the same thing as \\(n\\), \\(250\\) is equal to \\(n\\). <\/p>\n<div class=\"examplesentence\">\\(250=n\\)<\/div>\n<p>\n&nbsp;<br \/>\nSo \\(50\\) is <em>20<\/em>% of \\(250\\).<\/p>\n<p>Nice work!<\/p>\n<hr>\n<h2><span id=\"How_to_Figure_out_Percentage\" class=\"m-toc-anchor\"><\/span>How to Figure out Percentage<\/h2>\n<p>\nThe last percentage problem type involves finding the percent. In these scenarios, we are given the part and the whole and we need to find the percent. <\/p>\n<p>Consider the following percentage problem: <em>What percent of<\/em> \\(5\\) <em>is<\/em> \\(3\\)? To answer the question, we need to understand the information we are given in the problem. Let\u2019s look at each part of the word problem and translate it into an algebraic equation. The question starts with \u201cWhat percent\u201d. Since we don\u2019t know the percent, we\u2019ll use the variable \\(p\\) to represent this number:<\/p>\n<div class=\"examplesentence\">\\(p\\)<\/div>\n<p>\n&nbsp;<br \/>\nThe next word in the question is \u201cof.\u201d Remember, when translating written equations into algebraic equations, the word \u201cof\u201d indicates multiplication. Therefore, write a multiplication sign after \\(p\\) in the equation: <\/p>\n<div class=\"examplesentence\">\\(p\\times\\)<\/div>\n<p>\n&nbsp;<br \/>\nThe next part of the question is the number \\(5\\). Write \\(5\\) in the equation after the multiplication sign: <\/p>\n<div class=\"examplesentence\">\\(p\\times 5\\)<\/div>\n<p>\n&nbsp;<br \/>\nThe next part of the question is the word \u201cis.\u201d When translating written equations into algebraic equations, the word \u201cis\u201d means \u201cis equal to.\u201d Therefore, write an equal sign after \\(5\\) in the equation: <\/p>\n<div class=\"examplesentence\">\\(p\\times 5=\\)<\/div>\n<p>\n&nbsp;<br \/>\nThe next part of the equation is the number \\(3\\). Write \\(3\\) in the equation after the equal sign: <\/p>\n<div class=\"examplesentence\">\\(p\\times 5=3\\)<\/div>\n<p>\n&nbsp;<br \/>\nWhen multiplying a number by a variable, remember that no multiplication sign is needed. We can write the equation with the coefficient \\(5\\) next to the variable \\(p\\), like this:<\/p>\n<div class=\"examplesentence\">\\(5p=3\\)<\/div>\n<p>\n&nbsp;<br \/>\nFrom here, solve the equation for \\(p\\).<\/p>\n<p>To solve for \\(p\\), isolate the variable by doing inverse operations. The opposite of multiplying by \\(5\\) is dividing by \\(5\\), so divide both sides of the equation by \\(5\\). <\/p>\n<div class=\"examplesentence\">\\(\\frac{5p}{5}=\\frac{3}{5}\\)<\/div>\n<p>\n&nbsp;<br \/>\n\\(5\\div 5=1\\), so write \\(1p\\), or just \\(p\\), on the left side of the equation. \\(3\\div 5=0.60\\) so \\(p=0.60\\).<\/p>\n<div class=\"examplesentence\">\\(p = 0.60\\)<\/div>\n<p>\n&nbsp;<br \/>\nNow that we know \\(p=0.60\\), we need to convert the decimal into a percentage to answer the original question. \\(0.60\\) is equal to \\(\\frac{60}{100}\\), or <em>60%<\/em>. Therefore, \\(3\\) is <em>60%<\/em> of \\(5\\). <\/p>\n<p>Now it\u2019s your turn. Consider the following percentage problem: <em>11 is what percent of 20<\/em>? <\/p>\n<p>Pause the video here, convert the written equation into an algebraic equation, and solve.<\/p>\n<p>Now that you\u2019ve tried this one on your own, let\u2019s take a look at it together. The algebraic equation that represents this question is: <\/p>\n<div class=\"examplesentence\">\\(11 = 20p\\)<\/div>\n<p>\n&nbsp;<br \/>\nFrom here, solve the equation for \\(p\\).<\/p>\n<p>To solve for \\(p\\), isolate the variable by doing inverse operations. Simply divide both sides of the equation by \\(20\\).<\/p>\n<div class=\"examplesentence\">\\(\\frac{11}{20}=\\frac{20p}{20}\\)<\/div>\n<p>\n&nbsp;<br \/>\n\\(20\\div 20=1\\), so write \\(p\\) on the right side of the equation. And \\(11\\div 20=0.55\\), so \\(p\\) is equal to \\(0.55\\). <\/p>\n<div class=\"examplesentence\">\\(0.55=p\\)<\/div>\n<p>\n&nbsp;<br \/>\nNow that we know that \\(p=0.55\\), we need to convert this decimal into a percentage to answer our original question. \\(0.55\\) is equal to \\(\\frac{55}{100}\\), or <em>55%<\/em>. Therefore, \\(11\\) is <em>55%<\/em> of \\(20\\). <\/p>\n<p>Great work! <\/p>\n<hr>\n<p>\n<strong>Computations with percentages<\/strong> are used all the time in the real world. For instance, store discounts, interest rates, and test scores are often expressed as percentages. Percentages are also used when calculating the tip on a bill at a restaurant. <\/p>\n<p>I have one more problem for you to try. This one is a little more challenging, but I know you can handle it! Consider the following percentage problem: <\/p>\n<div class=\"transcriptcallout\" style=\"text-align: left;\">Rachael is taking her friend out to dinner. When she gets the check, the total is $56.75, not including the tip. Rachael wants to leave a 20% tip. How much money should Rachael leave for a tip?<\/div>\n<p>\n&nbsp;<br \/>\nPause the video here, translate the written equation into an algebraic equation, and then solve. <\/p>\n<p>Now that you\u2019ve tried this one on your own, let\u2019s take a look at it together. <\/p>\n<p>To answer this question, we need to figure out what number is equal to 20% of $56.75. The algebraic equation that represents this question is: <\/p>\n<div class=\"examplesentence\">\\(n=0.20\\times 56.75\\)<\/div>\n<p>\n&nbsp;<br \/>\nFrom here, solve the equation for \\(n. 0.20\\times 56.75=11.35\\), so \\(n=11.35\\). Therefore, for a 20% tip, Rachael should leave $11.35. <\/p>\n<p>Great job!<\/p>\n<p>I hope this video about computation with percentages was helpful. Thanks for watching, and happy studying!<\/p>\n<\/div>\n<div class=\"spoiler\" id=\"FAQs-spoiler\">\n<h2 style=\"text-align:center\"><span id=\"Frequently_Asked_Questions\" class=\"m-toc-anchor\"><\/span>Frequently Asked Questions<\/h2>\n<div class=\"faq-list\">\n<div class=\"qa_wrap\">\n<div class=\"q_item text_bold\">\n<h4 class=\"letter\">Q<\/h4>\n<p style=\"line-height: unset;\">How do you find the percentage of a number?<\/p>\n<\/p><\/div>\n<div class=\"a_item\">\n<h4 class=\"letter text_bold\">A<\/h4>\n<p>Find the percentage of a number by turning the percentage into a decimal and multiplying by the number. <\/p>\n<div class=\"lightbulb-example-2\"><span class=\"lightbulb-icon\">\ud83d\udca1<\/span><span class=\"faq-example-question\">Example: What is 75% of 152?<\/span><\/p>\n<hr style=\"padding: 0; margin-top: -0.2em; margin-bottom: 1.2em\">\n<p style=\"text-align: center; margin-bottom: 0em\">\\(0.75 \\times 152 = 114\\)<\/p>\n<\/div>\n<\/p><\/div>\n<\/p><\/div>\n<div class=\"qa_wrap\">\n<div class=\"q_item text_bold\">\n<h4 class=\"letter\">Q<\/h4>\n<p style=\"line-height: unset;\">How do you calculate percentage increase?<\/p>\n<\/p><\/div>\n<div class=\"a_item\">\n<h4 class=\"letter text_bold\">A<\/h4>\n<p>Calculate percentage increase using this formula:<\/p>\n<p style=\"text-align:center; font-size: 90%; line-height: 50px\">\\( \\text{% increase}\\) \\(\\:= \\dfrac{\\text{new}-\\text{old}}{\\text{old}} \\:\\times \\: 100\\)<\/p>\n<div class=\"lightbulb-example-2\"><span class=\"lightbulb-icon\">\ud83d\udca1<\/span><span class=\"faq-example-question\">Example: A student scored a 73 on his first test and a 92 on his second test. What is the percentage increase from his first test score to his second test score?<\/span><\/p>\n<hr style=\"padding: 0; margin-top: -0.2em; margin-bottom: 1.2em\">\n<p style=\"text-align: center; margin-bottom: 0em; font-size 90%; line-height: 40px\"> \\( \\text{% increase } =\\dfrac{92-73}{73}\\: \\times \\:100\\) \\(\\:= \\dfrac{19}{73}\\: \\times \\:100 = 26\\%\\)<\/p>\n<\/div>\n<\/p><\/div>\n<\/p><\/div>\n<div class=\"qa_wrap\">\n<div class=\"q_item text_bold\">\n<h4 class=\"letter\">Q<\/h4>\n<p style=\"line-height: unset;\">How do you calculate percentage change?<\/p>\n<\/p><\/div>\n<div class=\"a_item\">\n<h4 class=\"letter text_bold\">A<\/h4>\n<p>Calculate percentage change using this formula: <\/p>\n<p style = \"text-align:center; font-size: 90%; line-height: 40px\">\\(\\text{% change} = \\dfrac{\\text{new}-\\text{old}}{\\text{old}}\\: \\times \\:100\\)<\/p>\n<div class=\"lightbulb-example-2\"><span class=\"lightbulb-icon\">\ud83d\udca1<\/span><span class=\"faq-example-question\">Example: A house is originally priced at $350,000. After 6 months of not selling, the price is lowered to $315,000. What is the percent change from the original to the new price?<\/span><\/p>\n<hr style=\"padding: 0; margin-top: -0.2em; margin-bottom: 1.2em\">\n<p style=\"text-align:center; margin-bottom: 0em; font-size: 90%; line-height: 40px\">\\( \\text{% change }\\) \\(\\:= \\dfrac{315,000-350,000}{350,000}\\: \\times \\:100\\) \\(\\: = -10\\%\\)<\/p>\n<\/div>\n<\/p><\/div>\n<\/p><\/div>\n<div class=\"qa_wrap\">\n<div class=\"q_item text_bold\">\n<h4 class=\"letter\">Q<\/h4>\n<p style=\"line-height: unset;\">How do you calculate percentage difference?<\/p>\n<\/p><\/div>\n<div class=\"a_item\">\n<h4 class=\"letter text_bold\">A<\/h4>\n<p>Calculate percentage difference using this formula: <\/p>\n<p style=\"text-align:center; font-size: 90%; line-height: 50px\">\\(\\text{% difference }\\) \\(\\:= |\\dfrac{\\text{Value }1-\\text{Value }2}{\\dfrac{\\text{Value }1+\\text{Value }2}{2}}|\\:\u00d7\\:100\\%\\)<\/p>\n<div class=\"lightbulb-example-2\"><span class=\"lightbulb-icon\">\ud83d\udca1<\/span><span class=\"faq-example-question\">Example:  If chocolate ice cream costs $4.25 and cookie dough ice cream costs $6.35, what is the percentage difference between the two ice creams?<\/span><\/p>\n<hr style=\"padding: 0; margin-top: -0.2em; margin-bottom: 1.2em\">\n<p style=\"text-align:center; font-size: 90%; line-height: 40px; margin-bottom: 0em\">\\( \\text{% difference }\\) \\(\\:= |\\dfrac{4.25-6.35}{\\dfrac{(4.25+6.35)}{2}}|\\: \\times \\:100\\%\\) \\(\\:= |\\dfrac{-2.1}{5.3}|\\: \\times \\:100\\%\\) \\(\\:= 39.62\\%\\)<\/p>\n<\/div>\n<\/p><\/div>\n<\/p><\/div>\n<div class=\"qa_wrap\">\n<div class=\"q_item text_bold\">\n<h4 class=\"letter\">Q<\/h4>\n<p style=\"line-height: unset;\">How do you calculate a grade percentage?<\/p>\n<\/p><\/div>\n<div class=\"a_item\">\n<h4 class=\"letter text_bold\">A<\/h4>\n<p>To calculate a grade percentage, add each grade from one category and then divide by the number of grades in that category (take the average). Next, multiply by the weight (percentage) that category holds. Repeat for as many categories as there are and then add them together. <\/p>\n<div class=\"lightbulb-example-2\"><span class=\"lightbulb-icon\">\ud83d\udca1<\/span><span class=\"faq-example-question\">Example: At my school, major grades are worth 60% of my final grade, daily grades are worth 30% of my final grade, and my final exam is worth 10% of my final grade. If my grades are as follows, what is my final grade?<\/span> <\/p>\n<ul>\n<li>Daily Grades: <span style=\"font-weight: 500 !important\">95, 87, 73, 92, 98<\/span><\/li>\n<li>Major Grades: <span style=\"font-weight: 500 !important\">93, 88, 95<\/span><\/li>\n<li>Final Exam: <span style=\"font-weight: 500 !important\">94<\/span><\/li>\n<\/ul>\n<hr style=\"padding: 0; margin-top: -0.2em; margin-bottom: 1.2em\">\n<ul>\n<li style=\"margin-bottom: 1em; line-height: 32px\">Daily Grade Average<br \/>\\(\\frac{95+87+73+92+98}{5}\\)\\(\\: =\\frac{445}{5}=89\\)<\/li>\n<li style=\"margin-bottom: 1em\">Daily Grade Portion<br \/>\\(89\u00d730\\%=89\\times 0.3\\)\\(\\: =26.7\\%\\)<\/li>\n<li style=\"margin-bottom: 1em; line-height: 32px\">Major Grade Average<br \/>\\(\\frac{93+88+95}{3}=\\frac{276}{3}=92\\)<\/li>\n<li style=\"margin-bottom: 1em\">Major Grade Portion<br \/>\\(92 \\times 60\\%=92 \\times 0.6\\)\\(\\: =55.2\\%\\)<\/li>\n<li>Final Exam Portion<br \/>\\(94 \\times 10\\%=94 \\times 0.1\\)\\(\\: =9.4\\%\\)<\/li>\n<\/ul>\n<p style=\"margin-bottom: 0em\">This puts the final grade at \\(26.7+55.2+9.4=91.3\\%\\)<\/div>\n<\/p><\/div>\n<\/p><\/div>\n<div class=\"qa_wrap\">\n<div class=\"q_item text_bold\">\n<h4 class=\"letter\">Q<\/h4>\n<p style=\"line-height: unset;\">How do you calculate percentage with a calculator?<\/p>\n<\/p><\/div>\n<div class=\"a_item\">\n<h4 class=\"letter text_bold\">A<\/h4>\n<p>To calculate percentage with a calculator, divide the part by the whole and multiply by 100.<\/p>\n<div class=\"lightbulb-example-2\"><span class=\"lightbulb-icon\">\ud83d\udca1<\/span><span class=\"faq-example-question\">Example: What percentage of 20 is 5?<\/span><\/p>\n<hr style=\"padding: 0; margin-top: -0.2em; margin-bottom: 1.2em\">\n<p style=\"text-align:center; margin-bottom: 0em\"> \\(\\dfrac{5}{20}=0.25 \\times 100=25\\%\\)<\/p>\n<\/div>\n<\/p><\/div>\n<\/p><\/div>\n<div class=\"qa_wrap\">\n<div class=\"q_item text_bold\">\n<h4 class=\"letter\">Q<\/h4>\n<p style=\"line-height: unset;\">How do you multiply percentages?<\/p>\n<\/p><\/div>\n<div class=\"a_item\">\n<h4 class=\"letter text_bold\">A<\/h4>\n<p>Multiply percentages by first converting them to decimals. Then, multiply the decimals. Finally, convert back to a percentage, if necessary.<\/p>\n<div class=\"lightbulb-example-2\"><span class=\"lightbulb-icon\">\ud83d\udca1<\/span><span class=\"faq-example-question\">Example: Multiply \\(13\\% \\times 21\\%\\).<\/span><\/p>\n<hr style=\"padding: 0; margin-top: -0.2em; margin-bottom: 1.2em\">\n<p style=\"text-align: center; margin-bottom: 0em\">\\(13\\%\\: \\times \\:21\\%=0.13\\: \\times \\: 0.21\\) \\(\\:= 0.0273 = 2.73\\%\\)<\/p>\n<\/div>\n<\/p><\/div>\n<\/p><\/div>\n<\/div>\n<\/div>\n<div class=\"spoiler\" id=\"PQs-spoiler\">\n<h2 style=\"text-align:center\"><span id=\"Computation_with_Percentages_Practice_Questions\" class=\"m-toc-anchor\"><\/span>Computation with Percentages Practice Questions<\/h2>\n\n\t\t\t\t<div class=\"PQ\">\n\t\t\t\t\t<strong>Question #1:<\/strong>\n\t\t\t\t\t<div style=\"margin-left:10px;\"><p>&nbsp;<br \/>\nWhat is 90% of 30?<\/p>\n<\/div>\n\t\t\t\t\t<div class=\"PQ-Choices\"><div class=\"PQ\"  id=\"PQ-1-1\">29<\/div><div class=\"PQ\"  id=\"PQ-1-2\">24<\/div><div class=\"PQ correct_answer\"  id=\"PQ-1-3\">27<\/div><div class=\"PQ\"  id=\"PQ-1-4\">26<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t\t<input id=\"PQ-1\" type=\"checkbox\" class=\"spoiler_button\" \/><label for=\"PQ-1\" style=\"width: 150px;\">Show Answer<\/label>\n\t\t\t\t\t<div class=\"answer\" id=\"PQ-1-spoiler\">\n\t\t\t\t\t\t<strong>Answer:<\/strong><div style=\"margin-left:10px;\"><p>This problem is about finding the <em>part<\/em>. To solve, read the question carefully and form an equation from it. The word \u201cwhat\u201d is equivalent to the variable in the equation. Let\u2019s use \\(n\\), for the number that will solve the problem.<\/p>\n<p>Next, the word \u201cis\u201d is much like the word \u201cequals.\u201d Write an equals sign after \\(n\\).<\/p>\n<p style=\"text-align:center;\">\\(n=\u2026\\)<\/p>\n<p>Moving along, 90% is equivalent to \\(\\frac{90}{100}\\), which is also \\(0.90\\).<\/p>\n<p style=\"text-align:center;\">\\(n=0.90\u2026\\)<\/p>\n<p>Finally, we have \u201cof 30.\u201d Whenever you see the word \u201cof\u201d in a math problem, remember that it is equivalent to a multiplication sign! This means the equation from the problem statement will be:<\/p>\n<p style=\"text-align:center;\">\\(n=0.90\\times30\\)<\/p>\n<p>To solve for \\(n\\), simply multiply.<\/p>\n<p style=\"text-align:center;\">\\(n=27\\)<\/p>\n<p>The solution to this problem is 27 because 27 is 90% of 30.<\/p>\n<\/div>\n\t\t\t\t\t\t<input id=\"PQ-1-hide\" type=\"checkbox\" class=\"spoiler_button\" \/><label for=\"PQ-1-hide\" style=\"width: 150px;\">Hide Answer<\/label>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"PQ\">\n\t\t\t\t\t<strong>Question #2:<\/strong>\n\t\t\t\t\t<div style=\"margin-left:10px;\"><p>&nbsp;<br \/>\n20 is 40% of what number?<\/p>\n<\/div>\n\t\t\t\t\t<div class=\"PQ-Choices\"><div class=\"PQ correct_answer\"  id=\"PQ-2-1\">50<\/div><div class=\"PQ\"  id=\"PQ-2-2\">40<\/div><div class=\"PQ\"  id=\"PQ-2-3\">45<\/div><div class=\"PQ\"  id=\"PQ-2-4\">80<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t\t<input id=\"PQ-2\" type=\"checkbox\" class=\"spoiler_button\" \/><label for=\"PQ-2\" style=\"width: 150px;\">Show Answer<\/label>\n\t\t\t\t\t<div class=\"answer\" id=\"PQ-2-spoiler\">\n\t\t\t\t\t\t<strong>Answer:<\/strong><div style=\"margin-left:10px;\"><p>To answer this question, start by writing an equation from the problem statement. The first word is \u201c20.\u201d Since this is already in the language of math, go ahead and write it down in the equation.<\/p>\n<p style=\"text-align:center;\">\\(20\\)<\/p>\n<p>Next, the word \u201cis\u201d is much like the word \u201cequals.\u201d Write an equals sign after 20.<\/p>\n<p style=\"text-align:center;\">\\(20=\\)<\/p>\n<p>40% is the same as \\(\\frac{40}{100}\\) and 0.40. Write this down next.<\/p>\n<p style=\"text-align:center;\">\\(20=0.40\u2026\\)<\/p>\n<p>Remember, the word \u201cof\u201d implies multiplication. Write a multiplication sign after 0.40.<\/p>\n<p style=\"text-align:center;\">\\(20=0.40\\times\u2026\\)<\/p>\n<p>Finally, the problem statement has the words \u201cwhat number.\u201d In place of these words, write your variable. This can be any letter, but here we will use \\(n\\).<\/p>\n<p style=\"text-align:center;\">\\(20=0.40\\times n\\)<\/p>\n<p>To solve for the value of \\(n\\), you must get it all by itself on one side of the equals sign. Get rid of the \\(0.40\\) by dividing by \\(0.40\\) on both sides.<\/p>\n<p style=\"text-align:center;\">\\(\\dfrac{20}{0.40}=\\dfrac{0.40\\times n}{0.40}\\)<\/p>\n<p style=\"text-align:center;\">\\(50=n\\)<\/p>\n<p>This means that 20 is 40% of 50.<\/p>\n<\/div>\n\t\t\t\t\t\t<input id=\"PQ-2-hide\" type=\"checkbox\" class=\"spoiler_button\" \/><label for=\"PQ-2-hide\" style=\"width: 150px;\">Hide Answer<\/label>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"PQ\">\n\t\t\t\t\t<strong>Question #3:<\/strong>\n\t\t\t\t\t<div style=\"margin-left:10px;\"><p>&nbsp;<br \/>\nWhat percent of 75 is 15?<\/p>\n<\/div>\n\t\t\t\t\t<div class=\"PQ-Choices\"><div class=\"PQ correct_answer\"  id=\"PQ-3-1\">20%<\/div><div class=\"PQ\"  id=\"PQ-3-2\">15%<\/div><div class=\"PQ\"  id=\"PQ-3-3\">75%<\/div><div class=\"PQ\"  id=\"PQ-3-4\">[25%<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t\t<input id=\"PQ-3\" type=\"checkbox\" class=\"spoiler_button\" \/><label for=\"PQ-3\" style=\"width: 150px;\">Show Answer<\/label>\n\t\t\t\t\t<div class=\"answer\" id=\"PQ-3-spoiler\">\n\t\t\t\t\t\t<strong>Answer:<\/strong><div style=\"margin-left:10px;\"><p>To answer this question, it is again important to convert the problem statement into an algebraic expression. First, we have the words \u201cwhat percent.\u201d Let\u2019s use the variable \\(p\\) to represent this.<\/p>\n<p>Next is the word \u201cof.\u201d Like in the other problems, this word is equivalent to a multiplication sign. Now we have \\(p\\times &#8230;\\)<\/p>\n<p>Next is the number 75, followed by \u201cis 15.\u201d The word \u201cis\u201d should be replaced with an equals sign, and, of course, 75 and 15 should remain as numbers. Putting all the pieces together, we have the equation \\(p\\times75=15\\).<\/p>\n<p>To solve for \\(p\\), divide both sides by 75.<\/p>\n<p style=\"text-align:center;\">\\(\\dfrac{p\\times75}{75}=\\dfrac{15}{75}\\)<\/p>\n<p style=\"text-align:center;\">\\(p=\\dfrac{1}{5}=0.20\\)<\/p>\n<p>Converting this to a percent, \\(p=20\\%\\).<\/p>\n<\/div>\n\t\t\t\t\t\t<input id=\"PQ-3-hide\" type=\"checkbox\" class=\"spoiler_button\" \/><label for=\"PQ-3-hide\" style=\"width: 150px;\">Hide Answer<\/label>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"PQ\">\n\t\t\t\t\t<strong>Question #4:<\/strong>\n\t\t\t\t\t<div style=\"margin-left:10px;\"><p>&nbsp;<br \/>\nMiss Turner\u2019s chemistry students recently took an exam. Of the 40 students in her class, 16 of them made A\u2019s. What percent of the class made A\u2019s on the exam?<\/p>\n<\/div>\n\t\t\t\t\t<div class=\"PQ-Choices\"><div class=\"PQ\"  id=\"PQ-4-1\">20%<\/div><div class=\"PQ\"  id=\"PQ-4-2\">24%<\/div><div class=\"PQ\"  id=\"PQ-4-3\">33%<\/div><div class=\"PQ correct_answer\"  id=\"PQ-4-4\">40%<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t\t<input id=\"PQ-4\" type=\"checkbox\" class=\"spoiler_button\" \/><label for=\"PQ-4\" style=\"width: 150px;\">Show Answer<\/label>\n\t\t\t\t\t<div class=\"answer\" id=\"PQ-4-spoiler\">\n\t\t\t\t\t\t<strong>Answer:<\/strong><div style=\"margin-left:10px;\"><p>Word problems are a little trickier to solve, but we can make an equation just like in the previous problems by studying the information closely. Notice that the question at the end of the problem asks \u201cwhat percent of the class made A\u2019s.\u201d Let\u2019s use this to start building the equation.<\/p>\n<p>The words \u201cwhat percent\u201d indicate that we want to know a percentage, so let\u2019s use the variable \\(p\\). Next, the words \u201cof the class\u201d indicate that we need a multiplication sign, followed by the number of students in the class. Now we have \\(p\\times40\\).<\/p>\n<p>The next part of the question specifies that we are interested in the students who made A\u2019s. Since 16 students got an A on the exam, set the equation equal to 16.<\/p>\n<p style=\"text-align:center;\">\\(p\\times40=16\\)<\/p>\n<p>Now, solve for \\(p\\) by dividing both sides by 40.<\/p>\n<p style=\"text-align:center;\">\\(\\dfrac{p\\times40}{40}=\\dfrac{16}{40}\\)<\/p>\n<p style=\"text-align:center;\">\\(p=0.4\\)<\/p>\n<p>Converting this to a percentage, we see that \\(p=40\\%\\). So 40% of Miss Turner\u2019s students made an A on the chemistry exam.<\/p>\n<\/div>\n\t\t\t\t\t\t<input id=\"PQ-4-hide\" type=\"checkbox\" class=\"spoiler_button\" \/><label for=\"PQ-4-hide\" style=\"width: 150px;\">Hide Answer<\/label>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"PQ\">\n\t\t\t\t\t<strong>Question #5:<\/strong>\n\t\t\t\t\t<div style=\"margin-left:10px;\"><p>&nbsp;<br \/>\nGeorge and his family are out for lunch, and their bill comes out to $36.00. If they want to leave a 20% tip for their waiter, how much will the tip be?<\/p>\n<\/div>\n\t\t\t\t\t<div class=\"PQ-Choices\"><div class=\"PQ\"  id=\"PQ-5-1\">$6.00<\/div><div class=\"PQ\"  id=\"PQ-5-2\">$5.75<\/div><div class=\"PQ correct_answer\"  id=\"PQ-5-3\">$7.20<\/div><div class=\"PQ\"  id=\"PQ-5-4\">$8.25<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t\t<input id=\"PQ-5\" type=\"checkbox\" class=\"spoiler_button\" \/><label for=\"PQ-5\" style=\"width: 150px;\">Show Answer<\/label>\n\t\t\t\t\t<div class=\"answer\" id=\"PQ-5-spoiler\">\n\t\t\t\t\t\t<strong>Answer:<\/strong><div style=\"margin-left:10px;\"><p>To answer this question, first put the information into an equation. We know the cost of the bill and the percent of the tip. Recall that tips <em>are<\/em> a certain percent of the bill. Let\u2019s use the variable \\(t\\) to represent the tip amount.<\/p>\n<p>Notice that the word \u201care\u201d is another form of the word \u201cis.\u201d Write an equals sign after \\(t\\).<\/p>\n<p style=\"text-align:center;\">\\(t=\\)<\/p>\n<p>On the other side of the equation, we will write the tip percentage multiplied by the bill amount. This is because \u201ctips are a certain percent <em>of<\/em> the bill amount,\u201d and the word \u201cof\u201d indicates multiplication.<\/p>\n<p style=\"text-align:center;\">\\(t=20\\% \\times 36.00\\)<\/p>\n<p>To do this multiplication, convert 20% to a decimal.<\/p>\n<p style=\"text-align:center;\">\\(t=0.20\\times36\\)<\/p>\n<p style=\"text-align:center;\">\\(t=7.2\\)<\/p>\n<p>The tip should be $7.20.<\/p>\n<\/div>\n\t\t\t\t\t\t<input id=\"PQ-5-hide\" type=\"checkbox\" class=\"spoiler_button\" \/><label for=\"PQ-5-hide\" style=\"width: 150px;\">Hide Answer<\/label>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div><\/div>\n<\/div>\n\n<div class=\"home-buttons\">\n<p><a href=\"https:\/\/www.mometrix.com\/academy\/algebra-i\/\">Return to Algebra I Videos<\/a><\/p>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>Return to Algebra I Videos<\/p>\n","protected":false},"author":1,"featured_media":100288,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"open","template":"","meta":{"footnotes":""},"class_list":{"0":"post-4435","1":"page","2":"type-page","3":"status-publish","4":"has-post-thumbnail","6":"page_category-fractions-decimals-percentages-videos","7":"page_category-math-advertising-group","8":"page_category-percentage-videos","9":"page_category-percents","10":"page_category-ratios-and-percentages-videos","11":"page_category-ratios-and-proportions","12":"page_type-video","13":"content_type-practice-questions","14":"subject_matter-math"},"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/www.mometrix.com\/academy\/wp-json\/wp\/v2\/pages\/4435","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.mometrix.com\/academy\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/www.mometrix.com\/academy\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/www.mometrix.com\/academy\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.mometrix.com\/academy\/wp-json\/wp\/v2\/comments?post=4435"}],"version-history":[{"count":6,"href":"https:\/\/www.mometrix.com\/academy\/wp-json\/wp\/v2\/pages\/4435\/revisions"}],"predecessor-version":[{"id":279322,"href":"https:\/\/www.mometrix.com\/academy\/wp-json\/wp\/v2\/pages\/4435\/revisions\/279322"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.mometrix.com\/academy\/wp-json\/wp\/v2\/media\/100288"}],"wp:attachment":[{"href":"https:\/\/www.mometrix.com\/academy\/wp-json\/wp\/v2\/media?parent=4435"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}