{"id":38792,"date":"2018-03-15T13:42:37","date_gmt":"2018-03-15T13:42:37","guid":{"rendered":"https:\/\/www.mometrix.com\/academy\/?page_id=38792"},"modified":"2026-04-27T11:29:56","modified_gmt":"2026-04-27T16:29:56","slug":"translating-word-problems","status":"publish","type":"page","link":"https:\/\/www.mometrix.com\/academy\/translating-word-problems\/","title":{"rendered":"Understanding Word Problems"},"content":{"rendered":"\n\t\t\t<div id=\"mmDeferVideoEncompass_0DfB2vKu8Yk\" 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_0DfB2vKu8Yk\" data-source-videoID=\"0DfB2vKu8Yk\" src=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2023\/01\/circle-play-duotone.png\" alt=\"Understanding Word Problems Video\" height=\"464\" width=\"825\" class=\"size-full\" data-matomo-title = \"Understanding Word Problems\">\n\t\t\t<\/picture>\n\t\t\t<\/div>\n\t\t\t<style>img#videoThumbnailImage_0DfB2vKu8Yk:hover {cursor:pointer;} img#videoThumbnailImage_0DfB2vKu8Yk {background-size:contain;background-image:url(\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2023\/02\/179-understanding-word-problems-1.webp\");}<\/style>\n\t\t\t<script defer>\n\t\t\t  jQuery(\"img#videoThumbnailImage_0DfB2vKu8Yk\").click(function() {\n\t\t\t\tlet videoId = jQuery(this).attr(\"data-source-videoID\");\n\t\t\t\tlet helpTag = '<div id=\"mmDeferVideoYTMessage_0DfB2vKu8Yk\" 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\",\"Understanding Word Problems\");\n\t\t\t\tjQuery(\"div#mmDeferVideoEncompass_0DfB2vKu8Yk\").html(tag);\n\t\t\t\tjQuery(\"div#mmDeferVideoEncompass_0DfB2vKu8Yk\").prepend(helpTag);\n\t\t\t\tsetTimeout(function(){jQuery(\"div#mmDeferVideoYTMessage_0DfB2vKu8Yk\").css(\"display\", \"block\");}, 2000);\n\t\t\t  });\n\t\t\t  \n\t\t\t<\/script>\n\t\t\n<p><script>\nfunction Cys_Function() {\n  var x = document.getElementById(\"Cys\");\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=\"Cys_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=\"Cys\" style=\"display:none;\">\n<ul>\n<li class=\"toc-h2\"><a href=\"#Steps_for_Solving_Word_Problems\" class=\"smooth-scroll\">Steps for Solving Word Problems<\/a><\/li>\n<li class=\"toc-h2\"><a href=\"#Word_Problem_Practice_Questions\" class=\"smooth-scroll\">Word Problem 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=\"PQs\" type=\"checkbox\" class=\"spoiler_button\" \/><label for=\"PQs\">Practice<\/label>\n<div class=\"spoiler\" id=\"transcript-spoiler\">\n<p>Hey, guys! Welcome to this video on word problems.<\/p>\n<p>The hardest thing about doing word problems is the part where you need to take the English words and translate them into mathematics. Usually, once you get the math equation, you&#8217;re fine. The actual math involved is often very simple. But figuring out the actual equation can seem nearly impossible.<\/p>\n<p>What I&#8217;m going to talk about in this video is a list of hints and helps. Be advised, however, to really learn how to do word problems, you will need to practice, practice, practice! <\/p>\n<h2><span id=\"Steps_for_Solving_Word_Problems\" class=\"m-toc-anchor\"><\/span>Steps for Solving Word Problems<\/h2>\n<h3><span id=\"Reading_the_Problem\" class=\"m-toc-anchor\"><\/span>Reading the Problem<\/h3>\n<p>\nThe first step to effectively translating and solving word problems is to read the problem entirely. Don&#8217;t try solving anything when you&#8217;ve only read half a sentence! Try first to get a feel for the whole problem, then see what information you have and figure out what you still need.<\/p>\n<h3><span id=\"Working_Orderly\" class=\"m-toc-anchor\"><\/span>Working Orderly<\/h3>\n<p>\nThe second step is to work in an orderly fashion. Figure out what you need but don&#8217;t have, and begin to name things. Always pick variables to stand for the unknowns, clearly labeling the variables with exactly what they stand for. Draw and label pictures neatly. Explain your reasoning as you go along. And make sure you know just exactly what the problem is asking for.<\/p>\n<p>Working clearly will help you to think clearly, and figuring out what you will need will help you translate your final answer back into English.<\/p>\n<p>It can be really frustrating, and kind of embarrassing, to spend 15 minutes solving a word problem on a test only realize that, in the end, you no longer have any idea what \\(x\\) stands for, so you have to do the whole problem over again.<\/p>\n<h3><span id=\"Key_Words_for_Mathematical_Operations\" class=\"m-toc-anchor\"><\/span>Key Words for Mathematical Operations<\/h3>\n<p>\nThe third step is to look for key words. Certain words indicate certain mathematical operations.<\/p>\n<h4 style=\"margin-bottom: 0em; font-weight: 600 !important; font-size: 105%\"><span id=\"Addition\" class=\"m-toc-anchor\"><\/span>Addition<\/h4>\n<p>\nHere&#8217;s a list of words to be aware of when dealing with addition:<\/p>\n<ul>\n<li>Increased by<\/li>\n<li>More than<\/li>\n<li>Combined<\/li>\n<li>Together<\/li>\n<li>Total of<\/li>\n<li>Sum<\/li>\n<li>Plus<\/li>\n<li>Added to<\/li>\n<li>Comparatives (like &#8220;greater than&#8221;)<\/li>\n<\/ul>\n<h4 style=\"margin-bottom: 0em; font-weight: 600 !important; font-size: 105%\"><span id=\"Subtraction\" class=\"m-toc-anchor\"><\/span>Subtraction<\/h4>\n<p>\nHere is a list of terms to look out for when dealing with subtraction:<\/p>\n<ul>\n<li>Decreased by<\/li>\n<li>Minus<\/li>\n<li>Less<\/li>\n<li>Difference between<\/li>\n<li>Difference of<\/li>\n<li>Less than<\/li>\n<li>Fewer than<\/li>\n<li>Left<\/li>\n<li>Left over<\/li>\n<li>After<\/li>\n<li>Save (more of an old-fashioned term)<\/li>\n<li>Comparatives (like &#8220;smaller than&#8221;)<\/li>\n<\/ul>\n<h4 style=\"margin-bottom: 0em; font-weight: 600 !important; font-size: 105%\"><span id=\"Multiplication\" class=\"m-toc-anchor\"><\/span>Multiplication<\/h4>\n<p>\nHere are terms to be aware of when dealing with multiplication:<\/p>\n<ul>\n<li>Of<\/li>\n<li>Times<\/li>\n<li>Multiplied by<\/li>\n<li>Product of<\/li>\n<li>Increased\/decreased by a factor of<\/li>\n<li>Twice, triple, etc.<\/li>\n<li>Each<\/li>\n<\/ul>\n<h4 style=\"margin-bottom: 0em; font-weight: 600 !important; font-size: 105%\"><span id=\"Division\" class=\"m-toc-anchor\"><\/span>Division<\/h4>\n<p>\nNext are terms to be aware of when dealing with division: <\/p>\n<ul>\n<li>Per<\/li>\n<li>A<\/li>\n<li>Out of<\/li>\n<li><a class=\"ylist\" href=\"https:\/\/www.mometrix.com\/academy\/word-problems-with-ratios\/\">Ratio<\/a><\/li>\n<li>Quotient of<\/li>\n<li>Percent (divided by 100)<\/li>\n<li>Equal pieces<\/li>\n<li>Split<\/li>\n<li>Average<\/li>\n<\/ul>\n<h4 style=\"margin-bottom: 0em; font-weight: 600 !important; font-size: 105%\"><span id=\"Equality\" class=\"m-toc-anchor\"><\/span>Equality<\/h4>\n<p>\nLastly, here are terms to be aware of when dealing with things that are equal:<\/p>\n<ul>\n<li>Is<\/li>\n<li>Are<\/li>\n<li>Was<\/li>\n<li>Were<\/li>\n<li>Will be<\/li>\n<li>Gives<\/li>\n<li>Yields<\/li>\n<li>Sold for<\/li>\n<li>Cost<\/li>\n<\/ul>\n<p>As you work through word problems, be aware of these words and use them to help you identify what type of math is taking place.<\/p>\n<p>I hope that this video was helpful! See you guys next time!<\/p>\n<\/div>\n<div class=\"spoiler\" id=\"PQs-spoiler\">\n<h2 style=\"text-align:center\"><span id=\"Word_Problem_Practice_Questions\" class=\"m-toc-anchor\"><\/span>Word Problem 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 \/>\nWhich of the following is NOT a helpful strategy for solving word problems?<\/p>\n<\/div>\n\t\t\t\t\t<div class=\"PQ-Choices\"><div class=\"PQ\"  id=\"PQ-1-1\">Read the problem thoroughly, all the way to the end. Consider re-reading the problem a few times so that you are familiar with what the question is about. <\/div><div class=\"PQ\"  id=\"PQ-1-2\">Draw pictures or models that represent what is happening in the story. <\/div><div class=\"PQ\"  id=\"PQ-1-3\">Identify what you need to know, and label unknown values with variables. <\/div><div class=\"PQ correct_answer\"  id=\"PQ-1-4\">Locate the last sentence in the word problem because this is always where the question is located. <\/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>Word problems generally have the question as the last sentence, but this is not always the case. It can be helpful to underline the question in a word problem so that it is clearly identified within the text.<\/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 \/>\nWhich list provides key words that all indicate addition? <\/p>\n<\/div>\n\t\t\t\t\t<div class=\"PQ-Choices\"><div class=\"PQ\"  id=\"PQ-2-1\">Total of, quotient, more than<\/div><div class=\"PQ correct_answer\"  id=\"PQ-2-2\">Combined, more than, together<\/div><div class=\"PQ\"  id=\"PQ-2-3\">Plus, product, sum<\/div><div class=\"PQ\"  id=\"PQ-2-4\">More than, sum, less than<\/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>Terms that were listed that do not indicate addition are \u201cquotient\u201d (division), \u201cproduct\u201d (multiplication), and \u201cless than\u201d (subtraction). Paying close attention to key words can help you determine which operation to use when solving word problems.<\/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 \/>\nWhich list provides key words that all indicate multiplication? <\/p>\n<\/div>\n\t\t\t\t\t<div class=\"PQ-Choices\"><div class=\"PQ correct_answer\"  id=\"PQ-3-1\">Of, times, product of<\/div><div class=\"PQ\"  id=\"PQ-3-2\">Times, difference, sum<\/div><div class=\"PQ\"  id=\"PQ-3-3\">Groups of, product, quotient<\/div><div class=\"PQ\"  id=\"PQ-3-4\">Total, is, sum<\/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>There are many terms that refer to multiplication. The terms \u201cof,\u201d \u201ctimes,\u201d and \u201cproduct\u201d all indicate multiplication. When solving word problems, it is helpful to look for key words such as these in order to determine which operation the problem requires.<\/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 \/>\nWhich operations do the words &#8220;is&#8221; and &#8220;of&#8221; indicate in the following problem?<\/p>\n<div class=\"yellow-math-quote\">40 <strong>is<\/strong> what percent <strong>of<\/strong> 200?<\/div>\n<\/div>\n\t\t\t\t\t<div class=\"PQ-Choices\"><div class=\"PQ correct_answer\"  id=\"PQ-4-1\">&#8220;Is&#8221; represents \u201cequals.\u201d<\/br>\r\n&#8220;Of&#8221; represents \u201cmultiply.\u201d<\/div><div class=\"PQ\"  id=\"PQ-4-2\">&#8220;Is&#8221; represents \u201cequals.\u201d<\/br>\r\n&#8220;Of&#8221; represents \u201cdivide.\u201d<\/div><div class=\"PQ\"  id=\"PQ-4-3\">&#8220;Is&#8221; represents \u201caddition.\u201d<\/br>\r\n&#8220;Of&#8221; represents \u201cmultiply.\u201d<\/div><div class=\"PQ\"  id=\"PQ-4-4\">&#8220;Is&#8221; represents \u201csubtraction.\u201d<\/br>\r\n&#8220;Of&#8221; represents \u201cdivision.\u201d<\/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>In this example, the term \u201cis\u201d can be interpreted as \u201cequals,&#8221; and the term \u201cof\u201d can be interpreted as \u201cmultiplication.\u201d<\/p>\n<p>In this scenario, \u201c40 is what percent of 200\u201d can be re-written as an equation:<\/p>\n<p style=\"text-align: center\">\\(40=x\\times200\\)<\/p>\n<p>This can be manipulated in order to solve for \\(x\\). When both sides of the equation are divided by 200, the equation shows that \\(x=0.2\\), which is the same as 20%. <\/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 wants to purchase a computer that costs $1,000. George plans to use $455 from his savings account, $200 from his checking account, and his uncle says he can loan George the remaining cost. What is the leftover amount that George\u2019s uncle will need to contribute?<\/p>\n<\/div>\n\t\t\t\t\t<div class=\"PQ-Choices\"><div class=\"PQ\"  id=\"PQ-5-1\">$433<\/div><div class=\"PQ\"  id=\"PQ-5-2\">$223<\/div><div class=\"PQ correct_answer\"  id=\"PQ-5-3\">$345<\/div><div class=\"PQ\"  id=\"PQ-5-4\">$200<\/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>The key word \u201cleftover\u201d indicates subtraction in this scenario. George is able to contribute a total of $655 to the computer, so subtracting this from the total of $1,000 will provide the \u201cleftover\u201d amount that George\u2019s uncle will provide.<\/p>\n<p style=\"text-align: center\">\\(\\$1{,}000 \\: &#8211; \\: \\$655 = \\$345\\)<\/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","protected":false},"excerpt":{"rendered":"","protected":false},"author":1,"featured_media":91219,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"class_list":{"0":"post-38792","1":"page","2":"type-page","3":"status-publish","4":"has-post-thumbnail","6":"page_category-math-advertising-group","7":"page_category-video-pages-for-study-course-sidebar-ad","8":"page_category-word-problems","9":"page_type-video","10":"content_type-practice-questions","11":"subject_matter-math"},"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/www.mometrix.com\/academy\/wp-json\/wp\/v2\/pages\/38792","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=38792"}],"version-history":[{"count":5,"href":"https:\/\/www.mometrix.com\/academy\/wp-json\/wp\/v2\/pages\/38792\/revisions"}],"predecessor-version":[{"id":292445,"href":"https:\/\/www.mometrix.com\/academy\/wp-json\/wp\/v2\/pages\/38792\/revisions\/292445"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.mometrix.com\/academy\/wp-json\/wp\/v2\/media\/91219"}],"wp:attachment":[{"href":"https:\/\/www.mometrix.com\/academy\/wp-json\/wp\/v2\/media?parent=38792"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}