{"id":121171,"date":"2022-05-05T11:06:16","date_gmt":"2022-05-05T16:06:16","guid":{"rendered":"https:\/\/www.mometrix.com\/academy\/?page_id=121171"},"modified":"2026-03-28T11:51:42","modified_gmt":"2026-03-28T16:51:42","slug":"dividing-monomials","status":"publish","type":"page","link":"https:\/\/www.mometrix.com\/academy\/dividing-monomials\/","title":{"rendered":"Dividing Monomials"},"content":{"rendered":"\n\t\t\t<div id=\"mmDeferVideoEncompass_UIqGyCBg9iI\" 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_UIqGyCBg9iI\" data-source-videoID=\"UIqGyCBg9iI\" src=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2023\/01\/circle-play-duotone.png\" alt=\"Dividing Monomials Video\" height=\"464\" width=\"825\" class=\"size-full\" data-matomo-title = \"Dividing Monomials\">\n\t\t\t<\/picture>\n\t\t\t<\/div>\n\t\t\t<style>img#videoThumbnailImage_UIqGyCBg9iI:hover {cursor:pointer;} img#videoThumbnailImage_UIqGyCBg9iI {background-size:contain;background-image:url(\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2023\/02\/2339-thumbnail-1.webp\");}<\/style>\n\t\t\t<script defer>\n\t\t\t  jQuery(\"img#videoThumbnailImage_UIqGyCBg9iI\").click(function() {\n\t\t\t\tlet videoId = jQuery(this).attr(\"data-source-videoID\");\n\t\t\t\tlet helpTag = '<div id=\"mmDeferVideoYTMessage_UIqGyCBg9iI\" 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\",\"Dividing Monomials\");\n\t\t\t\tjQuery(\"div#mmDeferVideoEncompass_UIqGyCBg9iI\").html(tag);\n\t\t\t\tjQuery(\"div#mmDeferVideoEncompass_UIqGyCBg9iI\").prepend(helpTag);\n\t\t\t\tsetTimeout(function(){jQuery(\"div#mmDeferVideoYTMessage_UIqGyCBg9iI\").css(\"display\", \"block\");}, 2000);\n\t\t\t  });\n\t\t\t  \n\t\t\t<\/script>\n\t\t\n<p><script>\nfunction yks_Function() {\n  var x = document.getElementById(\"yks\");\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=\"yks_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=\"yks\" style=\"display:none;\">\n<ul>\n<li class=\"toc-h2\"><a href=\"#What_is_a_Monomial\" class=\"smooth-scroll\">What is a Monomial?<\/a><\/li>\n<li class=\"toc-h2\"><a href=\"#Dividing_Monomials\" class=\"smooth-scroll\">Dividing Monomials<\/a>\n<ul><\/li>\n<li class=\"toc-h3\"><a href=\"#Example_1\" class=\"smooth-scroll\">Example #1<\/a><\/li>\n<li class=\"toc-h3\"><a href=\"#Example_2\" class=\"smooth-scroll\">Example #2<\/a><\/li>\n<li class=\"toc-h3\"><a href=\"#Example_3\" class=\"smooth-scroll\">Example #3<\/a><\/li>\n<li class=\"toc-h3\"><a href=\"#Example_4\" class=\"smooth-scroll\">Example #4<\/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>\n<div class=\"spoiler\" id=\"transcript-spoiler\">\n<p>Hello, and welcome to this video on dividing monomials.<\/p>\n<h2><span id=\"What_is_a_Monomial\" class=\"m-toc-anchor\"><\/span>What is a Monomial?<\/h2>\n<p>\nA monomial is a mathematical expression that has only one term. \\(4x\\), \\(xy^{3}\\), and \\(23a^{4}\\) are all examples of monomials. So \\(xy^{3}\\) doesn&#8217;t quite look like this might be a monomial, but it is because \\(x\\) and \\(y^{3}\\) are multiplied together, just like 4 and \\(x\\) are multiplied together in \\(4x\\). So all three of these are examples of monomials.<\/p>\n<h2><span id=\"Dividing_Monomials\" class=\"m-toc-anchor\"><\/span>Dividing Monomials<\/h2>\n<p>\nWhen dividing monomials, we need to remember our exponent rules, specifically the rule \\(\\frac{x^{m}}{x^{n}}=x^{m-n}\\). This means that when bases raised to <a class=\"ylist\" href=\"https:\/\/www.mometrix.com\/academy\/laws-of-exponents\/\">exponents<\/a> are divided by one another, and the bases are the same, you keep the base the same and subtract the exponents.<\/p>\n<h3><span id=\"Example_1\" class=\"m-toc-anchor\"><\/span>Example #1<\/h3>\n<p>\nLet\u2019s start by working through a simple example. Remember, fraction bars always represent division, so we\u2019re dividing \\(5x\\) by \\(x\\).<\/p>\n<div class=\"examplesentence\" style=\"font-size: 120%;\">\\(\\frac{5x}{x}\\)<\/div>\n<p>\n&nbsp;<br \/>\nWhen dividing monomials, start by dividing the coefficients by one another. It doesn\u2019t look like there is a coefficient in the denominator, but remember, any variable without a coefficient has a coefficient of 1 because 1 times anything is itself. So we can divide 5 by 1.<\/p>\n<div class=\"examplesentence\">\\(5\\div 1=5\\)<\/div>\n<p>\n&nbsp;<br \/>\nThen, we move on to dividing our \\(x\\)-terms. Anything divided by itself is 1, so:<\/p>\n<div class=\"examplesentence\">\\(x\\div x=1\\)<\/div>\n<p>\n&nbsp;<br \/>\nNow, to get our final answer, we multiply these two things together.<\/p>\n<div class=\"examplesentence\">\\(5\\cdot 1=5\\)<\/div>\n<p>\n&nbsp;<br \/>\nThis means that \\(\\frac{5x}{x}=5\\).<\/p>\n<h3><span id=\"Example_2\" class=\"m-toc-anchor\"><\/span>Example #2<\/h3>\n<p>\nLet\u2019s try a slightly harder example. <\/p>\n<div class=\"examplesentence\" style=\"font-size: 120%;\">\\(\\frac{12x^{3}}{3x^{2}}\\)<\/div>\n<p>\n&nbsp;<br \/>\nSo in this example we&#8217;re going to have to use that exponent rule that I talked about earlier. But first, we&#8217;re going to start by dividing our coefficients by one another, just like we did last time.<\/p>\n<div class=\"examplesentence\">\\(12\\div 3=4\\)<\/div>\n<p>\n&nbsp;<br \/>\nNow, divide the \\(x\\)-terms by one another. This is where our exponent rule will come into play. Remember our bases are the same, so all we have to do is keep the base the same and subtract the exponents.<\/p>\n<div class=\"examplesentence\">\\(x^{3}x^{2}=x^{3-2}=x^{1}=x\\)<\/div>\n<p>\n&nbsp;<br \/>\nFinally, we multiply these two things together to get our answer.<\/p>\n<div class=\"examplesentence\">\\(\\frac{12x^{3}}{3x^{2}}=4x\\)<\/div>\n<p>\n&nbsp;<\/p>\n<h3><span id=\"Example_3\" class=\"m-toc-anchor\"><\/span>Example #3<\/h3>\n<p>\nLet\u2019s try another one.<\/p>\n<div class=\"examplesentence\">\\(8x^{5}y^{3}\\div x^{2}y\\)<\/div>\n<p>\n&nbsp;<br \/>\nFirst, divide the coefficients by one another. Remember, the second term has a coefficient of 1.<\/p>\n<div class=\"examplesentence\">\\(8\\div 1=8\\)<\/div>\n<p>\n&nbsp;<br \/>\nThen, divide the \\(x\\)-terms. Remember, the bases have to be the same for the exponent rule to work, so we will divide the \\(y\\)-terms in the next step.<\/p>\n<div class=\"examplesentence\">\\(x^{5}\\div x^{2}=x^{5-2}=x^{3}\\)<\/div>\n<p>\n&nbsp;<br \/>\nAnd now we move on to our \\(y\\)-terms. Remember, anything without an exponent is raised to the first power.<\/p>\n<div class=\"examplesentence\">\\(y^{3}\\div y=y^{3-1}=y^{2}\\)<\/div>\n<p>\n&nbsp;<br \/>\nFinally, multiply all three parts by each other.<\/p>\n<div class=\"examplesentence\">\\(8x^{5}y^{3}x^{2}y=8x^{3}y^{2}\\)<\/div>\n<p>\n&nbsp;<\/p>\n<h3><span id=\"Example_4\" class=\"m-toc-anchor\"><\/span>Example #4<\/h3>\n<p>\nBefore we go, I want to try one last problem. This one is slightly more challenging.<\/p>\n<div class=\"examplesentence\" style=\"font-size: 120%;\">\\(\\frac{5a^{24}b^{7}}{25a^{15}b^{13}}\\)<\/div>\n<p>\n&nbsp;<br \/>\nDon\u2019t be confused by the \\(a\\)\u2019s and \\(b\\)\u2019s. You can treat them just like you would \\(x\\)\u2019s and \\(y\\)\u2019s. First, divide the coefficients.<\/p>\n<div class=\"examplesentence\">\\(5\\div 25=\\frac{1}{5}\\)<\/div>\n<p>\n&nbsp;<br \/>\nThen, divide the \\(a\\)-terms.<\/p>\n<div class=\"examplesentence\">\\(a^{24}\\div a^{15}=a^{24-15}=a^{9}\\)<\/div>\n<p>\n&nbsp;<br \/>\nNext, divide the \\(b\\)-terms.<\/p>\n<div class=\"examplesentence\">\\(b^{7}\\div b^{13}=b^{7-13}=b^{-6}\\)<\/div>\n<p>\n&nbsp;<br \/>\nRemember, a negative exponent tells you to put the base raised to the positive exponent in the denominator of a fraction.<\/p>\n<div class=\"examplesentence\">\\(b^{-6}=\\frac{1}{b^{6}}\\)<\/div>\n<p>\n&nbsp;<br \/>\nNow, multiply all three parts together.<\/p>\n<div class=\"examplesentence\">\\(\\frac{1}{5}\\cdot a^{9}\\cdot \\frac{1}{b^{6}}\\)<\/div>\n<p>\n&nbsp;<br \/>\nFinally, simplify by combining this all as one fraction.<\/p>\n<div class=\"examplesentence\">\\(\\frac{5a^{24}b^{7}}{25a^{15}b^{13}}=\\frac{a^{9}}{5b^{6}}\\)<\/div>\n<p>\n&nbsp;<br \/>\nI hope this video on dividing monomials was helpful. 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