{"id":13768,"date":"2014-02-13T23:27:52","date_gmt":"2014-02-13T23:27:52","guid":{"rendered":"http:\/\/www.mometrix.com\/academy\/?page_id=13768"},"modified":"2026-03-25T11:25:59","modified_gmt":"2026-03-25T16:25:59","slug":"multiplying-and-dividing-fractions","status":"publish","type":"page","link":"https:\/\/www.mometrix.com\/academy\/multiplying-and-dividing-fractions\/","title":{"rendered":"Multiplying and Dividing Fractions"},"content":{"rendered":"\n\t\t\t<div id=\"mmDeferVideoEncompass_5Jl7l0W6fps\" 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_5Jl7l0W6fps\" data-source-videoID=\"5Jl7l0W6fps\" src=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2023\/01\/circle-play-duotone.png\" alt=\"Multiplying and Dividing Fractions Video\" height=\"464\" width=\"825\" class=\"size-full\" data-matomo-title = \"Multiplying and Dividing Fractions\">\n\t\t\t<\/picture>\n\t\t\t<\/div>\n\t\t\t<style>img#videoThumbnailImage_5Jl7l0W6fps:hover {cursor:pointer;} img#videoThumbnailImage_5Jl7l0W6fps {background-size:contain;background-image:url(\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2023\/02\/1209-multiplying-and-dividing-fractions-2.webp\");}<\/style>\n\t\t\t<script defer>\n\t\t\t  jQuery(\"img#videoThumbnailImage_5Jl7l0W6fps\").click(function() {\n\t\t\t\tlet videoId = jQuery(this).attr(\"data-source-videoID\");\n\t\t\t\tlet helpTag = '<div id=\"mmDeferVideoYTMessage_5Jl7l0W6fps\" 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\",\"Multiplying and Dividing Fractions\");\n\t\t\t\tjQuery(\"div#mmDeferVideoEncompass_5Jl7l0W6fps\").html(tag);\n\t\t\t\tjQuery(\"div#mmDeferVideoEncompass_5Jl7l0W6fps\").prepend(helpTag);\n\t\t\t\tsetTimeout(function(){jQuery(\"div#mmDeferVideoYTMessage_5Jl7l0W6fps\").css(\"display\", \"block\");}, 2000);\n\t\t\t  });\n\t\t\t  \n\t\t\t<\/script>\n\t\t\n<p><script>\nfunction uT6_Function() {\n  var x = document.getElementById(\"uT6\");\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=\"uT6_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=\"uT6\" style=\"display:none;\">\n<ul>\n<li class=\"toc-h2\"><a href=\"#Multiplying_Fractions\" class=\"smooth-scroll\">Multiplying Fractions<\/a><\/li>\n<li class=\"toc-h2\"><a href=\"#Dividing_Fractions\" class=\"smooth-scroll\">Dividing Fractions<\/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=\"#Multiplying_and_Dividing_Fractions_Problems\" class=\"smooth-scroll\">Multiplying and Dividing Fractions Problems<\/a><\/li>\n<li class=\"toc-h2\"><a href=\"#Multiplying_and_Dividing_Fraction_Worksheets\" class=\"smooth-scroll\">Multiplying and Dividing Fraction Worksheets<\/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><input id=\"worksheets\" type=\"checkbox\" class=\"spoiler_button\" \/><label for=\"worksheets\">Worksheets<\/label><a href=\"https:\/\/www.mometrix.com\/academy\/fractions-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>Many students have a real fear of fractions. However, if you can remember what a <a href=\"https:\/\/www.mometrix.com\/academy\/fractions\/\" class=\"ylist\">fraction<\/a> represents and a few mathematical rules on how to work with them algebraically, you will be able to face fractions with confidence.  In this video, we will review how to multiply and divide fractions. Let\u2019s get started.<\/p>\n<p>We should start by defining exactly what a fraction is. A fraction represents a <a href=\"https:\/\/www.mometrix.com\/academy\/ratios\/\" class=\"ylist\">ratio<\/a> of a \u201cpart\u201d to a \u201cwhole,\u201d or part over whole. The value above the division line is referred to as the <strong>numerator<\/strong>, and the value below the division line is the <strong>denominator<\/strong>.<\/p>\n<h2><span id=\"Multiplying_Fractions\" class=\"m-toc-anchor\"><\/span>Multiplying Fractions<\/h2>\n<p>\nTo multiply fractions, simply multiply \u201cstraight across,\u201d meaning the \u201cnumerator times the numerator\u201d divided by the \u201cdenominator times the denominator.\u201d  Let\u2019s look at a couple of quick examples: <\/p>\n<div class=\"examplesentence\" style=\"font-size: 110%;\">\\(\\frac{2}{3} \\times \\frac{2}{5}\\)<\/div>\n<p>\n&nbsp;<br \/>\nHere, we want to multiply \\(\\frac{2}{3}\\) by \\(\\frac{2}{5}\\). As we said earlier, we\u2019re going to multiply straight across. So we\u2019re going to have 2 times 2 over 3 times 5. Which is equal to four over fifteen. So our answer is \\(\\frac{4}{15}\\).<\/p>\n<div class=\"examplesentence\" style=\"font-size: 110%;\">\\(\\frac{2}{3} \\times \\frac{2}{5}= \\frac{2 \\times 2}{3 \\times 5}= \\frac{4}{15}\\)<\/div>\n<p>\n &nbsp;<br \/>\nNow let\u2019s try another one. We\u2019re going to try \\(\\frac{4}{7}\\) times \\(\\frac{3}{11}\\).<\/p>\n<div class=\"examplesentence\" style=\"font-size: 110%;\">\\(\\frac{4}{7} \\times \\frac{3}{11}\\)<\/div>\n<p>\n&nbsp;<br \/>\nAgain it\u2019s the same concept. We\u2019re going to multiply 4 times 3, divided by 7 times 11. Which gives us \\(\\frac{12}{77}\\).<\/p>\n<div class=\"examplesentence\" style=\"font-size: 110%;\">\\(\\frac{4}{7} \\times \\frac{3}{11}= \\frac{4 \\times 3}{7 \\times 11}= \\frac{12}{77}\\)<\/div>\n<p>\n &nbsp;<br \/>\nPretty simple, right? Now let\u2019s take a look at dividing fractions.<\/p>\n<h2><span id=\"Dividing_Fractions\" class=\"m-toc-anchor\"><\/span>Dividing Fractions<\/h2>\n<p>\nDividing fractions involves a slightly different process. Before we jump into the mechanics of the process, let\u2019s start by looking at an intuitive example of dividing a fraction by two. The effect of dividing by 2 is simply cutting the fraction in half, or simply multiplying the fraction by 1 over 2.<\/p>\n<p>So, \\(\\frac{4}{5}\\) divided by 2 is really the same as saying \\(\\frac{4}{5}\\) times \\(\\frac{1}{2}\\).<\/p>\n<div class=\"examplesentence\" style=\"font-size: 110%;\">\\(\\frac{4}{5}\\)<span style=\"font-style:normal; font-size:90%\">\\( \\div \\text{ } 2 \\text{ }\\)<\/span>\\( = \\frac{4}{5} \\times \\frac{1}{2}\\)<\/div>\n<p>\n&nbsp;<br \/>\nThen it\u2019s going to be multiplied across just like we did before. So we have 4 times 1 is four, over 5 times 2 is 10. Which then simplifies to \\(\\frac{2}{5}\\).<\/p>\n<div class=\"examplesentence\" style=\"font-size: 110%;\">\\(\\frac{4}{5}\\)<span style=\"font-style:normal; font-size:90%\">\\( \\div \\text{ } 2 \\text{ }\\)<\/span>\\( = \\frac{4}{5} \\times \\frac{1}{2}= \\frac{4}{10}= \\frac{2}{5}\\)<\/div>\n<p>\n&nbsp;<br \/>\nSo in other words, \\(\\frac{2}{5}\\) is half the size of \\(\\frac{4}{5}\\).<\/p>\n<p>Similarly, dividing a fraction by 3 would result in a fraction that is one-third the size of the original:<\/p>\n<div class=\"examplesentence\" style=\"font-size: 110%;\">\\(\\frac{2}{5}\\)<span style=\"font-style:normal; font-size:90%\">\\( \\div \\text{ } 3 \\text{ }\\)<\/span>\\( = \\frac{2}{5} \\times \\frac{1}{3}= \\frac{2}{15}\\)<\/div>\n<p>\n&nbsp;<br \/>\n\\(\\frac{2}{5}\\) divided by 3 is the same as saying \\(\\frac{2}{5}\\) times \\(\\frac{1}{3}\\), which gives you \\(\\frac{2}{15}\\).<\/p>\n<p>So, \\(\\frac{2}{15}\\) is one-third the size of \\(\\frac{2}{5}\\).<\/p>\n<p>Before we generalize this process, let\u2019s review some important terminology. Consider the relationship between 2 and \\(\\frac{1}{2}\\). These numbers are called <strong>reciprocals<\/strong> of one another, which means that the numerator of one number is the denominator of the other, and vice versa. Remember that 2 can be written as a fraction by writing it over 1, like this: \\(\\frac{2}{1}\\). Therefore, \\(\\frac{2}{1}\\) and \\(\\frac{1}{2}\\) are reciprocals. The same is true of 3 and \\(\\frac{1}{3}\\), because 3 can be written as \\(\\frac{3}{1}\\). Therefore, 3 and \\(\\frac{1}{3}\\) are reciprocals.<\/p>\n<p>With this in mind, what pattern do you see in the process for dividing fractions?<\/p>\n<h3><span id=\"Keep,_Change,_Flip\" class=\"m-toc-anchor\"><\/span>Keep, Change, Flip<\/h3>\n<p>\nThe process of dividing fractions is the same as multiplying the first fraction by the reciprocal of the second. A shorthand version of this wordy explanation that may help you remember the division process is \u201cKeep, Change, Flip\u201d:<\/p>\n<div class=\"transcriptcallout\" style=\"text-align: left;\"><strong>Keep<\/strong> the first fraction as is<br \/>\n<strong>Change<\/strong> the operation from division to multiplication<br \/>\n<strong>Flip<\/strong> (or take the reciprocal of) the second fraction.<\/div>\n<p>\n&nbsp;<\/p>\n<p>Once this adjustment is made, simply follow the rules for multiplying fractions by multiplying the numerators and dividing by the product of the denominators.<\/p>\n<p>Here is an example using the \u201cKeep, Change, Flip\u201d process:<\/p>\n<p>Say we want to divide \\(\\frac{3}{5}\\) by \\(\\frac{7}{5}\\). We\u2019ll keep the first fraction as is, change the operation from division to multiplication, and flip the second number. Now we just multiply our numerators, 3 times 5 is fifteen, over 5 times 7 is 35. And then from there, we simplify to \\(\\frac{3}{7}\\).<\/p>\n<div class=\"examplesentence\" style=\"font-size: 110%;\">\\(\\frac{3}{5} \\div \\frac{7}{5}= \\frac{3}{5} \\times \\frac{5}{7}= \\frac{15}{35}= \\frac{3}{7}\\)<\/div>\n<p>\n&nbsp;<br \/>\nI hope this video was helpful! Thanks for watching, and happy studying!<\/p>\n<p>For more help, check out our <a class=\"ylist\" target=\"_blank\" rel=\"noopener noreferrer\" href=\"https:\/\/www.mometrix.com\/academy\/fractions-calculator\/\">fractions calculator<\/a>!<\/p>\n<div style=\"text-align: center;\"><a href=\"https:\/\/www.mometrix.com\/academy\/cross-multiplying-fractions\/\" class=\"ylist\">Cross Multiplying Fractions<\/a> | <a href=\"https:\/\/www.mometrix.com\/academy\/proper-and-improper-fractions-and-mixed-numbers\/\" class=\"ylist\">Improper Fractions and Mixed Numbers<\/a><\/div>\n<p>\n&nbsp;<\/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 multiply fractions with whole numbers?<\/p>\n<\/p><\/div>\n<div class=\"a_item\">\n<h4 class=\"letter text_bold\">A<\/h4>\n<p>Multiply fractions by whole numbers by turning the whole number into a fraction by placing it over 1. Any number divided by itself is itself, so this does not change the value of the whole number. Then, multiply across as with normal fractions.<\/p>\n<div class=\"lightbulb-example-2\"><span class=\"lightbulb-icon\">\ud83d\udca1<\/span><span class=\"faq-example-question\">Example: Multiply \\(\\frac{2}{3}\u00d74\\).<\/span><\/p>\n<hr style=\"padding: 0; margin-top: -0.2em; margin-bottom: 1.2em\">\n<p style=\"text-align: center; margin-bottom: 0em\">\\(\\frac{2}{3}\u00d74=\\frac{2}{3}\u00d7\\frac{4}{1}\\) \\(=\\frac{8}{3}=2 \\frac{2}{3}\\)<\/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 mixed fractions?<\/p>\n<\/p><\/div>\n<div class=\"a_item\">\n<h4 class=\"letter text_bold\">A<\/h4>\n<p>Multiply mixed fractions by first turning them into improper fractions and then multiplying across as normal. If there are common factors in the numerator and denominator, cancel those out first to simplify multiplying across.<\/p>\n<p>To convert the fraction back to a mixed number, divide the numerator by the denominator. The number of full divisions becomes the whole number and the remainder becomes the numerator of the fractional part over the original denominator.<\/p>\n<div class=\"lightbulb-example-2\"><span class=\"lightbulb-icon\">\ud83d\udca1<\/span><span class=\"faq-example-question\">Example: Multiply \\(3 \\frac{1}{5}\u00d72 \\frac{7}{9}\\).<\/span><\/p>\n<hr style=\"padding: 0; margin-top: -0.2em; margin-bottom: 1.2em\">\n<p style=\"text-align: center; margin-bottom: 0em\">\\(3 \\frac{1}{5}\u00d72 \\frac{7}{9}=\\frac{16}{5}\u00d7\\frac{25}{9}\\) \\(=\\frac{16}{1}\u00d7\\frac{5}{9}=\\frac{80}{9}=8 \\frac{8}{9}\\)<\/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 divide fractions?<\/p>\n<\/p><\/div>\n<div class=\"a_item\">\n<h4 class=\"letter text_bold\">A<\/h4>\n<p>Divide fractions by using the phrase: \u201cKeep, Change, Flip.\u201d Keep the first fraction the same. Change the division sign to a multiplication sign. Flip the second fraction. Then multiply across and simplify if necessary.<\/p>\n<div class=\"lightbulb-example-2\"><span class=\"lightbulb-icon\">\ud83d\udca1<\/span><span class=\"faq-example-question\">Example: Divide \\(\\frac{4}{7}\u00f7\\frac{8}{13}\\).<\/span><\/p>\n<hr style=\"padding: 0; margin-top: -0.2em; margin-bottom: 1.2em\">\n<p style=\"text-align: center ; margin-bottom: 0em\"> \\(\\frac{4}{7}\u00f7\\frac{8}{13}=\\frac{4}{7}\u00d7\\frac{13}{8}\\) \\(=\\frac{52}{56}=\\frac{13}{14}\\)<\/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 divide fractions with whole numbers?<\/p>\n<\/p><\/div>\n<div class=\"a_item\">\n<h4 class=\"letter text_bold\">A<\/h4>\n<p>Divide fractions by whole numbers by first turning the whole number into a fraction and then dividing the fractions as normal by flipping the second fraction and multiplying across. Any number can be turned into a fraction by placing it over 1.<\/p>\n<div class=\"lightbulb-example-2\"><span class=\"lightbulb-icon\">\ud83d\udca1<\/span><span class=\"faq-example-question\">Example: Divide \\(\\frac{2}{3}\u00f74\\).<\/span><\/p>\n<hr style=\"padding: 0; margin-top: -0.2em; margin-bottom: 1.2em\">\n<p style=\"text-align: center; margin-bottom: 0em\"> \\(\\frac{2}{3}\u00f74=\\frac{2}{3}\u00f7\\frac{4}{1}=\\frac{2}{3}\u00d7\\frac{1}{4}\\) \\(=\\frac{2}{12}=\\frac{1}{6}\\)<\/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 divide mixed fractions?<\/p>\n<\/p><\/div>\n<div class=\"a_item\">\n<h4 class=\"letter text_bold\">A<\/h4>\n<p>Divide mixed fractions by first converting them to improper fractions and then dividing the fractions as normal.<\/p>\n<div class=\"lightbulb-example-2\"><span class=\"lightbulb-icon\">\ud83d\udca1<\/span><span class=\"faq-example-question\">Example:  Divide \\(4 \\frac{3}{5}\u00f72 \\frac{1}{2}\\).<\/span><\/p>\n<hr style=\"padding: 0; margin-top: -0.2em; margin-bottom: 1.2em\">\n<p style=\"text-align: center; margin-bottom: 0em\"> \\(4 \\frac{3}{5}\u00f72 \\frac{1}{2}=\\frac{23}{5}\u00f7\\frac{5}{2}\\) \\(=\\frac{23}{5}\u00d7\\frac{2}{5}=\\frac{46}{25}=1 \\frac{21}{25}\\)<\/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=\"Multiplying_and_Dividing_Fractions_Problems\" class=\"m-toc-anchor\"><\/span>Multiplying and Dividing Fractions Problems<\/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 \/>\n\\(\\dfrac{2}{3}\\times\\dfrac{7}{9}=\\)<\/p>\n<\/div>\n\t\t\t\t\t<div class=\"PQ-Choices\"><div class=\"PQ\"  id=\"PQ-1-1\">\\(\\dfrac{42}{9}\\)<\/div><div class=\"PQ\"  id=\"PQ-1-2\">\\(\\dfrac{42}{47}\\)<\/div><div class=\"PQ correct_answer\"  id=\"PQ-1-3\">\\(\\dfrac{14}{27}\\)<\/div><div class=\"PQ\"  id=\"PQ-1-4\">\\(\\dfrac{14}{9}\\)<\/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>To multiply fractions, simply multiply the numerators together to get the new numerator, and multiply the denominators together to get the new denominator.<\/p>\n<p style=\"text-align: center\">\\(\\dfrac{2}{3}\\times\\dfrac{7}{9}=\\dfrac{2\\times7}{3\\times9}=\\dfrac{14}{27}\\)<\/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 \/>\n\\(\\dfrac{7}{6}\\div\\dfrac{2}{3}=\\)<\/p>\n<\/div>\n\t\t\t\t\t<div class=\"PQ-Choices\"><div class=\"PQ correct_answer\"  id=\"PQ-2-1\">\\(\\dfrac{7}{4}\\)<\/div><div class=\"PQ\"  id=\"PQ-2-2\">\\(\\dfrac{9}{9}\\)<\/div><div class=\"PQ\"  id=\"PQ-2-3\">\\(\\dfrac{14}{18}\\)<\/div><div class=\"PQ\"  id=\"PQ-2-4\">\\(\\dfrac{7}{2}\\)<\/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 divide fractions, use the phrase: Keep, Change, Flip. Keep the first fraction the same. Change the division sign to a multiplication sign. Flip the second fraction so it is its reciprocal. That process looks like this:<\/p>\n<p style=\"text-align: center\">\\(\\dfrac{7}{6}\\div\\dfrac{2}{3}=\\dfrac{7}{6}\\times\\dfrac{3}{2}\\)<\/p>\n<p>Then, multiply and simplify the fractions.<\/p>\n<p style=\"text-align: center\">\\(\\dfrac{7}{6}\\times\\dfrac{3}{2}=\\dfrac{7\\times3}{6\\times2}=\\dfrac{21}{12}=\\dfrac{7}{4}\\)<\/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 \/>\n\\(\\dfrac{1}{4}\\times\\dfrac{6}{7}\\div\\dfrac{2}{9}=\\)<\/p>\n<\/div>\n\t\t\t\t\t<div class=\"PQ-Choices\"><div class=\"PQ\"  id=\"PQ-3-1\">\\(\\dfrac{7}{108}\\)<\/div><div class=\"PQ\"  id=\"PQ-3-2\">\\(\\dfrac{47}{52}\\)<\/div><div class=\"PQ\"  id=\"PQ-3-3\">\\(\\dfrac{12}{252}\\)<\/div><div class=\"PQ correct_answer\"  id=\"PQ-3-4\">\\(\\dfrac{27}{28}\\)<\/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>According to the Order of Operations (PEMDAS), multiplication and division can happen at the same time.<\/p>\n<p>For this example, let\u2019s work through the multiplication and division in order from left to right. Start by multiplying \\(\\frac{1}{4}\\) and \\(\\frac{6}{7}\\), simplifying if necessary.<\/p>\n<p style=\"text-align: center\">\\(\\dfrac{1}{4}\\times\\dfrac{6}{7}=\\dfrac{1\u00d76}{4\u00d77}=\\dfrac{6}{28}=\\dfrac{3}{14}\\)<\/p>\n<p>Then, divide \\(\\frac{3}{14}\\) by \\(\\frac{2}{9}\\).<\/p>\n<p style=\"text-align: center\">\\(\\dfrac{3}{14}\\div\\dfrac{2}{9}=\\dfrac{3}{14}\\times\\dfrac{9}{2}=\\dfrac{27}{28}\\)<\/p>\n<p>Therefore, \\(\\frac{1}{4}\\times\\frac{6}{7}\\div\\frac{2}{9}=\\frac{27}{28}\\).<\/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 \/>\nSarah Anne is baking cookies and the recipe calls for \\(\\frac{2}{3}\\) cups of butter. She needs a lot of cookies, so she decides to quadruple the recipe. Quickly realizing that\u2019s a lot of cookies, she decides to back off a bit and only make the recipe \\(3\\frac{1}{2}\\) times the original. In order to do this, how many cups of butter will Sarah Anne need?<\/p>\n<\/div>\n\t\t\t\t\t<div class=\"PQ-Choices\"><div class=\"PQ correct_answer\"  id=\"PQ-4-1\">\\(2\\frac{1}{3}\\) cups<\/div><div class=\"PQ\"  id=\"PQ-4-2\">\\(\\frac{4}{21}\\) cups<\/div><div class=\"PQ\"  id=\"PQ-4-3\">\\(1\\frac{2}{3}\\) cups<\/div><div class=\"PQ\"  id=\"PQ-4-4\">\\(\\frac{1}{7}\\) cups<\/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>The first thing that needs to happen in order to solve this problem is \\(3\\frac{1}{2}\\) needs to be converted to an improper fraction.<\/p>\n<p style=\"text-align: center\">\\(3\\frac{1}{2}=\\dfrac{3\u00d72+1}{2}=\\dfrac{7}{2}\\)<\/p>\n<p>Then, multiply the two fractions and simplify.<\/p>\n<p style=\"text-align: center\">\\(\\dfrac{2}{3}\\times\\dfrac{7}{2}=\\dfrac{14}{6}=\\dfrac{7}{3}\\)<\/p>\n<p>Finally, convert \\(\\frac{7}{3}\\) to a mixed number.<\/p>\n<p style=\"text-align: center\">\\(\\dfrac{7}{3}=2\\frac{1}{3}\\)<\/p>\n<p>Sarah Anne needs \\(2\\frac{1}{3}\\) cups of butter.<\/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 \/>\nAntonio has \\(\\frac{6}{8}\\) of a pizza left over and two hungry friends. If Antonio and his friends evenly split the pizza, what fraction of the pizza does each person get?<\/p>\n<\/div>\n\t\t\t\t\t<div class=\"PQ-Choices\"><div class=\"PQ\"  id=\"PQ-5-1\">\\(\\frac{1}{3}\\)<\/div><div class=\"PQ\"  id=\"PQ-5-2\">\\(\\frac{3}{4}\\)<\/div><div class=\"PQ correct_answer\"  id=\"PQ-5-3\">\\(\\frac{1}{4}\\)<\/div><div class=\"PQ\"  id=\"PQ-5-4\">\\(\\frac{2}{3}\\)<\/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>This question is asking us to divide \\(\\frac{6}{8}\\) by 3. Remember, any whole number can be turned into a fraction by placing it over 1. <\/p>\n<p>Here\u2019s what the division looks like:<\/p>\n<p style=\"text-align: center\">\\(\\dfrac{6}{8}\\div\\dfrac{3}{1}=\\dfrac{6}{8}\\times\\dfrac{1}{3}=\\dfrac{6}{24}=\\dfrac{1}{4}\\)<\/p>\n<p>Each person gets \\(\\frac{1}{4}\\) of the pizza.<\/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 class=\"spoiler\" id=\"worksheets-spoiler\">\n<h2 style=\"text-align:center;\"><span id=\"Multiplying_and_Dividing_Fraction_Worksheets\" class=\"m-toc-anchor\"><\/span>Multiplying and Dividing Fraction Worksheets<\/h2>\n<div style=\"display: flex;flex-flow: row wrap;justify-content: center;\">\n<p style=\"width:100%;\">Use our free printable multiplying and dividing fractions worksheets for additional practice!<\/p>\n<div style=\"text-align:center;max-width:300px;margin:15px;\">\n\t\t\t\t\t\t<strong>Multiplying and Dividing Fractions Worksheets<\/strong><br \/>\n\t\t\t\t\t\t<a href=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2025\/12\/Multiplying-and-Dividing-Fractions-Worksheets.pdf\"><br \/>\n\t\t\t\t\t\t\t<img decoding=\"async\" src=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2025\/12\/Multiplying-and-Dividing-Fractions-Worksheets-scaled.webp\" alt=\"Multiplying and Dividing Fractions Worksheets Worksheet Preview\" style=\"box-shadow: 1.5px 1.5px 5px grey;\"><br \/>\n\t\t\t\t\t\t\t<button class=\"buttonmltpctn\" style=\"width: 90%;color: black;font-size: 0.9em;\" data-uw-styling-context=\"true\">CLICK HERE TO DOWNLOAD<\/button><br \/>\n\t\t\t\t\t\t<\/a>\n\t\t\t\t\t<\/div>\n<div style=\"text-align:center;max-width:300px;margin:15px;\">\n\t\t\t\t\t\t<strong>Multiplying and Dividing Fractions (Answer Key)<\/strong><br \/>\n\t\t\t\t\t\t<a href=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2025\/12\/Multiplying-and-Dividing-Fractions-Worksheets-Answer-Keys.pdf\"><br \/>\n\t\t\t\t\t\t\t<img decoding=\"async\" src=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2025\/12\/Multiplying-and-Dividing-Fractions-Worksheets-Answer-Keys-scaled.webp\" alt=\"Multiplying and Dividing Fractions (Answer Key) Worksheet Preview\" style=\"box-shadow: 1.5px 1.5px 5px grey;\"><br \/>\n\t\t\t\t\t\t\t<button class=\"buttonmltpctn\" style=\"width: 90%;color: black;font-size: 0.9em;\" data-uw-styling-context=\"true\">CLICK HERE TO DOWNLOAD<\/button><br \/>\n\t\t\t\t\t\t<\/a>\n\t\t\t\t\t<\/div>\n<div style=\"text-align:center;max-width:300px;margin:15px;\">\n\t\t\t\t\t\t<strong>Multiplying Fractions Worksheets<\/strong><br \/>\n\t\t\t\t\t\t<a href=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2025\/12\/Multiplying-Fractions-Worksheet.pdf\"><br \/>\n\t\t\t\t\t\t\t<img decoding=\"async\" src=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2025\/12\/Multiplying-Fractions-Worksheet-scaled.webp\" alt=\"Multiplying Fractions Worksheets Worksheet Preview\" style=\"box-shadow: 1.5px 1.5px 5px grey;\"><br \/>\n\t\t\t\t\t\t\t<button class=\"buttonmltpctn\" style=\"width: 90%;color: black;font-size: 0.9em;\" data-uw-styling-context=\"true\">CLICK HERE TO DOWNLOAD<\/button><br \/>\n\t\t\t\t\t\t<\/a>\n\t\t\t\t\t<\/div>\n<div style=\"text-align:center;max-width:300px;margin:15px;\">\n\t\t\t\t\t\t<strong>Multiplying Fractions (Answer Key)<\/strong><br \/>\n\t\t\t\t\t\t<a href=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2025\/12\/Multiplying-Fractions-Worksheet-Answer-Key.pdf\"><br \/>\n\t\t\t\t\t\t\t<img decoding=\"async\" src=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2025\/12\/Multiplying-Fractions-Worksheet-Answer-Key-scaled.webp\" alt=\"Multiplying Fractions (Answer Key) Worksheet Preview\" style=\"box-shadow: 1.5px 1.5px 5px grey;\"><br \/>\n\t\t\t\t\t\t\t<button class=\"buttonmltpctn\" style=\"width: 90%;color: black;font-size: 0.9em;\" data-uw-styling-context=\"true\">CLICK HERE TO DOWNLOAD<\/button><br \/>\n\t\t\t\t\t\t<\/a>\n\t\t\t\t\t<\/div>\n<div style=\"text-align:center;max-width:300px;margin:15px;\">\n\t\t\t\t\t\t<strong>Dividing Fractions Worksheets<\/strong><br \/>\n\t\t\t\t\t\t<a href=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2025\/12\/Dividing-Fractions-Worksheet.pdf\"><br \/>\n\t\t\t\t\t\t\t<img decoding=\"async\" src=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2025\/12\/Dividing-Fractions-Worksheet-scaled.webp\" alt=\"Dividing Fractions Worksheets Worksheet Preview\" style=\"box-shadow: 1.5px 1.5px 5px grey;\"><br \/>\n\t\t\t\t\t\t\t<button class=\"buttonmltpctn\" style=\"width: 90%;color: black;font-size: 0.9em;\" data-uw-styling-context=\"true\">CLICK HERE TO DOWNLOAD<\/button><br \/>\n\t\t\t\t\t\t<\/a>\n\t\t\t\t\t<\/div>\n<div style=\"text-align:center;max-width:300px;margin:15px;\">\n\t\t\t\t\t\t<strong>Dividing Fractions (Answer Key)<\/strong><br \/>\n\t\t\t\t\t\t<a href=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2025\/12\/Dividing-Fractions-Worksheet-Answer-Key.pdf\"><br \/>\n\t\t\t\t\t\t\t<img decoding=\"async\" src=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2025\/12\/Dividing-Fractions-Worksheet-Answer-Key-scaled.webp\" alt=\"Dividing Fractions (Answer Key) Worksheet Preview\" style=\"box-shadow: 1.5px 1.5px 5px grey;\"><br \/>\n\t\t\t\t\t\t\t<button class=\"buttonmltpctn\" style=\"width: 90%;color: black;font-size: 0.9em;\" data-uw-styling-context=\"true\">CLICK HERE TO DOWNLOAD<\/button><br \/>\n\t\t\t\t\t\t<\/a>\n\t\t\t\t\t<\/div>\n<\/p><\/div>\n<\/p><\/div>\n<\/div>\n\n<div class=\"home-buttons\">\n<p><a href=\"https:\/\/www.mometrix.com\/academy\/complex-arithmetic\/\">Return to Complex Arithmetic Videos<\/a><\/p>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>Return to Complex Arithmetic 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