{"id":8252,"date":"2023-08-10T14:16:10","date_gmt":"2023-08-10T08:46:10","guid":{"rendered":"https:\/\/physicscatalyst.com\/article\/?p=8252"},"modified":"2023-08-07T18:57:43","modified_gmt":"2023-08-07T13:27:43","slug":"multiplying-fractions-with-different-denominators","status":"publish","type":"post","link":"https:\/\/physicscatalyst.com\/article\/multiplying-fractions-with-different-denominators\/","title":{"rendered":"Multiplying Fractions with Different Denominators"},"content":{"rendered":"<p><strong>Multiplying fractions with different denominators<\/strong> is the focus of this article. The method includes understanding fractions, finding the least common multiple (LCM), and step-by-step multiplication, providing a solid foundation for advanced mathematical concepts.<\/p>\n<p>If you are looking to calculate the LCM of specific numbers, you may utilize the <a title=\"lcm calculator\" href=\"https:\/\/physicscatalyst.com\/calculators\/maths\/lcm-calculator.php\" target=\"_new\" rel=\"noopener\">LCM Calculator<\/a>. This tool can effortlessly determine the LCM of two or more numbers, providing a quick and accurate result. Similarly, if you need to find the Greatest Common Divisor (GCD) of numbers, you can make use of the <a title=\"gcd calculator\" href=\"https:\/\/physicscatalyst.com\/calculators\/maths\/gcf-calculator.php\" target=\"_new\" rel=\"noopener\">GCD Calculator<\/a>.<\/p>\n<h2>Multiplying Fractions with Different Denominators<\/h2>\n<blockquote><p>Multiplying fractions with different denominators involves finding the LCM, converting to equivalent fractions, multiplying, and simplifying the result.<\/p><\/blockquote>\n<p>Let us first start by defining fractions and what are fractions with, unlike denominators and fractions with common denominators.<\/p>\n<p><strong>Definition of Fractions<\/strong><\/p>\n<p>A fraction is a mathematical expression that represents the division of one integer by another integer. A fraction is written in the form of \\(\\frac{a}{b}\\), where:<\/p>\n<ul>\n<li>\\(a\\) is the numerator (the top part of the fraction),<\/li>\n<li>\\(b\\) is the denominator (the bottom part of the fraction), and<\/li>\n<li>\\(b \\neq 0\\).<\/li>\n<\/ul>\n<p>So we now know <a href=\"https:\/\/physicscatalyst.com\/class-6\/fractions.php\">what are fractions<\/a>. Now, let us proceed to establish the definitions of fractions with dissimilar denominators and fractions with identical denominators.<\/p>\n<ol>\n<li><strong>Unlike Denominators<\/strong>: Unlike denominators refer to fractions where the denominators are not the same.<br \/>\n<strong>Example:-\u00a0<\/strong>Consider the fractions \\(\\frac{2}{3}\\) and \\(\\frac{5}{4}\\). Here, the denominators are 3 and 4, respectively. Since these numbers are not the same, we say that these fractions have unlike denominators. (learn more in the article <a href=\"https:\/\/physicscatalyst.com\/article\/fractions-with-different-denominators\/\">Fractions with different denominators<\/a>)<\/li>\n<li><strong>Common Denominator<\/strong>: Common denominators refer to fractions having the same number in the denominator, allowing for straightforward mathematical operations.<br \/>\n<strong>Example:-<\/strong> Consider the fractions \\(\\frac{3}{8}\\) and \\(\\frac{5}{8}\\) have a common denominator of 8, making them easily comparable or combinable.<\/li>\n<\/ol>\n<h3>Steps for Multiplying Fractions with Different Denominators<\/h3>\n<p>Given below are the steps for multiplying fractions with different (unlike) denominators<\/p>\n<ol>\n<li><strong>Find the Least Common Multiple (LCM):<\/strong> Determine the smallest number that is a multiple of both denominators.<\/li>\n<li><strong>Convert to Equivalent Fractions:<\/strong> Change the fractions to equivalent fractions with the common denominator (LCM).<\/li>\n<li><strong>Multiply the Fractions:<\/strong> Multiply the numerators together and the denominators together.<\/li>\n<li><strong>Simplify the Result:<\/strong> Reduce the resulting fraction to its simplest form by dividing both the numerator and denominator by their greatest common divisor (GCD).<\/li>\n<\/ol>\n<p>Let us now look at how to follow these steps for multiplying fractions with unlike denominators<\/p>\n<h4>Step 1: Find the Least Common Multiple (LCM)<\/h4>\n<p>The first step is to find the least common multiple of the denominators. The LCM is the smallest number that is a multiple of both denominators.<\/p>\n<p>For example, if you have two fractions \\(\\frac{1}{3}\\) and \\(\\frac{2}{5}\\), the LCM of 3 and 5 is 15.<\/p>\n<h4>Step 2: Convert to Equivalent Fractions<\/h4>\n<p>Next, you need to convert the fractions to equivalent fractions with the common denominator (LCM).<\/p>\n<p>For \\(\\frac{1}{3}\\), multiply both the numerator and denominator by 5 to get \\(\\frac{5}{15}\\).<br \/>\nFor \\(\\frac{2}{5}\\), multiply both the numerator and denominator by 3 to get \\(\\frac{6}{15}\\).<\/p>\n<h4>Step 3: Multiply the Fractions<\/h4>\n<p>Now, multiply the numerators together and the denominators together:<\/p>\n<p>\\(\\frac{5}{15} \\times \\frac{6}{15} = \\frac{5 \\times 6}{15 \\times 15} = \\frac{30}{225}\\)<\/p>\n<h4>Step 4: Simplify the Result<\/h4>\n<p>Finally, simplify the fraction by dividing both the numerator and denominator by their greatest common divisor (GCD):<\/p>\n<p>\\(\\frac{30}{225} = \\frac{2}{15}\\)<\/p>\n<h3>Solved Examples for multiplying fractions with unlike denominators<\/h3>\n<p>Given below are two more examples illustrating the process of multiplying fractions with different denominators:<\/p>\n<h4>Example 1<\/h4>\n<p>Multiply \\(\\frac{2}{3}\\) and \\(\\frac{4}{5}\\):<\/p>\n<p>1. Find the LCM: LCM of 3 and 5 is 15.<br \/>\n2. Convert to Equivalent Fractions: \\(\\frac{2}{3} = \\frac{10}{15}\\) and \\(\\frac{4}{5} = \\frac{12}{15}\\).<br \/>\n3. Multiply the Fractions: \\(\\frac{10}{15} \\times \\frac{12}{15} = \\frac{120}{225}\\).<br \/>\n4. Simplify the Result: \\(\\frac{120}{225} = \\frac{8}{15}\\).<\/p>\n<h4>Example 2<\/h4>\n<p>Multiply \\(\\frac{3}{4}\\) and \\(\\frac{7}{6}\\):<\/p>\n<p>1. Find the LCM: LCM of 4 and 6 is 12.<br \/>\n2. Convert to Equivalent Fractions: \\(\\frac{3}{4} = \\frac{9}{12}\\) and \\(\\frac{7}{6} = \\frac{14}{12}\\).<br \/>\n3. Multiply the Fractions: \\(\\frac{9}{12} \\times \\frac{14}{12} = \\frac{126}{144}\\).<br \/>\n4. Simplify the Result: \\(\\frac{126}{144} = \\frac{7}{8}\\).<\/p>\n<p>These examples demonstrate the systematic approach to multiplying fractions with different denominators, following the steps of finding the LCM, converting to equivalent fractions, performing the multiplication, and simplifying the result.<\/p>\n<h3>Questions<\/h3>\n<p>1. Multiply the fractions \\(\\frac{2}{3}\\) and \\(\\frac{3}{5}\\). What is the result?<br \/>\n2. How do you find the LCM of two numbers? Explain with an example.<br \/>\n3. Why is it necessary to find a common denominator when multiplying fractions with different denominators?<\/p>\n<details>\n<summary><strong>Answer<\/strong><\/summary>\n<p>1. \\(\\frac{2}{3} \\times \\frac{3}{5} = \\frac{6}{15} = \\frac{2}{5}\\)<br \/>\n2. The LCM of two numbers is found by dividing the product of the numbers by their GCD. For example, for 8 and 12, \\(\\text{LCM}(8, 12) = \\frac{8 \\times 12}{\\text{GCD}(8, 12)} = 24\\).<br \/>\n3. Finding a common denominator ensures that the fractions represent the same &#8220;whole&#8221; and hence can be multiplied together accurately.<\/p>\n<\/details>\n","protected":false},"excerpt":{"rendered":"<p>Multiplying fractions with different denominators is the focus of this article. The method includes understanding fractions, finding the least common multiple (LCM), and step-by-step multiplication, providing a solid foundation for advanced mathematical concepts. If you are looking to calculate the LCM of specific numbers, you may utilize the LCM Calculator. This tool can effortlessly determine [&hellip;]<\/p>\n","protected":false},"author":8,"featured_media":0,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_uag_custom_page_level_css":"","site-sidebar-layout":"default","site-content-layout":"default","ast-site-content-layout":"default","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","theme-transparent-header-meta":"default","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"default","ast-page-background-enabled":"default","ast-page-background-meta":{"desktop":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"ast-content-background-meta":{"desktop":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"footnotes":""},"categories":[498],"tags":[],"class_list":["post-8252","post","type-post","status-publish","format-standard","hentry","category-maths"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v27.3 - https:\/\/yoast.com\/product\/yoast-seo-wordpress\/ -->\n<title>Multiplying Fractions with Different Denominators - physicscatalyst&#039;s Blog<\/title>\n<meta name=\"description\" content=\"Multiplying fractions with different denominators: Find LCM, convert, multiply, simplify. 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The method includes understanding fractions, finding the least common multiple (LCM), and step-by-step multiplication, providing a solid foundation for advanced mathematical concepts. If you are looking to calculate the LCM of specific numbers, you may utilize the LCM Calculator. 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