{"id":8270,"date":"2023-08-11T12:35:18","date_gmt":"2023-08-11T07:05:18","guid":{"rendered":"https:\/\/physicscatalyst.com\/article\/?p=8270"},"modified":"2023-08-08T19:36:41","modified_gmt":"2023-08-08T14:06:41","slug":"subtracting-fractions-with-unlike-denominators","status":"publish","type":"post","link":"https:\/\/physicscatalyst.com\/article\/subtracting-fractions-with-unlike-denominators\/","title":{"rendered":"Subtracting fractions with unlike denominators"},"content":{"rendered":"<p>In this article, we will learn about subtracting fractions with unlike denominators. If you do not know what are fractions with unlike denominators consider reading this article<\/p>\n<ul>\n<li><a href=\"https:\/\/physicscatalyst.com\/article\/fractions-with-different-denominators\/\">Fractions with different denominators<\/a><\/li>\n<\/ul>\n<h2>Subtracting fractions with unlike denominators<\/h2>\n<h3>Definitions and Concepts<\/h3>\n<h4>Fraction<\/h4>\n<ul>\n<li>A fraction represents a part of a whole and consists of a numerator and a denominator. For example, \\(\\frac{a}{b}\\), where \\(a\\) is the numerator and \\(b\\) is the denominator.<\/li>\n<\/ul>\n<h4>Unlike Denominators<\/h4>\n<ul>\n<li>Two fractions have unlike denominators if the denominators are not the same.<\/li>\n<\/ul>\n<h3>Subtracting Fractions with Unlike Denominators<\/h3>\n<h4>Step 1: Finding the Least Common Multiple (LCM)<\/h4>\n<p>To subtract fractions with unlike denominators, find the least common multiple of the denominators.<\/p>\n<h5>Example:<\/h5>\n<p>LCM of 4 and 6:<\/p>\n<p>\\[<br \/>\n\\text{LCM}(4, 6) = 12<br \/>\n\\]<\/p>\n<h4>Step 2: Rewriting the Fractions with the Common Denominator<\/h4>\n<p>Next, rewrite both fractions using the LCM as the common denominator.<\/p>\n<h5>Example:<\/h5>\n<p>Rewrite \\(\\frac{3}{4}\\) and \\(\\frac{5}{6}\\) with 12 as the common denominator.<\/p>\n<p>\\[<br \/>\n\\frac{3}{4} = \\frac{3 \\times 3}{4 \\times 3} = \\frac{9}{12}<br \/>\n\\]<br \/>\n\\[<br \/>\n\\frac{5}{6} = \\frac{5 \\times 2}{6 \\times 2} = \\frac{10}{12}<br \/>\n\\]<\/p>\n<h4>Step 3: Subtracting the Fractions<\/h4>\n<p>Subtract the numerators and place the result over the common denominator.<\/p>\n<p>\\[<br \/>\n\\frac{9}{12} &#8211; \\frac{10}{12} = \\frac{9 &#8211; 10}{12} = \\frac{-1}{12}<br \/>\n\\]<\/p>\n<p><a href=\"https:\/\/physicscatalyst.com\/article\/wp-content\/uploads\/2023\/08\/subtracting-fraction-with-unlike-denominators.png\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-large wp-image-8271\" src=\"https:\/\/physicscatalyst.com\/article\/wp-content\/uploads\/2023\/08\/subtracting-fraction-with-unlike-denominators-1024x702.png\" alt=\"subtracting fractions with unlike denominators\" width=\"1024\" height=\"702\" srcset=\"https:\/\/physicscatalyst.com\/article\/wp-content\/uploads\/2023\/08\/subtracting-fraction-with-unlike-denominators-1024x702.png 1024w, https:\/\/physicscatalyst.com\/article\/wp-content\/uploads\/2023\/08\/subtracting-fraction-with-unlike-denominators-300x206.png 300w, https:\/\/physicscatalyst.com\/article\/wp-content\/uploads\/2023\/08\/subtracting-fraction-with-unlike-denominators-768x527.png 768w, https:\/\/physicscatalyst.com\/article\/wp-content\/uploads\/2023\/08\/subtracting-fraction-with-unlike-denominators.png 1047w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/a><\/p>\n<h2>Solved Examples<\/h2>\n<p>let us have a look at two examples of subtracting fractions with unlike denominators.<\/p>\n<h3>Example 1: Subtracting \\(\\frac{2}{7}\\) from \\(\\frac{3}{5}\\)<\/h3>\n<h4>Step 1: Finding the Least Common Multiple (LCM)<br \/>\nFind the LCM of 7 and 5:<\/h4>\n<p>\\[<br \/>\n\\text{LCM}(7, 5) = 35<br \/>\n\\]<\/p>\n<h4>Step 2: Rewriting the Fractions with the Common Denominator<\/h4>\n<p>\\[<br \/>\n\\frac{2}{7} = \\frac{2 \\times 5}{7 \\times 5} = \\frac{10}{35}<br \/>\n\\]<br \/>\n\\[<br \/>\n\\frac{3}{5} = \\frac{3 \\times 7}{5 \\times 7} = \\frac{21}{35}<br \/>\n\\]<\/p>\n<h4>Step 3: Subtracting the Fractions<\/h4>\n<p>\\[<br \/>\n\\frac{3}{5} &#8211; \\frac{2}{7} = \\frac{21}{35} &#8211; \\frac{10}{35} = \\frac{11}{35}<br \/>\n\\]<\/p>\n<hr \/>\n<h3>Example 2: Subtracting \\(\\frac{7}{8}\\) from \\(\\frac{3}{5}\\)<\/h3>\n<h4>Step 1: Finding the Least Common Multiple (LCM)<\/h4>\n<p>\\[<br \/>\n\\text{LCM}(8, 5) = 40<br \/>\n\\]<\/p>\n<h4>Step 2: Rewriting the Fractions with the Common Denominator<\/h4>\n<p>\\[<br \/>\n\\frac{7}{8} = \\frac{35}{40}<br \/>\n\\]<br \/>\n\\[<br \/>\n\\frac{3}{5} = \\frac{24}{40}<br \/>\n\\]<\/p>\n<h4>Step 3: Subtracting the Fractions<\/h4>\n<p>\\[<br \/>\n\\frac{3}{5} &#8211; \\frac{7}{8} = \\frac{-11}{40}<br \/>\n\\]<\/p>\n<hr \/>\n<p>These two examples shows the methodical approach of subtracting fractions with unlike denominators. By finding the LCM, rewriting the fractions, and performing the subtraction, we can obtain the desired results.<\/p>\n<h3>Questions and Answers<\/h3>\n<p>1. Subtract \\(\\frac{2}{3}\\) from \\(\\frac{5}{6}\\):<br \/>\n\\[<br \/>\n\\frac{5}{6} &#8211; \\frac{2}{3} = \\frac{5}{6} &#8211; \\frac{4}{6} = \\frac{1}{6}<br \/>\n\\]<\/p>\n<p>2. What if the fractions are mixed numbers?<br \/>\nConvert them into improper fractions and then follow the steps above.<\/p>\n<hr \/>\n<h3>Further Reading<\/h3>\n<p>If you are interested in building a strong foundation in mathematics, particularly focusing on basics suitable for younger grades, we invite you to explore our resources tailored for students. Visit <a href=\"https:\/\/physicscatalyst.com\/class6-maths.php\" target=\"_new\" rel=\"noopener\">Class 6 Maths<\/a> for fundamental concepts, and <a href=\"https:\/\/physicscatalyst.com\/class-7-math.php\" target=\"_new\" rel=\"noopener\">Class 7 Math<\/a>\u00a0to continue your learning journey.<\/p>\n<p>&nbsp;<\/p>\n","protected":false},"excerpt":{"rendered":"<p>In this article, we will learn about subtracting fractions with unlike denominators. If you do not know what are fractions with unlike denominators consider reading this article Fractions with different denominators Subtracting fractions with unlike denominators Definitions and Concepts Fraction A fraction represents a part of a whole and consists of a numerator and a [&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-8270","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>Subtracting fractions with unlike denominators - physicscatalyst&#039;s Blog<\/title>\n<meta name=\"description\" content=\"Subtracting Fractions with Unlike Denominators: Learn through examples and follow simple steps to master this essential mathematical concept.\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/physicscatalyst.com\/article\/subtracting-fractions-with-unlike-denominators\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Subtracting fractions with unlike denominators - physicscatalyst&#039;s Blog\" \/>\n<meta property=\"og:description\" content=\"Subtracting Fractions with Unlike Denominators: Learn through examples and follow simple steps to master this essential mathematical concept.\" \/>\n<meta property=\"og:url\" content=\"https:\/\/physicscatalyst.com\/article\/subtracting-fractions-with-unlike-denominators\/\" \/>\n<meta property=\"og:site_name\" content=\"physicscatalyst&#039;s Blog\" \/>\n<meta property=\"article:publisher\" content=\"https:\/\/www.facebook.com\/PhysicsCatalyst\" \/>\n<meta property=\"article:author\" content=\"https:\/\/www.facebook.com\/PhysicsCatalyst\" \/>\n<meta property=\"article:published_time\" content=\"2023-08-11T07:05:18+00:00\" \/>\n<meta property=\"og:image\" content=\"https:\/\/physicscatalyst.com\/article\/wp-content\/uploads\/2023\/08\/subtracting-fraction-with-unlike-denominators-1024x702.png\" \/>\n<meta name=\"author\" content=\"physicscatalyst\" \/>\n<meta name=\"twitter:label1\" content=\"Written by\" \/>\n\t<meta name=\"twitter:data1\" content=\"physicscatalyst\" \/>\n\t<meta name=\"twitter:label2\" content=\"Est. reading time\" \/>\n\t<meta name=\"twitter:data2\" content=\"3 minutes\" \/>\n<!-- \/ Yoast SEO plugin. -->","yoast_head_json":{"title":"Subtracting fractions with unlike denominators - physicscatalyst&#039;s Blog","description":"Subtracting Fractions with Unlike Denominators: Learn through examples and follow simple steps to master this essential mathematical concept.","robots":{"index":"index","follow":"follow","max-snippet":"max-snippet:-1","max-image-preview":"max-image-preview:large","max-video-preview":"max-video-preview:-1"},"canonical":"https:\/\/physicscatalyst.com\/article\/subtracting-fractions-with-unlike-denominators\/","og_locale":"en_US","og_type":"article","og_title":"Subtracting fractions with unlike denominators - physicscatalyst&#039;s Blog","og_description":"Subtracting Fractions with Unlike Denominators: Learn through examples and follow simple steps to master this essential mathematical concept.","og_url":"https:\/\/physicscatalyst.com\/article\/subtracting-fractions-with-unlike-denominators\/","og_site_name":"physicscatalyst&#039;s Blog","article_publisher":"https:\/\/www.facebook.com\/PhysicsCatalyst","article_author":"https:\/\/www.facebook.com\/PhysicsCatalyst","article_published_time":"2023-08-11T07:05:18+00:00","og_image":[{"url":"https:\/\/physicscatalyst.com\/article\/wp-content\/uploads\/2023\/08\/subtracting-fraction-with-unlike-denominators-1024x702.png","type":"","width":"","height":""}],"author":"physicscatalyst","twitter_misc":{"Written by":"physicscatalyst","Est. reading time":"3 minutes"},"schema":{"@context":"https:\/\/schema.org","@graph":[{"@type":"Article","@id":"https:\/\/physicscatalyst.com\/article\/subtracting-fractions-with-unlike-denominators\/#article","isPartOf":{"@id":"https:\/\/physicscatalyst.com\/article\/subtracting-fractions-with-unlike-denominators\/"},"author":{"name":"physicscatalyst","@id":"https:\/\/physicscatalyst.com\/article\/#\/schema\/person\/9b302efdc9b32e459cb1e61ab7506d3f"},"headline":"Subtracting fractions with unlike denominators","datePublished":"2023-08-11T07:05:18+00:00","mainEntityOfPage":{"@id":"https:\/\/physicscatalyst.com\/article\/subtracting-fractions-with-unlike-denominators\/"},"wordCount":390,"commentCount":0,"publisher":{"@id":"https:\/\/physicscatalyst.com\/article\/#organization"},"image":{"@id":"https:\/\/physicscatalyst.com\/article\/subtracting-fractions-with-unlike-denominators\/#primaryimage"},"thumbnailUrl":"https:\/\/physicscatalyst.com\/article\/wp-content\/uploads\/2023\/08\/subtracting-fraction-with-unlike-denominators-1024x702.png","articleSection":["Maths"],"inLanguage":"en-US","potentialAction":[{"@type":"CommentAction","name":"Comment","target":["https:\/\/physicscatalyst.com\/article\/subtracting-fractions-with-unlike-denominators\/#respond"]}]},{"@type":"WebPage","@id":"https:\/\/physicscatalyst.com\/article\/subtracting-fractions-with-unlike-denominators\/","url":"https:\/\/physicscatalyst.com\/article\/subtracting-fractions-with-unlike-denominators\/","name":"Subtracting fractions with unlike denominators - physicscatalyst&#039;s Blog","isPartOf":{"@id":"https:\/\/physicscatalyst.com\/article\/#website"},"primaryImageOfPage":{"@id":"https:\/\/physicscatalyst.com\/article\/subtracting-fractions-with-unlike-denominators\/#primaryimage"},"image":{"@id":"https:\/\/physicscatalyst.com\/article\/subtracting-fractions-with-unlike-denominators\/#primaryimage"},"thumbnailUrl":"https:\/\/physicscatalyst.com\/article\/wp-content\/uploads\/2023\/08\/subtracting-fraction-with-unlike-denominators-1024x702.png","datePublished":"2023-08-11T07:05:18+00:00","description":"Subtracting Fractions with Unlike Denominators: Learn through examples and follow simple steps to master this essential mathematical concept.","breadcrumb":{"@id":"https:\/\/physicscatalyst.com\/article\/subtracting-fractions-with-unlike-denominators\/#breadcrumb"},"inLanguage":"en-US","potentialAction":[{"@type":"ReadAction","target":["https:\/\/physicscatalyst.com\/article\/subtracting-fractions-with-unlike-denominators\/"]}]},{"@type":"ImageObject","inLanguage":"en-US","@id":"https:\/\/physicscatalyst.com\/article\/subtracting-fractions-with-unlike-denominators\/#primaryimage","url":"https:\/\/physicscatalyst.com\/article\/wp-content\/uploads\/2023\/08\/subtracting-fraction-with-unlike-denominators.png","contentUrl":"https:\/\/physicscatalyst.com\/article\/wp-content\/uploads\/2023\/08\/subtracting-fraction-with-unlike-denominators.png","width":1047,"height":718,"caption":"subtracting fractions with unlike denominators"},{"@type":"BreadcrumbList","@id":"https:\/\/physicscatalyst.com\/article\/subtracting-fractions-with-unlike-denominators\/#breadcrumb","itemListElement":[{"@type":"ListItem","position":1,"name":"Home","item":"https:\/\/physicscatalyst.com\/article\/"},{"@type":"ListItem","position":2,"name":"Maths","item":"https:\/\/physicscatalyst.com\/article\/maths\/"},{"@type":"ListItem","position":3,"name":"Subtracting fractions with unlike denominators"}]},{"@type":"WebSite","@id":"https:\/\/physicscatalyst.com\/article\/#website","url":"https:\/\/physicscatalyst.com\/article\/","name":"physicscatalyst's Blog","description":"Learn free for class 9th, 10th science\/maths , 12th and IIT-JEE Physics and maths.","publisher":{"@id":"https:\/\/physicscatalyst.com\/article\/#organization"},"potentialAction":[{"@type":"SearchAction","target":{"@type":"EntryPoint","urlTemplate":"https:\/\/physicscatalyst.com\/article\/?s={search_term_string}"},"query-input":{"@type":"PropertyValueSpecification","valueRequired":true,"valueName":"search_term_string"}}],"inLanguage":"en-US"},{"@type":"Organization","@id":"https:\/\/physicscatalyst.com\/article\/#organization","name":"physicscatalyst","url":"https:\/\/physicscatalyst.com\/article\/","logo":{"@type":"ImageObject","inLanguage":"en-US","@id":"https:\/\/physicscatalyst.com\/article\/#\/schema\/logo\/image\/","url":"https:\/\/physicscatalyst.com\/article\/wp-content\/uploads\/2024\/08\/cropped-logo-1.jpg","contentUrl":"https:\/\/physicscatalyst.com\/article\/wp-content\/uploads\/2024\/08\/cropped-logo-1.jpg","width":96,"height":96,"caption":"physicscatalyst"},"image":{"@id":"https:\/\/physicscatalyst.com\/article\/#\/schema\/logo\/image\/"},"sameAs":["https:\/\/www.facebook.com\/PhysicsCatalyst","https:\/\/x.com\/physicscatalyst","https:\/\/www.youtube.com\/user\/thephysicscatalyst","https:\/\/www.instagram.com\/physicscatalyst\/"]},{"@type":"Person","@id":"https:\/\/physicscatalyst.com\/article\/#\/schema\/person\/9b302efdc9b32e459cb1e61ab7506d3f","name":"physicscatalyst","sameAs":["https:\/\/physicscatalyst.com","https:\/\/www.facebook.com\/PhysicsCatalyst","https:\/\/x.com\/physicscatalyst"]}]}},"uagb_featured_image_src":{"full":false,"thumbnail":false,"medium":false,"medium_large":false,"large":false,"1536x1536":false,"2048x2048":false,"shareaholic-thumbnail":false},"uagb_author_info":{"display_name":"physicscatalyst","author_link":"https:\/\/physicscatalyst.com\/article\/author\/physicscatalyst\/"},"uagb_comment_info":0,"uagb_excerpt":"In this article, we will learn about subtracting fractions with unlike denominators. If you do not know what are fractions with unlike denominators consider reading this article Fractions with different denominators Subtracting fractions with unlike denominators Definitions and Concepts Fraction A fraction represents a part of a whole and consists of a numerator and a&hellip;","_links":{"self":[{"href":"https:\/\/physicscatalyst.com\/article\/wp-json\/wp\/v2\/posts\/8270","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/physicscatalyst.com\/article\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/physicscatalyst.com\/article\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/physicscatalyst.com\/article\/wp-json\/wp\/v2\/users\/8"}],"replies":[{"embeddable":true,"href":"https:\/\/physicscatalyst.com\/article\/wp-json\/wp\/v2\/comments?post=8270"}],"version-history":[{"count":3,"href":"https:\/\/physicscatalyst.com\/article\/wp-json\/wp\/v2\/posts\/8270\/revisions"}],"predecessor-version":[{"id":8274,"href":"https:\/\/physicscatalyst.com\/article\/wp-json\/wp\/v2\/posts\/8270\/revisions\/8274"}],"wp:attachment":[{"href":"https:\/\/physicscatalyst.com\/article\/wp-json\/wp\/v2\/media?parent=8270"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/physicscatalyst.com\/article\/wp-json\/wp\/v2\/categories?post=8270"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/physicscatalyst.com\/article\/wp-json\/wp\/v2\/tags?post=8270"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}