{"id":154506,"date":"2024-10-14T19:02:19","date_gmt":"2024-10-14T19:02:19","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=154506"},"modified":"2024-10-14T19:02:21","modified_gmt":"2024-10-14T19:02:21","slug":"9-40-in-simplest-form","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2024\/10\/14\/9-40-in-simplest-form\/","title":{"rendered":"9\/40 in simplest form"},"content":{"rendered":"\n<p>9\/40 in simplest form?<\/p>\n\n\n\n<p><strong><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-ast-global-color-6-color\">The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n<p>To simplify the fraction ( \\frac{9}{40} ), we need to find the greatest common divisor (GCD) of the numerator (9) and the denominator (40). The GCD is the largest number that divides both numbers without leaving a remainder.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Step 1: Find the Prime Factorization<\/h3>\n\n\n\n<p><strong>Prime factorization of 9:<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>The number 9 can be expressed as ( 3 \\times 3 ) or ( 3^2 ).<\/li>\n<\/ul>\n\n\n\n<p><strong>Prime factorization of 40:<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>The number 40 can be expressed as ( 2 \\times 20 ).<\/li>\n\n\n\n<li>Further breaking it down, ( 20 = 2 \\times 10 ), and ( 10 = 2 \\times 5 ).<\/li>\n\n\n\n<li>Thus, the complete prime factorization of 40 is ( 2^3 \\times 5 ).<\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading\">Step 2: Determine the GCD<\/h3>\n\n\n\n<p>Now, we can identify the common prime factors between 9 and 40.<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>The prime factorization of 9 is ( 3^2 ).<\/li>\n\n\n\n<li>The prime factorization of 40 is ( 2^3 \\times 5 ).<\/li>\n<\/ul>\n\n\n\n<p>Since there are no common factors between 9 and 40, the GCD is 1.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Step 3: Simplify the Fraction<\/h3>\n\n\n\n<p>To simplify the fraction ( \\frac{9}{40} ), we divide both the numerator and the denominator by their GCD (which is 1):<\/p>\n\n\n\n<p>[<br>\\frac{9 \\div 1}{40 \\div 1} = \\frac{9}{40}<br>]<\/p>\n\n\n\n<p>Since the GCD is 1, the fraction ( \\frac{9}{40} ) is already in its simplest form.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Conclusion<\/h3>\n\n\n\n<p>In summary, the fraction ( \\frac{9}{40} ) cannot be simplified further since 9 and 40 share no common factors other than 1. Therefore, the final simplified form of ( \\frac{9}{40} ) remains ( \\frac{9}{40} ). This process demonstrates the importance of finding the GCD when simplifying fractions, as it ensures that the fraction is expressed in the lowest terms possible.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>9\/40 in simplest form? The Correct Answer and Explanation is: To simplify the fraction ( \\frac{9}{40} ), we need to find the greatest common divisor (GCD) of the numerator (9) and the denominator (40). The GCD is the largest number that divides both numbers without leaving a remainder. Step 1: Find the Prime Factorization Prime [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"","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":"","ast-disable-related-posts":"","theme-transparent-header-meta":"","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":[25],"tags":[],"class_list":["post-154506","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/154506","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/comments?post=154506"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/154506\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=154506"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=154506"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=154506"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}