{"id":232269,"date":"2025-06-11T22:15:28","date_gmt":"2025-06-11T22:15:28","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=232269"},"modified":"2025-06-11T22:15:30","modified_gmt":"2025-06-11T22:15:30","slug":"which-of-the-following-pairs-consists-of-equivalent-fractions","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/06\/11\/which-of-the-following-pairs-consists-of-equivalent-fractions\/","title":{"rendered":"Which of the following pairs consists of equivalent fractions"},"content":{"rendered":"\n
Which of the following pairs consists of equivalent fractions? 9\/12 and 2\/3 4\/10 and 10\/4 9\/24 and 21\/56 3\/4 and 4\/5<\/pre>\n\n\n\n
The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n
Correct Answer: 9\/12 and 2\/3<\/strong><\/p>\n\n\n\n
Explanation:<\/h3>\n\n\n\n
Fractions are considered equivalent<\/strong> when they represent the same value or proportion<\/strong>, even if they have different numerators and denominators. To determine if two fractions are equivalent, one can either:<\/p>\n\n\n\n
    \n
  1. Simplify both fractions<\/strong> to their lowest terms and compare them.<\/li>\n\n\n\n
  2. Cross-multiply<\/strong> and check if the products are equal.<\/li>\n<\/ol>\n\n\n\n
    Let\u2019s apply these methods to each pair:<\/p>\n\n\n\n
    \n\n\n\n
    1. 9\/12 and 2\/3<\/strong><\/p>\n\n\n\n
    Simplify 9\/12:<\/p>\n\n\n\n
      \n
    • GCD of 9 and 12 is 3.<\/li>\n\n\n\n
    • 912=9\u00f7312\u00f73=34\\frac{9}{12} = \\frac{9 \u00f7 3}{12 \u00f7 3} = \\frac{3}{4}129\u200b=12\u00f739\u00f73\u200b=43\u200b<\/li>\n<\/ul>\n\n\n\n
      Oops! This was an error. Let’s double-check.<\/p>\n\n\n\n
      Actually, the GCD of 9 and 12 is 3<\/strong>, and:<\/p>\n\n\n\n
        \n
      • 912=34\\frac{9}{12} = \\frac{3}{4}129\u200b=43\u200b<\/li>\n<\/ul>\n\n\n\n
        So 9\/12 is not<\/strong> equal to 2\/3.<\/p>\n\n\n\n
        Wait! That contradicts the earlier statement. Let’s fix this step-by-step.<\/p>\n\n\n\n
        Correct Simplification:<\/h3>\n\n\n\n
          \n
        • 912=34\\frac{9}{12} = \\frac{3}{4}129\u200b=43\u200b<\/li>\n\n\n\n
        • 23\\frac{2}{3}32\u200b is already simplified.<\/li>\n<\/ul>\n\n\n\n
          Clearly, 3\/4 \u2260 2\/3<\/strong>, so they are not equivalent<\/strong>.<\/p>\n\n\n\n
          Let’s check the other pairs.<\/p>\n\n\n\n
          \n\n\n\n
          2. 4\/10 and 10\/4<\/strong><\/p>\n\n\n\n
            \n
          • 4\/10 = 0.4<\/li>\n\n\n\n
          • 10\/4 = 2.5<\/li>\n<\/ul>\n\n\n\n
            Not equal \u21d2 Not equivalent<\/p>\n\n\n\n
            \n\n\n\n
            3. 9\/24 and 21\/56<\/strong><\/p>\n\n\n\n
            Simplify 9\/24:<\/p>\n\n\n\n
              \n
            • GCD is 3 \u21d2 924=38\\frac{9}{24} = \\frac{3}{8}249\u200b=83\u200b<\/li>\n<\/ul>\n\n\n\n
              Simplify 21\/56:<\/p>\n\n\n\n
                \n
              • GCD is 7 \u21d2 2156=38\\frac{21}{56} = \\frac{3}{8}5621\u200b=83\u200b<\/li>\n<\/ul>\n\n\n\n
                So, they are equivalent!<\/strong><\/p>\n\n\n\n
                \u2705 Correct Answer: 9\/24 and 21\/56<\/strong><\/p>\n\n\n\n
                \n\n\n\n
                4. 3\/4 and 4\/5<\/strong><\/p>\n\n\n\n
                  \n
                • 3\/4 = 0.75<\/li>\n\n\n\n
                • 4\/5 = 0.8<\/li>\n<\/ul>\n\n\n\n
                  Not equal \u21d2 Not equivalent<\/p>\n\n\n\n
                  \n\n\n\n
                  Final Answer: \u2705 9\/24 and 21\/56<\/strong><\/h3>\n\n\n\n
                  Book-style Explanation<\/h3>\n\n\n\n
                  To determine whether two fractions are equivalent, we compare their values by simplifying them to their lowest terms. Two fractions are said to be equivalent if they reduce to the same simplest form or if the cross-products of the numerators and denominators are equal.<\/p>\n\n\n\n
                  Let\u2019s consider the pair 9\/24 and 21\/56<\/strong>. First, simplify both fractions:<\/p>\n\n\n\n
                  Start with 9\/24:<\/p>\n\n\n\n
                    \n
                  • Find the greatest common divisor (GCD) of 9 and 24, which is 3.<\/li>\n\n\n\n
                  • Divide numerator and denominator by 3:
                    9\u00f7324\u00f73=38\\frac{9 \u00f7 3}{24 \u00f7 3} = \\frac{3}{8}24\u00f739\u00f73\u200b=83\u200b<\/li>\n<\/ul>\n\n\n\n
                    Now simplify 21\/56:<\/p>\n\n\n\n
                      \n
                    • The GCD of 21 and 56 is 7.<\/li>\n\n\n\n
                    • Divide numerator and denominator by 7:
                      21\u00f7756\u00f77=38\\frac{21 \u00f7 7}{56 \u00f7 7} = \\frac{3}{8}56\u00f7721\u00f77\u200b=83\u200b<\/li>\n<\/ul>\n\n\n\n
                      Since both simplified fractions equal 3\/8, they are equivalent.<\/p>\n\n\n\n
                      Alternatively, we can cross-multiply the original fractions to check equivalence:<\/p>\n\n\n\n
                        \n
                      • 9\u00d756=5049 \u00d7 56 = 5049\u00d756=504<\/li>\n\n\n\n
                      • 24\u00d721=50424 \u00d7 21 = 50424\u00d721=504<\/li>\n<\/ul>\n\n\n\n
                        Since both cross-products are equal, this confirms that the fractions are equivalent.<\/p>\n\n\n\n
                        Understanding equivalent fractions is essential in mathematics as it helps in comparing, adding, subtracting, and solving fraction problems. Equivalent fractions represent the same part of a whole, even though they may look different. Identifying and working with them is a fundamental skill in arithmetic and algebra.<\/p>\n\n\n\n
                        Hence, among the given options, only 9\/24 and 21\/56<\/strong> are equivalent fractions.<\/p>\n\n\n\n
                        \"\"<\/figure>\n","protected":false},"excerpt":{"rendered":"
                        Which of the following pairs consists of equivalent fractions? 9\/12 and 2\/3 4\/10 and 10\/4 9\/24 and 21\/56 3\/4 and 4\/5 The Correct Answer and Explanation is: Correct Answer: 9\/12 and 2\/3 Explanation: Fractions are considered equivalent when they represent the same value or proportion, even if they have different numerators and denominators. To determine […]<\/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-232269","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/232269","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=232269"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/232269\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=232269"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=232269"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=232269"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}