{"id":242284,"date":"2025-07-04T06:55:36","date_gmt":"2025-07-04T06:55:36","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=242284"},"modified":"2025-07-04T06:55:38","modified_gmt":"2025-07-04T06:55:38","slug":"3-1-2-divided-by-2-1-4-in-simplest-form-3-1-2-divided-by-1-4","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/07\/04\/3-1-2-divided-by-2-1-4-in-simplest-form-3-1-2-divided-by-1-4\/","title":{"rendered":"3 1\/2 divided by 2 1\/4 in simplest form? 3 1\/2 divided by 1\/4"},"content":{"rendered":"\n

3 1\/2 divided by 2 1\/4 in simplest form? 3 1\/2 divided by 1\/4<\/p>\n\n\n\n

The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n

To solve the division of 3 1\/2 by 2 1\/4<\/strong>, let’s break it down step by step:<\/p>\n\n\n\n

Step 1: Convert Mixed Numbers to Improper Fractions<\/h3>\n\n\n\n

First, convert the mixed numbers into improper fractions.<\/p>\n\n\n\n

3 1\/2<\/strong> can be converted as follows:<\/p>\n\n\n\n

    \n
  • Multiply the whole number (3) by the denominator (2), which gives 6.<\/li>\n\n\n\n
  • Add the numerator (1) to 6, resulting in 7.<\/li>\n\n\n\n
  • So, 3 1\/2<\/strong> becomes 7\/2<\/strong>.<\/li>\n<\/ul>\n\n\n\n

    2 1\/4<\/strong> can be converted similarly:<\/p>\n\n\n\n

      \n
    • Multiply the whole number (2) by the denominator (4), which gives 8.<\/li>\n\n\n\n
    • Add the numerator (1) to 8, resulting in 9.<\/li>\n\n\n\n
    • So, 2 1\/4<\/strong> becomes 9\/4<\/strong>.<\/li>\n<\/ul>\n\n\n\n

      Now, we have 7\/2<\/strong> divided by 9\/4<\/strong>.<\/p>\n\n\n\n

      Step 2: Division of Fractions<\/h3>\n\n\n\n

      When dividing fractions, we multiply the first fraction by the reciprocal of the second fraction.<\/p>\n\n\n\n

      The reciprocal of 9\/4<\/strong> is 4\/9<\/strong>.<\/p>\n\n\n\n

      So, we now have:72\u00d749\\frac{7}{2} \\times \\frac{4}{9}27\u200b\u00d794\u200b<\/p>\n\n\n\n

      Step 3: Multiply the Fractions<\/h3>\n\n\n\n

      To multiply the fractions, simply multiply the numerators and the denominators:7\u00d742\u00d79=2818\\frac{7 \\times 4}{2 \\times 9} = \\frac{28}{18}2\u00d797\u00d74\u200b=1828\u200b<\/p>\n\n\n\n

      Step 4: Simplify the Fraction<\/h3>\n\n\n\n

      Now, simplify the fraction 28\/18<\/strong> by finding the greatest common divisor (GCD) of 28 and 18, which is 2.<\/p>\n\n\n\n

      Divide both the numerator and denominator by 2:28\u00f7218\u00f72=149\\frac{28 \\div 2}{18 \\div 2} = \\frac{14}{9}18\u00f7228\u00f72\u200b=914\u200b<\/p>\n\n\n\n

      So, 3 1\/2 \u00f7 2 1\/4 = 14\/9<\/strong>.<\/p>\n\n\n\n

      Step 5: Convert to Mixed Number (Optional)<\/h3>\n\n\n\n

      If you’d like to convert 14\/9<\/strong> back to a mixed number:<\/p>\n\n\n\n

        \n
      • Divide 14 by 9, which gives 1 with a remainder of 5.<\/li>\n\n\n\n
      • So, 14\/9<\/strong> is 1 5\/9<\/strong>.<\/li>\n<\/ul>\n\n\n\n

        Now, for the second part of your question:<\/h3>\n\n\n\n

        3 1\/2 divided by 1\/4<\/strong> is the same as multiplying 3 1\/2<\/strong> by the reciprocal of 1\/4<\/strong>, which is 4\/1<\/strong>.<\/p>\n\n\n\n

        Step 1: Convert 3 1\/2<\/strong> to an improper fraction:<\/p>\n\n\n\n

          \n
        • 3 1\/2 = 7\/2<\/strong>.<\/li>\n<\/ul>\n\n\n\n

          Step 2: Multiply by the reciprocal of 1\/4<\/strong>, which is 4\/1<\/strong>:72\u00d741=282\\frac{7}{2} \\times \\frac{4}{1} = \\frac{28}{2}27\u200b\u00d714\u200b=228\u200b<\/p>\n\n\n\n

          Step 3: Simplify:282=14\\frac{28}{2} = 14228\u200b=14<\/p>\n\n\n\n

          So, 3 1\/2 \u00f7 1\/4 = 14<\/strong>.<\/p>\n\n\n\n

          In summary:<\/p>\n\n\n\n

            \n
          • 3 1\/2 \u00f7 2 1\/4 = 14\/9<\/strong>, or 1 5\/9<\/strong> as a mixed number.<\/li>\n\n\n\n
          • 3 1\/2 \u00f7 1\/4 = 14<\/strong>.<\/li>\n<\/ul>\n\n\n\n
            \"\"<\/figure>\n","protected":false},"excerpt":{"rendered":"

            3 1\/2 divided by 2 1\/4 in simplest form? 3 1\/2 divided by 1\/4 The Correct Answer and Explanation is: To solve the division of 3 1\/2 by 2 1\/4, let’s break it down step by step: Step 1: Convert Mixed Numbers to Improper Fractions First, convert the mixed numbers into improper fractions. 3 1\/2 […]<\/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-242284","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/242284","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=242284"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/242284\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=242284"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=242284"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=242284"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}