{"id":151123,"date":"2024-10-09T16:58:36","date_gmt":"2024-10-09T16:58:36","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=151123"},"modified":"2024-10-09T16:58:39","modified_gmt":"2024-10-09T16:58:39","slug":"simplifying-a-fraction-write-the-fraction-12-40-in-simplest-form","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2024\/10\/09\/simplifying-a-fraction-write-the-fraction-12-40-in-simplest-form\/","title":{"rendered":"Simplifying a fraction Write the fraction (12)\/(40) in simplest form"},"content":{"rendered":"\n

Simplifying a fraction Write the fraction (12)\/(40) in simplest form.<\/p>\n\n\n\n

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

The correct answer is: (\\frac{3}{10}).<\/strong><\/mark><\/p>\n\n\n\n

To simplify the fraction (\\frac{12}{40}), we need to find the greatest common divisor (GCD) of the numerator (12) and the denominator (40). The GCD is the largest number that can evenly divide both numbers.<\/p>\n\n\n\n

Step 1: Find the GCD of 12 and 40<\/h3>\n\n\n\n

We can find the GCD using the prime factorization method or by listing the factors:<\/p>\n\n\n\n

    \n
  • Prime Factorization:<\/strong><\/li>\n\n\n\n
  • The prime factorization of 12 is (2^2 \\times 3).<\/li>\n\n\n\n
  • The prime factorization of 40 is (2^3 \\times 5).<\/li>\n<\/ul>\n\n\n\n

    From the prime factorizations, we can identify the common factors:<\/p>\n\n\n\n

      \n
    • The only prime factor common to both 12 and 40 is (2). The lowest power of (2) common to both is (2^2) (which is (4)). Thus, the GCD is (4).<\/li>\n<\/ul>\n\n\n\n

      Step 2: Divide the Numerator and Denominator by the GCD<\/h3>\n\n\n\n

      Now that we have the GCD, we divide both the numerator and the denominator by (4):<\/p>\n\n\n\n

      [
      \\frac{12 \\div 4}{40 \\div 4} = \\frac{3}{10}
      ]<\/p>\n\n\n\n

      Step 3: Write the Simplified Fraction<\/h3>\n\n\n\n

      The fraction (\\frac{12}{40}) in its simplest form is (\\frac{3}{10}).<\/p>\n\n\n\n

      Step 4: Explanation of the Process<\/h3>\n\n\n\n

      Simplifying fractions is essential in mathematics because it allows us to express numbers in their simplest and most understandable form. This is particularly useful in various applications, such as in cooking, construction, or when performing calculations in science.<\/p>\n\n\n\n

      When we simplify a fraction, we are essentially finding an equivalent fraction that has a smaller numerator and denominator but retains the same value. This makes it easier to work with and understand the relationship between the two numbers.<\/p>\n\n\n\n

      In this case, (\\frac{12}{40}) simplifies to (\\frac{3}{10}), indicating that both fractions represent the same part of a whole. The process of finding the GCD ensures that we reduce the fraction correctly without changing its value. Thus, understanding how to simplify fractions is a fundamental skill in mathematics that can enhance our problem-solving abilities.<\/p>\n","protected":false},"excerpt":{"rendered":"

      Simplifying a fraction Write the fraction (12)\/(40) in simplest form. The Correct Answer and Explanation is : The correct answer is: (\\frac{3}{10}). To simplify the fraction (\\frac{12}{40}), we need to find the greatest common divisor (GCD) of the numerator (12) and the denominator (40). The GCD is the largest number that can evenly divide both […]<\/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-151123","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/151123","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=151123"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/151123\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=151123"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=151123"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=151123"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}