{"id":222835,"date":"2025-06-01T03:32:30","date_gmt":"2025-06-01T03:32:30","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=222835"},"modified":"2025-06-01T03:32:32","modified_gmt":"2025-06-01T03:32:32","slug":"1216-and-7296-determine-if-the-ratios-are-equivalent","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/06\/01\/1216-and-7296-determine-if-the-ratios-are-equivalent\/","title":{"rendered":"12:16 and 72:96 Determine if the ratios are equivalent"},"content":{"rendered":"\n

12:16 and 72:96 Determine if the ratios are equivalent
12:16 and 72:96 Determine if the ratios are equivalent<\/p>\n\n\n\n

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

To determine if the ratios 12:16<\/strong> and 72:96<\/strong> are equivalent, we need to simplify each ratio<\/strong> and compare them.<\/p>\n\n\n\n

\n\n\n\n

\u2705 Step 1: Simplify both ratios<\/h3>\n\n\n\n

1. Simplify 12:16<\/strong><\/p>\n\n\n\n

Find the greatest common divisor (GCD) of 12 and 16:<\/p>\n\n\n\n

    \n
  • Factors of 12: 1, 2, 3, 4, 6, 12<\/strong><\/li>\n\n\n\n
  • Factors of 16: 1, 2, 4, 8, 16<\/strong><\/li>\n<\/ul>\n\n\n\n

    \u2705 GCD = 4<\/p>\n\n\n\n

    Now divide both terms by 4: 124:164=3:4\\frac{12}{4} : \\frac{16}{4} = 3:4<\/p>\n\n\n\n

    \n\n\n\n

    2. Simplify 72:96<\/strong><\/p>\n\n\n\n

    Find the GCD of 72 and 96:<\/p>\n\n\n\n

      \n
    • Factors of 72: 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72<\/strong><\/li>\n\n\n\n
    • Factors of 96: 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 96<\/strong><\/li>\n<\/ul>\n\n\n\n

      \u2705 GCD = 24<\/p>\n\n\n\n

      Now divide both terms by 24: 7224:9624=3:4\\frac{72}{24} : \\frac{96}{24} = 3:4<\/p>\n\n\n\n

      \n\n\n\n

      \u2705 Step 2: Compare simplified ratios<\/h3>\n\n\n\n
        \n
      • 12:16 simplifies to 3:4<\/strong><\/li>\n\n\n\n
      • 72:96 simplifies to 3:4<\/strong><\/li>\n<\/ul>\n\n\n\n

        Since both simplify to the same ratio (3:4)<\/strong>, the original ratios are equivalent<\/strong>.<\/p>\n\n\n\n

        \n\n\n\n

        \ud83d\udcd8 Explanation<\/h3>\n\n\n\n

        To determine if two ratios are equivalent, we compare their simplified forms. A ratio is a comparison of two quantities and can be written in various forms such as a:b or a\/b. Simplifying a ratio means reducing it to its lowest terms\u2014just like simplifying a fraction\u2014by dividing both parts by their greatest common divisor (GCD).<\/p>\n\n\n\n

        For the first ratio, 12:16, the GCD is 4. Dividing both numbers by 4, we get 3:4. This means for every 3 parts of the first quantity, there are 4 parts of the second.<\/p>\n\n\n\n

        For the second ratio, 72:96, the GCD is 24. Dividing both terms by 24 also gives 3:4. This shows that 72:96 represents the same proportional relationship as 12:16.<\/p>\n\n\n\n

        Another way to check if two ratios are equivalent is by converting them to fractions and simplifying:<\/p>\n\n\n\n

          \n
        • 12\/16 = 0.75<\/li>\n\n\n\n
        • 72\/96 = 0.75<\/li>\n<\/ul>\n\n\n\n

          Since both fractions are equal, the ratios are equivalent.<\/p>\n\n\n\n

          Understanding ratios is important in real life because they are used in scaling recipes, comparing prices, or converting measurements. Recognizing equivalent ratios helps in identifying proportional relationships between quantities.<\/p>\n\n\n\n

          In conclusion, since both 12:16 and 72:96 reduce to the same ratio (3:4), they are equivalent. This confirms that the two original ratios express the same relationship, just on different scales.<\/p>\n\n\n\n

          \"\"<\/figure>\n","protected":false},"excerpt":{"rendered":"

          12:16 and 72:96 Determine if the ratios are equivalent12:16 and 72:96 Determine if the ratios are equivalent The Correct Answer and Explanation is: To determine if the ratios 12:16 and 72:96 are equivalent, we need to simplify each ratio and compare them. \u2705 Step 1: Simplify both ratios 1. Simplify 12:16 Find the greatest common […]<\/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-222835","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/222835","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=222835"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/222835\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=222835"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=222835"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=222835"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}