{"id":144619,"date":"2024-09-24T23:06:36","date_gmt":"2024-09-24T23:06:36","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=144619"},"modified":"2024-09-24T23:06:40","modified_gmt":"2024-09-24T23:06:40","slug":"determine-if-1216-and-7296-are-equivalent-ratios","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2024\/09\/24\/determine-if-1216-and-7296-are-equivalent-ratios\/","title":{"rendered":"Determine if 12:16 and 72:96 :are equivalent ratios"},"content":{"rendered":"\n<p>Determine if 12:16 and 72:96 :are equivalent ratios<\/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 determine whether the ratios 12:16 and 72:96 are equivalent, we need to simplify each ratio and check if they are equal.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Simplifying the Ratios<\/h3>\n\n\n\n<p><strong>1. Simplifying 12:16:<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>To simplify the ratio 12:16, we find the greatest common divisor (GCD) of 12 and 16. The GCD is 4.<\/li>\n\n\n\n<li>Now, we divide both numbers by their GCD:\n<ul class=\"wp-block-list\">\n<li>(12 \u00f7 4 = 3)<\/li>\n\n\n\n<li>(16 \u00f7 4 = 4)<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li>Thus, the simplified form of the ratio 12:16 is 3:4.<\/li>\n<\/ul>\n\n\n\n<p><strong>2. Simplifying 72:96:<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Next, we simplify the ratio 72:96 by finding the GCD of 72 and 96. The GCD is 24.<\/li>\n\n\n\n<li>We divide both numbers by their GCD:\n<ul class=\"wp-block-list\">\n<li>(72 \u00f7 24 = 3)<\/li>\n\n\n\n<li>(96 \u00f7 24 = 4)<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li>Therefore, the simplified form of the ratio 72:96 is also 3:4.<\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading\">Comparing the Simplified Ratios<\/h3>\n\n\n\n<p>Now that we have simplified both ratios, we can compare them:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>The simplified form of 12:16 is 3:4.<\/li>\n\n\n\n<li>The simplified form of 72:96 is also 3:4.<\/li>\n<\/ul>\n\n\n\n<p>Since both ratios reduce to the same value (3:4), we can conclude that 12:16 and 72:96 are indeed equivalent ratios.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Conclusion<\/h3>\n\n\n\n<p>In conclusion, equivalent ratios express the same relationship between two quantities, even if the numbers used differ. In this case, both 12:16 and 72:96 simplify to the same ratio of 3:4, confirming their equivalence. This property is essential in various fields, including mathematics and real-life applications like cooking, scaling recipes, and comparing proportions in data analysis. Understanding how to simplify and compare ratios is a crucial skill that can aid in problem-solving across many disciplines.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Determine if 12:16 and 72:96 :are equivalent ratios The Correct answer and Explanation is: To determine whether the ratios 12:16 and 72:96 are equivalent, we need to simplify each ratio and check if they are equal. Simplifying the Ratios 1. Simplifying 12:16: 2. Simplifying 72:96: Comparing the Simplified Ratios Now that we have simplified both [&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-144619","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/144619","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=144619"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/144619\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=144619"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=144619"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=144619"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}