{"id":164684,"date":"2024-11-10T12:25:55","date_gmt":"2024-11-10T12:25:55","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=164684"},"modified":"2024-11-10T12:25:58","modified_gmt":"2024-11-10T12:25:58","slug":"select-all-the-ratios-that-are-equivalent-to-the-ratio-12-3","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2024\/11\/10\/select-all-the-ratios-that-are-equivalent-to-the-ratio-12-3\/","title":{"rendered":"Select all the ratios that are equivalent to the ratio 12 : 3."},"content":{"rendered":"\n<p>Select all the ratios that are equivalent to the ratio 12 : 3. Explain how you know.<br>A. 6:1<br>B. 1:4<br>C. 4:1<br>D. 24 : 6<br>E. 15:6<br>F. 1,200 : 300<br>G. 112: 13<\/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>The correct equivalent ratios to 12:3 are <strong>A. 6:1<\/strong>, <strong>D. 24:6<\/strong>, and <strong>F. 1,200:300<\/strong>.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Explanation:<\/h3>\n\n\n\n<p>A <strong>ratio<\/strong> compares two quantities. To determine if two ratios are equivalent, we can simplify both ratios and check if they reduce to the same value.<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>Starting with the ratio 12:3<\/strong>, let&#8217;s simplify it:<\/li>\n<\/ol>\n\n\n\n<ul class=\"wp-block-list\">\n<li>The greatest common divisor (GCD) of 12 and 3 is 3.<\/li>\n\n\n\n<li>Dividing both parts of the ratio by 3, we get:<br>[<br>\\frac{12}{3} : \\frac{3}{3} = 4 : 1<br>]<br>So, the simplified form of 12:3 is <strong>4:1<\/strong>.<\/li>\n<\/ul>\n\n\n\n<p>Now, let&#8217;s check each option.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Option A: <strong>6:1<\/strong><\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li>To check if this ratio is equivalent to 12:3, simplify it by dividing both parts by their GCD, which is 6:<br>[<br>\\frac{6}{6} : \\frac{1}{6} = 1 : 1<br>]<br>Thus the ratio is indeed simplified, and we can see that it is equivalent to 12:3. So, the answer is &#8220;yes.&#8221;<\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading\">Option B: <strong>1:4<\/strong><\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li>In this case, the ratio of 1:4 is different from 12:3, as simplifying 12:3 equals 4:1, not 1:4. Therefore, this ratio is not equivalent.<\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading\">Option C: <strong>4:1<\/strong><\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li>As explained earlier, 12:3 simplifies to 4:1. So, this ratio is equivalent to 12:3.<\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading\">Option D: <strong>24:6<\/strong><\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Let&#8217;s simplify 24:6 by dividing both parts by their GCD, which is 6:<br>[<br>\\frac{24}{6} : \\frac{6}{6} = 4:1<br>]<br>Thus, 24:6 simplifies to 4:1, which is equivalent to 12:3.<\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading\">Option E: <strong>15:6<\/strong><\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Simplifying 15:6 by dividing both parts by their GCD (3):<br>[<br>\\frac{15}{3} : \\frac{6}{3} = 5:2<br>]<br>This ratio simplifies to 5:2, not 4:1, so it is not equivalent to 12:3.<\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading\">Option F: <strong>1,200:300<\/strong><\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Simplifying 1,200:300 by dividing both parts by their GCD (300):<br>[<br>\\frac{1200}{300} : \\frac{300}{300} = 4:1<br>]<br>Thus, 1,200:300 simplifies to 4:1, which is equivalent to 12:3.<\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading\">Option G: <strong>112:13<\/strong><\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Simplifying 112:13 shows that there is no common divisor between 112 and 13, so the ratio does not simplify to 4:1. Therefore, this ratio is not equivalent to 12:3.<\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading\">Final Answer:<\/h3>\n\n\n\n<p>The ratios that are equivalent to 12:3 are <strong>A. 6:1<\/strong>, <strong>D. 24:6<\/strong>, and <strong>F. 1,200:300<\/strong>.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Select all the ratios that are equivalent to the ratio 12 : 3. Explain how you know.A. 6:1B. 1:4C. 4:1D. 24 : 6E. 15:6F. 1,200 : 300G. 112: 13 The Correct Answer and Explanation is: The correct equivalent ratios to 12:3 are A. 6:1, D. 24:6, and F. 1,200:300. Explanation: A ratio compares two quantities. 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