{"id":24268,"date":"2025-06-18T12:21:05","date_gmt":"2025-06-18T12:21:05","guid":{"rendered":"https:\/\/gaviki.com\/blog\/?p=24268"},"modified":"2025-06-18T12:21:06","modified_gmt":"2025-06-18T12:21:06","slug":"point-x-is-at-2-3-on-the-number-line","status":"publish","type":"post","link":"https:\/\/gaviki.com\/blog\/point-x-is-at-2-3-on-the-number-line\/","title":{"rendered":"Point x is at 2\/3 on the number line"},"content":{"rendered":"\n<p>Point x is at 2\/3 on the number line. On the same number line, point y is the same distance from 0 as point x but has a numerator of 8. What is the denominator line to model the problem?<\/p>\n\n\n\n<p><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-vivid-cyan-blue-color\"><strong>The correct answer and explanation is:<\/strong><\/mark><\/p>\n\n\n\n<p><strong>Correct Answer:<\/strong><br>The denominator line to model the problem is <strong>12<\/strong>.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\"><strong>Explanation (300 words):<\/strong><\/h3>\n\n\n\n<p>We are given that:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Point <strong>x<\/strong> is located at <strong>2\/3<\/strong> on the number line.<\/li>\n\n\n\n<li>Point <strong>y<\/strong> is <strong>the same distance from 0 as point x<\/strong>, meaning its absolute value is also <strong>2\/3<\/strong>, but it has a <strong>numerator of 8<\/strong>.<\/li>\n\n\n\n<li>We are to find the <strong>denominator<\/strong> that would make <strong>8\/n = 2\/3<\/strong>, where <code>n<\/code> is what we are solving for.<\/li>\n<\/ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\"><strong>Step-by-step Reasoning:<\/strong><\/h3>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>Understand the position of point x:<\/strong>\n<ul class=\"wp-block-list\">\n<li>Point x is at <strong>2\/3<\/strong>, which is a positive fraction 2 units away from 0, on a scale where the whole is divided into 3 parts.<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li><strong>Equal Distance from 0:<\/strong>\n<ul class=\"wp-block-list\">\n<li>Point y is the same distance from 0 as point x, so y must also be <strong>2\/3<\/strong>, but the fraction is expressed <strong>with a numerator of 8<\/strong>.<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li><strong>Write an equation using the information:<\/strong> 8d=23\\frac{8}{d} = \\frac{2}{3} Here, we are solving for the denominator <strong>d<\/strong> that would make this statement true.<\/li>\n\n\n\n<li><strong>Solve for d:<\/strong> 8d=23\\frac{8}{d} = \\frac{2}{3} Cross-multiply: 8\u22c53=2\u22c5d24=2d8 \\cdot 3 = 2 \\cdot d \\\\ 24 = 2d Divide both sides by 2: d=12d = 12<\/li>\n<\/ol>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\"><strong>Conclusion:<\/strong><\/h3>\n\n\n\n<p>To represent a fraction that is equivalent to <strong>2\/3<\/strong> but has a numerator of <strong>8<\/strong>, you need a denominator of <strong>12<\/strong>, because: 812=23\\frac{8}{12} = \\frac{2}{3}<\/p>\n\n\n\n<p>So, <strong>a denominator line of 12 divisions<\/strong> on the number line will correctly model both points x and y.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Point x is at 2\/3 on the number line. On the same number line, point y is the same distance from 0 as point x but has a numerator of 8. What is the denominator line to model the problem? The correct answer and explanation is: Correct Answer:The denominator line to model the problem is [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[],"class_list":["post-24268","post","type-post","status-publish","format-standard","hentry","category-quiz-questions"],"_links":{"self":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/24268","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/comments?post=24268"}],"version-history":[{"count":1,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/24268\/revisions"}],"predecessor-version":[{"id":24269,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/24268\/revisions\/24269"}],"wp:attachment":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/media?parent=24268"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/categories?post=24268"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/tags?post=24268"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}