{"id":234831,"date":"2025-06-14T13:40:54","date_gmt":"2025-06-14T13:40:54","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=234831"},"modified":"2025-06-14T13:40:56","modified_gmt":"2025-06-14T13:40:56","slug":"which-of-the-following-pairs-of-rational-numbers-are-equivalent","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/06\/14\/which-of-the-following-pairs-of-rational-numbers-are-equivalent\/","title":{"rendered":"Which of the following pairs of rational numbers are equivalent"},"content":{"rendered":"\n

Which of the following pairs of rational numbers are equivalent? 18 46 (0) 14:42 () -27 -6<\/p>\n\n\n\n

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

Correct Answer: -27 and -6<\/strong><\/p>\n\n\n\n

To determine which pairs of rational numbers are equivalent, simplify each pair of numbers by expressing them as fractions and reducing them to their lowest terms.<\/p>\n\n\n\n

\n\n\n\n

1. First Pair: 18 and 46<\/strong><\/p>\n\n\n\n

Express these numbers as a fraction:1846\\frac{18}{46}4618\u200b<\/p>\n\n\n\n

Find the greatest common divisor (GCD) of 18 and 46.
The GCD is 2. Divide both numerator and denominator by 2:18\u00f7246\u00f72=923\\frac{18 \\div 2}{46 \\div 2} = \\frac{9}{23}46\u00f7218\u00f72\u200b=239\u200b<\/p>\n\n\n\n

Since 923\\frac{9}{23}239\u200b is in its simplest form, it cannot be simplified further. It does not equal 1 or any commonly known simplified fraction equivalent to a whole number or another rational number in this list.<\/p>\n\n\n\n

\n\n\n\n

2. Second Pair: 14 and 42<\/strong><\/p>\n\n\n\n

Express these numbers as a fraction:1442\\frac{14}{42}4214\u200b<\/p>\n\n\n\n

The GCD of 14 and 42 is 14. Simplify the fraction:14\u00f71442\u00f714=13\\frac{14 \\div 14}{42 \\div 14} = \\frac{1}{3}42\u00f71414\u00f714\u200b=31\u200b<\/p>\n\n\n\n

This results in a simplified fraction 13\\frac{1}{3}31\u200b, which again does not equal 1 or any fraction equivalent to -27 or -6. So, this pair is not equivalent to any others.<\/p>\n\n\n\n

\n\n\n\n

3. Third Pair: -27 and -6<\/strong><\/p>\n\n\n\n

Write the two numbers as a fraction:\u221227\u22126\\frac{-27}{-6}\u22126\u221227\u200b<\/p>\n\n\n\n

Dividing a negative number by another negative number results in a positive value:\u221227\u22126=276\\frac{-27}{-6} = \\frac{27}{6}\u22126\u221227\u200b=627\u200b<\/p>\n\n\n\n

Now simplify 276\\frac{27}{6}627\u200b. The GCD of 27 and 6 is 3.27\u00f736\u00f73=92\\frac{27 \\div 3}{6 \\div 3} = \\frac{9}{2}6\u00f7327\u00f73\u200b=29\u200b<\/p>\n\n\n\n

Since the simplified fraction is 92\\frac{9}{2}29\u200b, the pair is equivalent in value \u2014 both values can be represented as 92\\frac{9}{2}29\u200b.<\/p>\n\n\n\n

\n\n\n\n

Conclusion:<\/strong>
The only equivalent pair of rational numbers is -27 and -6<\/strong>, because their ratio simplifies to the same positive rational number.<\/p>\n\n\n\n

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

Which of the following pairs of rational numbers are equivalent? 18 46 (0) 14:42 () -27 -6 The Correct Answer and Explanation is: Correct Answer: -27 and -6 To determine which pairs of rational numbers are equivalent, simplify each pair of numbers by expressing them as fractions and reducing them to their lowest terms. 1. […]<\/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-234831","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/234831","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=234831"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/234831\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=234831"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=234831"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=234831"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}