{"id":25499,"date":"2025-06-19T03:19:57","date_gmt":"2025-06-19T03:19:57","guid":{"rendered":"https:\/\/gaviki.com\/blog\/?p=25499"},"modified":"2025-06-19T03:19:58","modified_gmt":"2025-06-19T03:19:58","slug":"the-reciprocal-of-6-7-is-7-6","status":"publish","type":"post","link":"https:\/\/gaviki.com\/blog\/the-reciprocal-of-6-7-is-7-6\/","title":{"rendered":"The reciprocal of -6\/7 is -7\/6."},"content":{"rendered":"\n<p>The reciprocal of -6\/7 is -7\/6. The product of two rational numbers is always a rational number. The numbers 1 and -1 are their own reciprocals. The reciprocal of 1\/4 is 4. 0 is the additive identity of the rational numbers. 1 is the multiplicative identity of the rational numbers. The negative of -5 is 5. 3\/5 x -4 = -12\/5 x 3\/5.<\/p>\n\n\n\n<p><strong><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-light-green-cyan-color\">The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<p><strong>Corrected Statements and Explanations:<\/strong><\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>The reciprocal of -6\/7 is -7\/6.<\/strong><br>\u2705 <strong>Correct.<\/strong><br>The reciprocal of a number is found by flipping the numerator and denominator. The reciprocal of -6\/7 is indeed -7\/6.<\/li>\n\n\n\n<li><strong>The product of two rational numbers is always a rational number.<\/strong><br>\u2705 <strong>Correct.<\/strong><br>Multiplying any two rational numbers will always result in another rational number. This is because the product of two fractions or integers still fits the definition of a rational number.<\/li>\n\n\n\n<li><strong>The numbers 1 and -1 are their own reciprocals.<\/strong><br>\u2705 <strong>Correct.<\/strong><br>The reciprocal of 1 is 1. The reciprocal of -1 is -1. So this statement is true.<\/li>\n\n\n\n<li><strong>The reciprocal of 1\/4 is 4.<\/strong><br>\u2705 <strong>Correct.<\/strong><br>Flipping 1\/4 gives 4\/1, which simplifies to 4.<\/li>\n\n\n\n<li><strong>0 is the additive identity of the rational numbers.<\/strong><br>\u2705 <strong>Correct.<\/strong><br>Adding 0 to any rational number does not change its value. That is why 0 is called the additive identity.<\/li>\n\n\n\n<li><strong>1 is the multiplicative identity of the rational numbers.<\/strong><br>\u2705 <strong>Correct.<\/strong><br>Multiplying any rational number by 1 does not change its value, so 1 is the multiplicative identity.<\/li>\n\n\n\n<li><strong>The negative of -5 is 5.<\/strong><br>\u2705 <strong>Correct.<\/strong><br>Taking the negative of a negative number gives a positive. So the negative of -5 is indeed 5.<\/li>\n\n\n\n<li><strong>3\/5 \u00d7 -4 = -12\/5 \u00d7 3\/5.<\/strong><br>\u274c <strong>Incorrect.<\/strong><br>Let\u2019s compute both sides:<\/li>\n<\/ol>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Left side:<br>3\/5 \u00d7 -4 = -12\/5<\/li>\n\n\n\n<li>Right side:<br>-12\/5 \u00d7 3\/5 = -36\/25<\/li>\n<\/ul>\n\n\n\n<p>Since -12\/5 \u2260 -36\/25, this statement is false.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<p><strong>Conclusion:<\/strong><br>All statements are true except for the last one. Rational number operations follow specific rules. Reciprocals involve flipping fractions. Identities like 0 and 1 preserve value under addition or multiplication. But you must always verify computations, as in the last case.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"852\" height=\"1024\" src=\"https:\/\/gaviki.com\/blog\/wp-content\/uploads\/2025\/06\/learnexams-banner8-41.jpeg\" alt=\"\" class=\"wp-image-25500\" srcset=\"https:\/\/gaviki.com\/blog\/wp-content\/uploads\/2025\/06\/learnexams-banner8-41.jpeg 852w, https:\/\/gaviki.com\/blog\/wp-content\/uploads\/2025\/06\/learnexams-banner8-41-250x300.jpeg 250w, https:\/\/gaviki.com\/blog\/wp-content\/uploads\/2025\/06\/learnexams-banner8-41-768x923.jpeg 768w\" sizes=\"auto, (max-width: 852px) 100vw, 852px\" \/><\/figure>\n","protected":false},"excerpt":{"rendered":"<p>The reciprocal of -6\/7 is -7\/6. The product of two rational numbers is always a rational number. The numbers 1 and -1 are their own reciprocals. The reciprocal of 1\/4 is 4. 0 is the additive identity of the rational numbers. 1 is the multiplicative identity of the rational numbers. The negative of -5 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-25499","post","type-post","status-publish","format-standard","hentry","category-quiz-questions"],"_links":{"self":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/25499","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=25499"}],"version-history":[{"count":1,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/25499\/revisions"}],"predecessor-version":[{"id":25501,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/25499\/revisions\/25501"}],"wp:attachment":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/media?parent=25499"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/categories?post=25499"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/tags?post=25499"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}