{"id":246155,"date":"2025-07-06T19:59:46","date_gmt":"2025-07-06T19:59:46","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=246155"},"modified":"2025-07-06T19:59:48","modified_gmt":"2025-07-06T19:59:48","slug":"what-are-the-quotient-and-remainder-when-72-is-divided-by-14","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/07\/06\/what-are-the-quotient-and-remainder-when-72-is-divided-by-14\/","title":{"rendered":"What are the quotient and remainder when -72 is divided by 14"},"content":{"rendered":"\n


. (b) What are the quotient and remainder when -72 is divided by 14? Be sure to give your remainder as an integer
such that
.
(a) What are the quotient and remainder when 87 is divided by 12? Be sure to give your remainder as an integer
such that
. (b) What are the quotient and remainder when -72 is divided by 14? Be sure to give your remainder as an integer
such that<\/p>\n\n\n\n

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

Quotient and Remainder when 87 is divided by 12:<\/h3>\n\n\n\n

To find the quotient and remainder, we perform the division of 87 by 12.<\/p>\n\n\n\n

    \n
  1. Division<\/strong>: 87\u00f712=7\u00a0(quotient)with\u00a0a\u00a0remainder.87 \\div 12 = 7 \\text{ (quotient)} \\quad \\text{with a remainder}.87\u00f712=7\u00a0(quotient)with\u00a0a\u00a0remainder.<\/li>\n\n\n\n
  2. Calculation of remainder<\/strong>:
    Multiply the quotient by the divisor: 7\u00d712=847 \\times 12 = 847\u00d712=84 Now subtract 84 from 87: 87\u221284=387 – 84 = 387\u221284=3 So the remainder is 3.<\/li>\n<\/ol>\n\n\n\n

    Thus, the quotient is 7 and the remainder is 3.<\/p>\n\n\n\n

    (b) Quotient and Remainder when -72 is divided by 14:<\/h3>\n\n\n\n

    Now, let’s perform the division of -72 by 14. To get the remainder as a non-negative integer, we follow the same steps but adjust for the negative dividend.<\/p>\n\n\n\n

      \n
    1. Division<\/strong>: \u221272\u00f714=\u22125\u00a0(quotient)with\u00a0a\u00a0remainder.-72 \\div 14 = -5 \\text{ (quotient)} \\quad \\text{with a remainder}.\u221272\u00f714=\u22125\u00a0(quotient)with\u00a0a\u00a0remainder.<\/li>\n\n\n\n
    2. Calculation of remainder<\/strong>:
      Multiply the quotient by the divisor: \u22125\u00d714=\u221270-5 \\times 14 = -70\u22125\u00d714=\u221270 Now subtract -70 from -72: \u221272\u2212(\u221270)=\u221272+70=\u22122-72 – (-70) = -72 + 70 = -2\u221272\u2212(\u221270)=\u221272+70=\u22122 To make the remainder a non-negative integer, we need to adjust it by adding the divisor (14): \u22122+14=12-2 + 14 = 12\u22122+14=12 Thus, the remainder becomes 12, and we adjust the quotient to reflect this change. The correct quotient is one less than -5 (i.e., -6).<\/li>\n<\/ol>\n\n\n\n

      Thus, the quotient is -6 and the remainder is 12.<\/p>\n\n\n\n

      Summary:<\/h3>\n\n\n\n
        \n
      • (a)<\/strong> When 87 is divided by 12, the quotient is 7, and the remainder is 3.<\/li>\n\n\n\n
      • (b)<\/strong> When -72 is divided by 14, the quotient is -6, and the remainder is 12.<\/li>\n<\/ul>\n\n\n\n

        These calculations are consistent with the rule that the remainder must be a non-negative integer that is less than the divisor.<\/p>\n\n\n\n

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

        . (b) What are the quotient and remainder when -72 is divided by 14? Be sure to give your remainder as an integersuch that.(a) What are the quotient and remainder when 87 is divided by 12? Be sure to give your remainder as an integersuch that. (b) What are the quotient and remainder when -72 […]<\/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-246155","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/246155","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=246155"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/246155\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=246155"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=246155"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=246155"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}