{"id":256196,"date":"2025-07-14T04:58:34","date_gmt":"2025-07-14T04:58:34","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=256196"},"modified":"2025-07-19T06:46:24","modified_gmt":"2025-07-19T06:46:24","slug":"simplify-the-following-5-8-8-9-0-13-3-17-24","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/07\/14\/simplify-the-following-5-8-8-9-0-13-3-17-24\/","title":{"rendered":"simplify the following 5\/8 + -8\/9 + 0+ -13\/3 + 17\/24"},"content":{"rendered":"\n

simplify the following 5\/8 + -8\/9 + 0+ -13\/3 + 17\/24<\/p>\n\n\n\n

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

Let’s simplify the expression: 58+(\u221289)+0+(\u2212133)+1724\\frac{5}{8} + \\left(-\\frac{8}{9}\\right) + 0 + \\left(-\\frac{13}{3}\\right) + \\frac{17}{24}85\u200b+(\u221298\u200b)+0+(\u2212313\u200b)+2417\u200b<\/p>\n\n\n\n

Step 1: Identify the fractions and simplify<\/h3>\n\n\n\n

The given fractions are: 58,\u221289,0,\u2212133,1724\\frac{5}{8}, -\\frac{8}{9}, 0, -\\frac{13}{3}, \\frac{17}{24}85\u200b,\u221298\u200b,0,\u2212313\u200b,2417\u200b<\/p>\n\n\n\n

The zero doesn\u2019t affect the sum, so we focus on the fractions: 58,\u221289,\u2212133,1724\\frac{5}{8}, -\\frac{8}{9}, -\\frac{13}{3}, \\frac{17}{24}85\u200b,\u221298\u200b,\u2212313\u200b,2417\u200b<\/p>\n\n\n\n

Step 2: Find a common denominator<\/h3>\n\n\n\n

To add and subtract fractions, we need to express all fractions with the same denominator. The denominators are 8, 9, 3, and 24. The least common denominator (LCD) for these numbers is 72<\/strong>.<\/p>\n\n\n\n

Step 3: Convert each fraction to have a denominator of 72<\/h3>\n\n\n\n
    \n
  • For 58\\frac{5}{8}85\u200b:
    Multiply the numerator and denominator by 9: 58=5\u00d798\u00d79=4572\\frac{5}{8} = \\frac{5 \\times 9}{8 \\times 9} = \\frac{45}{72}85\u200b=8\u00d795\u00d79\u200b=7245\u200b<\/li>\n\n\n\n
  • For \u221289-\\frac{8}{9}\u221298\u200b:
    Multiply the numerator and denominator by 8: \u221289=\u22128\u00d789\u00d78=\u22126472-\\frac{8}{9} = \\frac{-8 \\times 8}{9 \\times 8} = \\frac{-64}{72}\u221298\u200b=9\u00d78\u22128\u00d78\u200b=72\u221264\u200b<\/li>\n\n\n\n
  • For \u2212133-\\frac{13}{3}\u2212313\u200b:
    Multiply the numerator and denominator by 24: \u2212133=\u221213\u00d7243\u00d724=\u221231272-\\frac{13}{3} = \\frac{-13 \\times 24}{3 \\times 24} = \\frac{-312}{72}\u2212313\u200b=3\u00d724\u221213\u00d724\u200b=72\u2212312\u200b<\/li>\n\n\n\n
  • For 1724\\frac{17}{24}2417\u200b:
    Multiply the numerator and denominator by 3: 1724=17\u00d7324\u00d73=5172\\frac{17}{24} = \\frac{17 \\times 3}{24 \\times 3} = \\frac{51}{72}2417\u200b=24\u00d7317\u00d73\u200b=7251\u200b<\/li>\n<\/ul>\n\n\n\n

    Step 4: Add the fractions<\/h3>\n\n\n\n

    Now that we have a common denominator of 72, we can add and subtract the numerators: 4572+\u22126472+\u221231272+5172\\frac{45}{72} + \\frac{-64}{72} + \\frac{-312}{72} + \\frac{51}{72}7245\u200b+72\u221264\u200b+72\u2212312\u200b+7251\u200b<\/p>\n\n\n\n

    Add the numerators: 45+(\u221264)+(\u2212312)+51=45\u221264\u2212312+51=\u221228045 + (-64) + (-312) + 51 = 45 – 64 – 312 + 51 = -28045+(\u221264)+(\u2212312)+51=45\u221264\u2212312+51=\u2212280<\/p>\n\n\n\n

    Thus, the sum is: \u221228072\\frac{-280}{72}72\u2212280\u200b<\/p>\n\n\n\n

    Step 5: Simplify the fraction<\/h3>\n\n\n\n

    To simplify \u221228072\\frac{-280}{72}72\u2212280\u200b, divide both the numerator and denominator by their greatest common divisor, which is 8<\/strong>: \u2212280\u00f7872\u00f78=\u2212359\\frac{-280 \\div 8}{72 \\div 8} = \\frac{-35}{9}72\u00f78\u2212280\u00f78\u200b=9\u221235\u200b<\/p>\n\n\n\n

    Final Answer:<\/h3>\n\n\n\n

    The simplified sum is: \u2212359\\boxed{-\\frac{35}{9}}\u2212935\u200b\u200b<\/p>\n\n\n\n

    Explanation:<\/h3>\n\n\n\n

    To add and subtract fractions, you first find a common denominator. Here, the least common denominator (LCD) was 72. After converting each fraction to have a denominator of 72, the numerators were added and subtracted. The final step was to simplify the resulting fraction by dividing both the numerator and denominator by their greatest common divisor. The simplified fraction is \u2212359-\\frac{35}{9}\u2212935\u200b.<\/p>\n\n\n\n

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

    simplify the following 5\/8 + -8\/9 + 0+ -13\/3 + 17\/24 The Correct Answer and Explanation is: Let’s simplify the expression: 58+(\u221289)+0+(\u2212133)+1724\\frac{5}{8} + \\left(-\\frac{8}{9}\\right) + 0 + \\left(-\\frac{13}{3}\\right) + \\frac{17}{24}85\u200b+(\u221298\u200b)+0+(\u2212313\u200b)+2417\u200b Step 1: Identify the fractions and simplify The given fractions are: 58,\u221289,0,\u2212133,1724\\frac{5}{8}, -\\frac{8}{9}, 0, -\\frac{13}{3}, \\frac{17}{24}85\u200b,\u221298\u200b,0,\u2212313\u200b,2417\u200b The zero doesn\u2019t affect the sum, so we focus […]<\/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-256196","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/256196","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=256196"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/256196\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=256196"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=256196"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=256196"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}