{"id":225673,"date":"2025-06-04T11:30:01","date_gmt":"2025-06-04T11:30:01","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=225673"},"modified":"2025-06-04T11:30:04","modified_gmt":"2025-06-04T11:30:04","slug":"i-thought-of-a-number-multiplied-it-by-2-1-2-divided-the-result-by-1-1-5-subtracted-7-18-from-it-and-got-1-5-6","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/06\/04\/i-thought-of-a-number-multiplied-it-by-2-1-2-divided-the-result-by-1-1-5-subtracted-7-18-from-it-and-got-1-5-6\/","title":{"rendered":"I thought of a number, multiplied it by 2 1\/2 , divided the result by 1 1\/5 , subtracted 7\/18 from it, and got 1 5\/6"},"content":{"rendered":"\n<p>I thought of a number, multiplied it by 2 1\/2 , divided the result by 1 1\/5 , subtracted 7\/18 from it, and got 1 5\/6 . What was my number?<\/p>\n\n\n\n<p><strong><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-ast-global-color-0-color\">The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n<p>Let the number you thought of be <strong>x<\/strong>.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Step-by-step:<\/h3>\n\n\n\n<p>You:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Multiplied it by <strong>2\u00bd<\/strong> \u2192 x\u00d752x \\times \\frac{5}{2}<\/li>\n\n\n\n<li>Divided the result by <strong>1\u2155<\/strong> \u2192 x\u22c55265=x\u22c552\u22c556=x\u22c52512\\frac{x \\cdot \\frac{5}{2}}{\\frac{6}{5}} = x \\cdot \\frac{5}{2} \\cdot \\frac{5}{6} = x \\cdot \\frac{25}{12}<\/li>\n\n\n\n<li>Subtracted <strong>7\/18<\/strong> from it: x\u22c52512\u2212718x \\cdot \\frac{25}{12} &#8211; \\frac{7}{18}<\/li>\n\n\n\n<li>The result was <strong>1\u215a<\/strong>, which is: 116\\frac{11}{6}<\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading\">Equation:<\/h3>\n\n\n\n<p>x\u22c52512\u2212718=116x \\cdot \\frac{25}{12} &#8211; \\frac{7}{18} = \\frac{11}{6}<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Solve step-by-step:<\/h3>\n\n\n\n<ol class=\"wp-block-list\">\n<li>Add 718\\frac{7}{18} to both sides: x\u22c52512=116+718x \\cdot \\frac{25}{12} = \\frac{11}{6} + \\frac{7}{18}<\/li>\n\n\n\n<li>Get common denominator (LCM of 6 and 18 is 18): 3318+718=4018=209\\frac{33}{18} + \\frac{7}{18} = \\frac{40}{18} = \\frac{20}{9}<\/li>\n\n\n\n<li>So: x\u22c52512=209x \\cdot \\frac{25}{12} = \\frac{20}{9}<\/li>\n\n\n\n<li>Multiply both sides by the reciprocal of 2512\\frac{25}{12}: x=209\u22c51225=240225=1615x = \\frac{20}{9} \\cdot \\frac{12}{25} = \\frac{240}{225} = \\frac{16}{15}<\/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\">\u2705 Final Answer:<\/h3>\n\n\n\n<p>1615\\boxed{\\frac{16}{15}}<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">Explanation<\/h3>\n\n\n\n<p>To solve this type of algebraic problem, we begin by translating each step of the word problem into a mathematical expression. The unknown number is represented by <strong>x<\/strong>. You are told that the number was first multiplied by 2\u00bd, or 52\\frac{5}{2}, and then the result was divided by 1\u2155, which is 65\\frac{6}{5}.<\/p>\n\n\n\n<p>When dividing by a fraction, we multiply by its reciprocal. So: x\u00d752\u00f765=x\u22c552\u22c556=x\u22c52512x \\times \\frac{5}{2} \\div \\frac{6}{5} = x \\cdot \\frac{5}{2} \\cdot \\frac{5}{6} = x \\cdot \\frac{25}{12}<\/p>\n\n\n\n<p>Next, you subtract 718\\frac{7}{18} from this result. We are told this final expression equals 116\\frac{11}{6}, which is the improper fraction form of 1\u215a. This gives the equation: x\u22c52512\u2212718=116x \\cdot \\frac{25}{12} &#8211; \\frac{7}{18} = \\frac{11}{6}<\/p>\n\n\n\n<p>Solving this equation requires first isolating the term with <strong>x<\/strong> by adding 718\\frac{7}{18} to both sides. This gives: x\u22c52512=116+718x \\cdot \\frac{25}{12} = \\frac{11}{6} + \\frac{7}{18}<\/p>\n\n\n\n<p>With a common denominator, these become: 3318+718=4018=209\\frac{33}{18} + \\frac{7}{18} = \\frac{40}{18} = \\frac{20}{9}<\/p>\n\n\n\n<p>Then, to isolate <strong>x<\/strong>, divide both sides by 2512\\frac{25}{12}, or multiply by its reciprocal: x=209\u22c51225=240225=1615x = \\frac{20}{9} \\cdot \\frac{12}{25} = \\frac{240}{225} = \\frac{16}{15}<\/p>\n\n\n\n<p>Thus, the number you originally thought of was 1615\\boxed{\\frac{16}{15}}.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" src=\"https:\/\/learnexams.com\/blog\/wp-content\/uploads\/2025\/06\/learnexams-banner4-343.jpeg\" alt=\"\" class=\"wp-image-225674\"\/><\/figure>\n","protected":false},"excerpt":{"rendered":"<p>I thought of a number, multiplied it by 2 1\/2 , divided the result by 1 1\/5 , subtracted 7\/18 from it, and got 1 5\/6 . What was my number? The Correct Answer and Explanation is: Let the number you thought of be x. Step-by-step: You: Equation: x\u22c52512\u2212718=116x \\cdot \\frac{25}{12} &#8211; \\frac{7}{18} = \\frac{11}{6} [&hellip;]<\/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-225673","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/225673","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=225673"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/225673\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=225673"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=225673"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=225673"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}