Equation:<\/strong> Step 1: Translate the words into an algebraic equation.<\/strong> “The quotient of a number and 8” means w8\\frac{w}{8}8w\u200b. Step 2: Solve the equation.<\/strong> Subtract 9 from both sides:w8+9\u22129=3\u22129\\frac{w}{8} + 9 – 9 = 3 – 98w\u200b+9\u22129=3\u22129w8=\u22126\\frac{w}{8} = -68w\u200b=\u22126<\/p>\n\n\n\n Next, multiply both sides by 8 to eliminate the denominator:8\u22c5w8=\u22126\u22c588 \\cdot \\frac{w}{8} = -6 \\cdot 88\u22c58w\u200b=\u22126\u22c58w=\u221248w = -48w=\u221248<\/p>\n\n\n\n Final Answer:<\/strong>w=\u221248w = -48w=\u221248<\/p>\n\n\n\n Explanation (Textbook Style):<\/strong> To solve this equation, begin by simplifying it. Subtracting 9 from both sides isolates the fraction:w8=\u22126\\frac{w}{8} = -68w\u200b=\u22126<\/p>\n\n\n\n Then, to eliminate the denominator and solve for the variable www, multiply both sides of the equation by 8:w=\u221248w = -48w=\u221248<\/p>\n\n\n\n Thus, the value of the unknown number is \u221248-48\u221248. This means that if \u221248-48\u221248 is divided by 8, the result is \u22126-6\u22126, and adding 9 to this gives the final value of 3, which confirms the correctness of the solution.<\/p>\n\n\n\n nine more than the quotient of a number and 8 is equal to 3 Use the variable w for the unknown number. The Correct Answer and Explanation is: Equation:Nine more than the quotient of a number and 8 is equal to 3. Step 1: Translate the words into an algebraic equation.Let the unknown number be […]<\/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-233006","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/233006","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=233006"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/233006\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=233006"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=233006"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=233006"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}
Nine more than the quotient of a number and 8 is equal to 3.<\/p>\n\n\n\n
Let the unknown number be represented by the variable www.<\/p>\n\n\n\n
“Nine more than” this quotient means w8+9\\frac{w}{8} + 98w\u200b+9.
This expression is “equal to 3,” so the full equation is:w8+9=3\\frac{w}{8} + 9 = 38w\u200b+9=3<\/p>\n\n\n\n
Start by isolating the variable term.<\/p>\n\n\n\n
\n\n\n\n
In solving algebraic equations that involve words, the first step is to translate the written statement into a mathematical equation. The phrase “the quotient of a number and 8” refers to a division, specifically dividing a number www by 8, which gives the expression w8\\frac{w}{8}8w\u200b. Next, the phrase “nine more than” tells to add 9 to this expression, resulting in w8+9\\frac{w}{8} + 98w\u200b+9. This sum is stated to be equal to 3, which sets up the equation w8+9=3\\frac{w}{8} + 9 = 38w\u200b+9=3.<\/p>\n\n\n\n![\"\"](\"https:\/\/learnexams.com\/blog\/wp-content\/uploads\/2025\/06\/learnexams-banner5-396.jpeg\")
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