1. \u201cThe quotient of a number and five\u201d<\/strong> 2. \u201cEight less than twice a number\u201d<\/strong> 3. \u201cFour times the difference of a number and two\u201d<\/strong> These expressions are examples of how everyday language translates into mathematical symbols. The first phrase, \u201cthe quotient of a number and five,\u201d<\/em> refers to dividing a number by five. In mathematics, division is represented using the division symbol (\u00f7) or a fraction. When we say \u201cthe quotient of x and 5,\u201d we write it as x \u00f7 5<\/strong> or more commonly in algebra, as x\/5<\/strong>. This is a simple rational expression where the numerator is the unknown and the denominator is 5.<\/p>\n\n\n\n The second phrase, \u201ceight less than twice a number,\u201d<\/em> is slightly more complex. \u201cTwice a number\u201d means multiplying the unknown by 2, which gives 2x<\/strong>. The phrase \u201ceight less than\u201d tells us to subtract 8 from that product. In mathematics, subtraction is order-sensitive, so 2x – 8<\/strong> is correct, not 8 – 2x<\/strong>.<\/p>\n\n\n\n The third phrase, \u201cfour times the difference of a number and two,\u201d<\/em> involves both subtraction and multiplication. \u201cThe difference of a number and two\u201d becomes x – 2<\/strong>, and \u201cfour times\u201d that difference means multiplying the entire difference by 4. In algebra, when multiplying an expression like this, we use parentheses: 4(x – 2)<\/strong>. This tells us to first find the difference inside the parentheses and then multiply it by 4.<\/p>\n\n\n\n Understanding how words translate into mathematical expressions helps in solving word problems and writing equations.<\/p>\n\n\n\n What is “the quotient of a number and five”, “eight less than twice a number”, and “four times the difference of a number and two” The Correct Answer and Explanation is: 1. \u201cThe quotient of a number and five\u201dLet the unknown number be represented by the variable x.The word \u201cquotient\u201d means division.So, the phrase translates […]<\/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-238795","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/238795","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=238795"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/238795\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=238795"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=238795"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=238795"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}
Let the unknown number be represented by the variable x<\/strong>.
The word \u201cquotient\u201d<\/strong> means division.
So, the phrase translates to: x5\\frac{x}{5}5x\u200b<\/p>\n\n\n\n
\n\n\n\n
Again, let the number be x<\/strong>.
\u201cTwice a number\u201d<\/strong> means 2 multiplied by the number, or 2x<\/strong>.
\u201cEight less than\u201d<\/strong> means subtract 8 from the result.
So, the phrase becomes: 2x\u221282x – 82x\u22128<\/p>\n\n\n\n
\n\n\n\n
We still use x<\/strong> as the number.
\u201cThe difference of a number and two\u201d<\/strong> means subtract 2 from the number: x – 2<\/strong>.
\u201cFour times\u201d<\/strong> this difference means multiply the entire expression by 4.
So, the full expression is: 4(x\u22122)4(x – 2)4(x\u22122)<\/p>\n\n\n\n
\n\n\n\nDetailed Explanation <\/h3>\n\n\n\n
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