{"id":214311,"date":"2025-05-14T05:24:52","date_gmt":"2025-05-14T05:24:52","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=214311"},"modified":"2025-05-14T05:24:54","modified_gmt":"2025-05-14T05:24:54","slug":"mrs-cho-wrote-the-following-problem-on-the-board","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/05\/14\/mrs-cho-wrote-the-following-problem-on-the-board\/","title":{"rendered":"Mrs. Cho wrote the following problem on the board."},"content":{"rendered":"\n<p class=\"wp-block-paragraph\">Mrs. Cho wrote the following problem on the board. Problem: ((1)\/(x^(2))-(2)\/(y))\/(y-2x^(2)) Step 1: ((y)\/(x^(2)y)-(2x^(2))\/(x^(2)y))\/(y-2x^(2)) Step 2: ((y-2x^(2))\/(x^(2)y))\/((y-2x^(2))\/(1))x<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><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 class=\"wp-block-paragraph\">Let&#8217;s carefully evaluate the expression Mrs. Cho wrote and explain the steps in detail.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">Given Expression:<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">1&#215;2\u22122yy\u22122&#215;2\\frac{\\frac{1}{x^2} &#8211; \\frac{2}{y}}{y &#8211; 2x^2}<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">Step 1:<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Mrs. Cho rewrote the numerator with a common denominator: yx2y\u22122x2x2yy\u22122&#215;2\\frac{\\frac{y}{x^2y} &#8211; \\frac{2x^2}{x^2y}}{y &#8211; 2x^2}<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">This is correct. The least common denominator (LCD) of the two terms in the numerator 1&#215;2\\frac{1}{x^2} and 2y\\frac{2}{y} is x2yx^2y. So:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>1&#215;2=yx2y\\frac{1}{x^2} = \\frac{y}{x^2y}<\/li>\n\n\n\n<li>2y=2x2x2y\\frac{2}{y} = \\frac{2x^2}{x^2y}<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">Now the numerator becomes: y\u22122x2x2y\\frac{y &#8211; 2x^2}{x^2y}<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">So the entire expression becomes: y\u22122x2x2yy\u22122&#215;2\\frac{\\frac{y &#8211; 2x^2}{x^2y}}{y &#8211; 2x^2}<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">Step 2:<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Mrs. Cho wrote: (y\u22122x2x2y)\u00f7(y\u22122&#215;21)\\left( \\frac{y &#8211; 2x^2}{x^2y} \\right) \\div \\left( \\frac{y &#8211; 2x^2}{1} \\right)<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">This is a correct transformation because dividing by a number is the same as multiplying by its reciprocal. So: y\u22122x2x2yy\u22122&#215;21=y\u22122x2x2y\u22c51y\u22122&#215;2\\frac{\\frac{y &#8211; 2x^2}{x^2y}}{\\frac{y &#8211; 2x^2}{1}} = \\frac{y &#8211; 2x^2}{x^2y} \\cdot \\frac{1}{y &#8211; 2x^2}<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Now cancel the common factor (y\u22122&#215;2)(y &#8211; 2x^2) in the numerator and denominator: =1x2y= \\frac{1}{x^2y}<\/p>\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 class=\"wp-block-paragraph\">1x2y\\boxed{\\frac{1}{x^2y}}<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">300-Word Explanation:<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Mrs. Cho presents a rational algebraic expression involving division of fractions. The original problem is a complex fraction: 1&#215;2\u22122yy\u22122&#215;2\\frac{\\frac{1}{x^2} &#8211; \\frac{2}{y}}{y &#8211; 2x^2}<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">To simplify, start by combining the two fractions in the numerator. The least common denominator (LCD) of x2x^2 and yy is x2yx^2y. Rewriting each term with this denominator:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>1&#215;2=yx2y\\frac{1}{x^2} = \\frac{y}{x^2y}<\/li>\n\n\n\n<li>2y=2x2x2y\\frac{2}{y} = \\frac{2x^2}{x^2y}<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">Now subtract the two fractions: y\u22122x2x2y\\frac{y &#8211; 2x^2}{x^2y}<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">So the entire expression becomes: y\u22122x2x2yy\u22122&#215;2\\frac{\\frac{y &#8211; 2x^2}{x^2y}}{y &#8211; 2x^2}<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">This is now a division of two expressions. Since dividing by a number is the same as multiplying by its reciprocal, rewrite as: y\u22122x2x2y\u22c51y\u22122&#215;2\\frac{y &#8211; 2x^2}{x^2y} \\cdot \\frac{1}{y &#8211; 2x^2}<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">At this point, the common factor y\u22122x2y &#8211; 2x^2 in the numerator and denominator cancels out. The result is: 1x2y\\frac{1}{x^2y}<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Thus, Mrs. Cho&#8217;s simplification is valid, and the final answer is 1x2y\\boxed{\\frac{1}{x^2y}}. This process demonstrates the importance of identifying common denominators and using algebraic rules for fraction operations such as multiplying by the reciprocal and canceling common terms.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Mrs. Cho wrote the following problem on the board. Problem: ((1)\/(x^(2))-(2)\/(y))\/(y-2x^(2)) Step 1: ((y)\/(x^(2)y)-(2x^(2))\/(x^(2)y))\/(y-2x^(2)) Step 2: ((y-2x^(2))\/(x^(2)y))\/((y-2x^(2))\/(1))x The Correct Answer And Explanation is: Let&#8217;s carefully evaluate the expression Mrs. Cho wrote and explain the steps in detail. Given Expression: 1&#215;2\u22122yy\u22122&#215;2\\frac{\\frac{1}{x^2} &#8211; \\frac{2}{y}}{y &#8211; 2x^2} Step 1: Mrs. Cho rewrote the numerator with a common denominator: [&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-214311","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/214311","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=214311"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/214311\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=214311"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=214311"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=214311"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}