{"id":238950,"date":"2025-06-18T13:52:45","date_gmt":"2025-06-18T13:52:45","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=238950"},"modified":"2025-06-18T13:52:47","modified_gmt":"2025-06-18T13:52:47","slug":"equivalent-fractions-on-the-area-model","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/06\/18\/equivalent-fractions-on-the-area-model\/","title":{"rendered":"Equivalent fractions on the area model."},"content":{"rendered":"\n

Equivalent fractions on the area model. Draw two 4 by 5 units on the grid paper. Show the fraction as a second model divided into 20ths and determine the fractional amount shaded. Therefore, draw two 4 by 3 units on the grid paper. Show the fraction as a partition of the second model to show a fraction equivalent to . Name the new modeled fraction and write an equivalency statement. Draw a 4 by 6 unit and model %. Now draw additional units and partition so that three equivalent fractions can be found. Model each fraction and write the equivalency statement.<\/p>\n\n\n\n

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

Part 1: Draw two 4 by 5 units (grids)<\/strong><\/h3>\n\n\n\n

Draw two rectangles that are 4 units tall and 5 units wide. This gives each rectangle a total of:4\u00d75=20 units4 \\times 5 = 20 \\text{ units}4\u00d75=20 units<\/p>\n\n\n\n

Shade a portion of the first rectangle, for example, 10 squares out of 20. This shows the fraction:1020\\frac{10}{20}2010\u200b<\/p>\n\n\n\n

Now, in the second 4 by 5 rectangle, divide each square in half vertically. Now, each original square becomes 2 smaller parts. You now have:20\u00d72=40 parts20 \\times 2 = 40 \\text{ parts}20\u00d72=40 parts<\/p>\n\n\n\n

If you shade the same area as before (10 squares), now it becomes:10\u00d72=20 shaded parts out of 4010 \\times 2 = 20 \\text{ shaded parts out of 40}10\u00d72=20 shaded parts out of 40<\/p>\n\n\n\n

The new fraction is:2040\\frac{20}{40}4020\u200b<\/p>\n\n\n\n

So, we have:1020=2040\\frac{10}{20} = \\frac{20}{40}2010\u200b=4020\u200b<\/p>\n\n\n\n

\n\n\n\n

Part 2: Draw two 4 by 3 units<\/strong><\/h3>\n\n\n\n

Draw two rectangles of size 4 by 3, each having:4\u00d73=12 units4 \\times 3 = 12 \\text{ units}4\u00d73=12 units<\/p>\n\n\n\n

Shade, for instance, 6 squares to show:612\\frac{6}{12}126\u200b<\/p>\n\n\n\n

Now in the second rectangle, divide each unit into 2 smaller parts horizontally. Now there are:12\u00d72=24 parts12 \\times 2 = 24 \\text{ parts}12\u00d72=24 parts<\/p>\n\n\n\n

If you shade the same area, it becomes:6\u00d72=12 parts6 \\times 2 = 12 \\text{ parts}6\u00d72=12 parts<\/p>\n\n\n\n

So the new fraction is:1224\\frac{12}{24}2412\u200b<\/p>\n\n\n\n

Equivalency statement:612=1224\\frac{6}{12} = \\frac{12}{24}126\u200b=2412\u200b<\/p>\n\n\n\n

\n\n\n\n

Part 3: Draw a 4 by 6 unit and model a percent<\/strong><\/h3>\n\n\n\n

Let\u2019s say we want to model 50%. A 4 by 6 rectangle has:4\u00d76=24 units4 \\times 6 = 24 \\text{ units}4\u00d76=24 units<\/p>\n\n\n\n

Shade half of it:1224\\frac{12}{24}2412\u200b<\/p>\n\n\n\n

Now let\u2019s draw additional models:<\/p>\n\n\n\n

    \n
  • Divide each square into 2 parts \u2192 48 parts \u2192 shade 24 \u2192 2448\\frac{24}{48}4824\u200b<\/li>\n\n\n\n
  • Divide each square into 3 parts \u2192 72 parts \u2192 shade 36 \u2192 3672\\frac{36}{72}7236\u200b<\/li>\n\n\n\n
  • Divide each square into 4 parts \u2192 96 parts \u2192 shade 48 \u2192 4896\\frac{48}{96}9648\u200b<\/li>\n<\/ul>\n\n\n\n

    Equivalency statements:1224=2448=3672=4896\\frac{12}{24} = \\frac{24}{48} = \\frac{36}{72} = \\frac{48}{96}2412\u200b=4824\u200b=7236\u200b=9648\u200b<\/p>\n\n\n\n

    These area models show that different fractions can represent the same value.<\/p>\n\n\n\n

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

    Equivalent fractions on the area model. Draw two 4 by 5 units on the grid paper. Show the fraction as a second model divided into 20ths and determine the fractional amount shaded. Therefore, draw two 4 by 3 units on the grid paper. Show the fraction as a partition of the second model to show […]<\/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-238950","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/238950","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=238950"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/238950\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=238950"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=238950"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=238950"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}