{"id":217,"date":"2022-04-08T05:19:03","date_gmt":"2022-04-08T05:19:03","guid":{"rendered":"http:\/\/6thclass.deltapublications.in\/?page_id=217"},"modified":"2025-02-08T11:54:56","modified_gmt":"2025-02-08T11:54:56","slug":"m-9-solve-the-proportion","status":"publish","type":"page","link":"https:\/\/6thclass.deltapublications.in\/index.php\/m-9-solve-the-proportion\/","title":{"rendered":"M.9 Solve the proportion"},"content":{"rendered":"\n<h2 class=\"wp-block-heading has-text-align-center has-text-color\" style=\"color:#00056d;text-transform:uppercase\"><strong> Solve the proportion<\/strong><\/h2>\n\n\n\n<p class=\"has-text-color has-link-color has-huge-font-size wp-elements-8550df6181cd5d83aa7a08ef336a4ca1\" style=\"color:#74008b\">Key Notes :<\/p>\n\n\n\n<p class=\"has-text-color has-link-color has-large-font-size wp-elements-293fce3ea1369cc456e739cdd86f10b1\" style=\"color:#000060\"><strong>Definition of Proportion<\/strong><\/p>\n\n\n\n<ul class=\"has-large-font-size wp-block-list\">\n<li>A proportion is an equation that shows two ratios are equal.<\/li>\n\n\n\n<li>Example: 2\/3 = 4\/6\u200b.<\/li>\n<\/ul>\n\n\n\n<p class=\"has-text-color has-link-color has-large-font-size wp-elements-77c7a7eb6d6f7b7c381259529f9ddf78\" style=\"color:#000060\"><strong>Parts of a Proportion<\/strong><\/p>\n\n\n\n<ul class=\"has-large-font-size wp-block-list\">\n<li>A proportion consists of two fractions or ratios.<\/li>\n\n\n\n<li>Example: a\/b = c\/d\u200b, where a,b,c, and d are numbers.<\/li>\n<\/ul>\n\n\n\n<p class=\"has-text-color has-link-color has-large-font-size wp-elements-d74d17d20c13a4889f7df6e00913c6df\" style=\"color:#000060\"><strong>Solving a Proportion using Cross Multiplication<\/strong><\/p>\n\n\n\n<p class=\"has-large-font-size\">Multiply the numerator of the first ratio by the denominator of the second ratio.<\/p>\n\n\n\n<p class=\"has-large-font-size\">Multiply the denominator of the first ratio by the numerator of the second ratio.<\/p>\n\n\n\n<p class=\"has-large-font-size\">Set both products equal to each other and solve for the unknown.<\/p>\n\n\n\n<p class=\"has-large-font-size\">Example: Solve 3\/4 = x\/8\u200b<\/p>\n\n\n\n<ul class=\"has-large-font-size wp-block-list\">\n<li>3 \u00d7 8 = 4 \u00d7 x3 <\/li>\n\n\n\n<li>24 = 4x<\/li>\n\n\n\n<li>x = 6.<\/li>\n<\/ul>\n\n\n\n<p class=\"has-text-color has-link-color has-large-font-size wp-elements-55438a150f2490bede26972a64c4482d\" style=\"color:#000060\"><strong>Finding a Missing Number in a Proportion<\/strong><\/p>\n\n\n\n<p class=\"has-large-font-size\">If one value is unknown, use cross multiplication to find it.<\/p>\n\n\n\n<p class=\"has-large-font-size\">Example: 5\/x = 10\/20\u200b<\/p>\n\n\n\n<ul class=\"has-large-font-size wp-block-list\">\n<li>5 \u00d7 20 = x \u00d7 10<\/li>\n\n\n\n<li>100 = 10x<\/li>\n\n\n\n<li>x = 10.<\/li>\n<\/ul>\n\n\n\n<p class=\"has-text-color has-link-color has-large-font-size wp-elements-60e88b2b5eb6b7a965d0e6c7f420490d\" style=\"color:#000060\"><strong>Checking if Two Ratios Form a Proportion<\/strong><\/p>\n\n\n\n<p class=\"has-large-font-size\">Cross multiply and see if the products are equal.<\/p>\n\n\n\n<p class=\"has-large-font-size\">Example: Is 6\/9 = 8\/12\u200b?<\/p>\n\n\n\n<ul class=\"has-large-font-size wp-block-list\">\n<li>6 \u00d7 12 = 72<\/li>\n\n\n\n<li>9 \u00d7 8 = 72<\/li>\n<\/ul>\n\n\n\n<p class=\"has-large-font-size\">Since both products are equal, the ratios form a proportion.<\/p>\n\n\n\n<p class=\"has-text-color has-link-color has-large-font-size wp-elements-2267d6ce0c85576d34d812315466ebaf\" style=\"color:#000060\"><strong>Real-Life Applications of Proportion<\/strong><\/p>\n\n\n\n<ul class=\"has-large-font-size wp-block-list\">\n<li><strong>Recipe Adjustments:<\/strong> If a recipe needs 2 cups of flour for 4 servings, how much flour is needed for 6 servings?<\/li>\n\n\n\n<li><strong>Map Scale:<\/strong> A map shows 1 inch = 10 miles. If the distance between two cities is 5 inches on the map, the actual distance is 50 miles.<\/li>\n\n\n\n<li><strong>Conversions:<\/strong> If 5 pencils cost $10, then how much do 8 pencils cost?<\/li>\n<\/ul>\n\n\n\n<p class=\"has-text-color has-link-color has-large-font-size wp-elements-80fd63929789d2ab0955895331c3685f\" style=\"color:#000060\"><strong>Solving Word Problems Involving Proportion<\/strong><\/p>\n\n\n\n<ul class=\"has-large-font-size wp-block-list\">\n<li>Identify the two ratios in the problem.<\/li>\n\n\n\n<li>Set up a proportion equation.<\/li>\n\n\n\n<li>Use cross multiplication to solve for the missing value.<\/li>\n\n\n\n<li>Check if the answer makes sense in the given context.<\/li>\n<\/ul>\n\n\n\n<p class=\"has-text-align-center has-text-color has-link-color has-large-font-size wp-elements-b44cda021ddeb2e340f30f73263e8e53\" style=\"color:#000060\"><strong>Learn with an example<\/strong><\/p>\n\n\n\n<div class=\"wp-block-group has-background has-large-font-size\" style=\"background-color:#e6ebab\"><div class=\"wp-block-group__inner-container is-layout-flow wp-block-group-is-layout-flow\">\n<div class=\"wp-block-group has-background-background-color has-background\"><div class=\"wp-block-group__inner-container is-layout-flow wp-block-group-is-layout-flow\">\n<p class=\"has-text-color has-link-color wp-elements-883d9306f5b173208236467f40421da8\" style=\"color:#b00012\"><strong>\u270f\ufe0f Solve for&nbsp;g&nbsp;in the proportion.<\/strong><\/p>\n\n\n\n<p>21\/g = 7\/16<\/p>\n\n\n\n<p>g = ____<\/p>\n<\/div><\/div>\n\n\n\n<p>Solve for&nbsp;<em>g<\/em>&nbsp;in the proportion.<\/p>\n\n\n\n<p>21\/g = 7\/16<\/p>\n\n\n\n<p>21\/g ( 16g ) = 7\/16 ( 16g )          Multiply both sides by 16g <\/p>\n\n\n\n<p>16 \u00b7 21 = 7g           Simplify<\/p>\n\n\n\n<p>336 = 7g             Simplify<\/p>\n\n\n\n<p>48 = g            Divide both sides by 7<\/p>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-group has-background has-large-font-size\" style=\"background-color:#d4eab7\"><div class=\"wp-block-group__inner-container is-layout-flow wp-block-group-is-layout-flow\">\n<div class=\"wp-block-group has-background-background-color has-background\"><div class=\"wp-block-group__inner-container is-layout-flow wp-block-group-is-layout-flow\">\n<p class=\"has-text-color has-link-color wp-elements-1f13338b02fa181ec53fc71c2e864772\" style=\"color:#b00012\"><strong>\u270f\ufe0f Solve for&nbsp;<em>y<\/em>&nbsp;in the proportion.<\/strong><\/p>\n\n\n\n<p>y\/32 = 45\/36<\/p>\n\n\n\n<p>y = _____<\/p>\n<\/div><\/div>\n\n\n\n<p>Solve for&nbsp;<em>y<\/em>&nbsp;in the proportion.<\/p>\n\n\n\n<p>y\/32 = 45\/36<\/p>\n\n\n\n<p>y\/32 ( 32 . 36 ) = 45\/36 ( 32 . 36 )            Multiply<em> <\/em>both sides by 32 \u00b7 36<\/p>\n\n\n\n<p>36y = 45 \u00b7 32                 Simplify<\/p>\n\n\n\n<p>36y = 1,440                Simplify<\/p>\n\n\n\n<p>y = 40                     Divide both sides by 36<\/p>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-group has-background has-large-font-size\" style=\"background-color:#eaa5a5\"><div class=\"wp-block-group__inner-container is-layout-flow wp-block-group-is-layout-flow\">\n<div class=\"wp-block-group has-background-background-color has-background\"><div class=\"wp-block-group__inner-container is-layout-flow wp-block-group-is-layout-flow\">\n<p class=\"has-text-color has-link-color wp-elements-5281f774c659c5556e1adb358aaa414e\" style=\"color:#b00012\"><strong>\u270f\ufe0f Solve for&nbsp;d&nbsp;in the proportion.<\/strong><\/p>\n\n\n\n<p>d\/26 = 18\/12<\/p>\n\n\n\n<p>d = ____<\/p>\n<\/div><\/div>\n\n\n\n<p>Solve for&nbsp;<em>d<\/em>&nbsp;in the proportion.<\/p>\n\n\n\n<p>d\/26 = 18\/12<\/p>\n\n\n\n<p>d\/26 ( 26.12 ) = 18\/12 ( 26 . 12 )           Multiply both sides by 26 \u00b7 12<\/p>\n\n\n\n<p>12d = 18 \u00b7 26                     Simplify<\/p>\n\n\n\n<p>12<em>d<\/em>&nbsp;=&nbsp;468                        Simplify<\/p>\n\n\n\n<p>d = 39                          Divide both sides by 12<\/p>\n<\/div><\/div>\n\n\n\n<p class=\"has-text-color has-large-font-size\" style=\"color:#d90000\">let&#8217;s practice! \ud83d\udd8a\ufe0f<\/p>\n\n\n\n<div class=\"wp-block-columns is-layout-flex wp-container-core-columns-is-layout-9d6595d7 wp-block-columns-is-layout-flex\">\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\">\n<figure class=\"wp-block-image size-full\"><a href=\"https:\/\/wordwall.net\/play\/83764\/411\/149 \"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/6thclass.deltapublications.in\/wp-content\/uploads\/2023\/04\/Worksheet-1-3-32.png\" alt=\"\" class=\"wp-image-5498\" srcset=\"https:\/\/6thclass.deltapublications.in\/wp-content\/uploads\/2023\/04\/Worksheet-1-3-32.png 500w, https:\/\/6thclass.deltapublications.in\/wp-content\/uploads\/2023\/04\/Worksheet-1-3-32-300x300.png 300w, https:\/\/6thclass.deltapublications.in\/wp-content\/uploads\/2023\/04\/Worksheet-1-3-32-150x150.png 150w, https:\/\/6thclass.deltapublications.in\/wp-content\/uploads\/2023\/04\/Worksheet-1-3-32-400x400.png 400w\" sizes=\"auto, (max-width: 500px) 100vw, 500px\" \/><\/a><\/figure>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\">\n<figure class=\"wp-block-image size-full\"><a href=\"https:\/\/wordwall.net\/play\/86076\/913\/864\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/6thclass.deltapublications.in\/wp-content\/uploads\/2023\/04\/Worksheet-1-1-2-33.png\" alt=\"\" class=\"wp-image-5499\" srcset=\"https:\/\/6thclass.deltapublications.in\/wp-content\/uploads\/2023\/04\/Worksheet-1-1-2-33.png 500w, https:\/\/6thclass.deltapublications.in\/wp-content\/uploads\/2023\/04\/Worksheet-1-1-2-33-300x300.png 300w, https:\/\/6thclass.deltapublications.in\/wp-content\/uploads\/2023\/04\/Worksheet-1-1-2-33-150x150.png 150w, https:\/\/6thclass.deltapublications.in\/wp-content\/uploads\/2023\/04\/Worksheet-1-1-2-33-400x400.png 400w\" sizes=\"auto, (max-width: 500px) 100vw, 500px\" \/><\/a><\/figure>\n<\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>Solve the proportion Key Notes : Definition of Proportion Parts of a Proportion Solving a Proportion using Cross Multiplication Multiply the numerator of the first ratio by the denominator of the second ratio. Multiply the denominator of the first ratio by the numerator of the second ratio. Set both products equal to each other and<a class=\"more-link\" href=\"https:\/\/6thclass.deltapublications.in\/index.php\/m-9-solve-the-proportion\/\">Continue reading <span class=\"screen-reader-text\">&#8220;M.9 Solve the proportion&#8221;<\/span><\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"om_disable_all_campaigns":false,"_mi_skip_tracking":false,"_monsterinsights_sitenote_active":false,"_monsterinsights_sitenote_note":"","_monsterinsights_sitenote_category":0,"footnotes":""},"class_list":["post-217","page","type-page","status-publish","hentry","entry"],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/6thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/217","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/6thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/6thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/6thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/6thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/comments?post=217"}],"version-history":[{"count":13,"href":"https:\/\/6thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/217\/revisions"}],"predecessor-version":[{"id":15466,"href":"https:\/\/6thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/217\/revisions\/15466"}],"wp:attachment":[{"href":"https:\/\/6thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/media?parent=217"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}