{"id":210,"date":"2022-04-12T09:53:59","date_gmt":"2022-04-12T09:53:59","guid":{"rendered":"http:\/\/7thclass.deltapublications.in\/?page_id=210"},"modified":"2025-12-19T05:31:13","modified_gmt":"2025-12-19T05:31:13","slug":"j-10-solve-proportions","status":"publish","type":"page","link":"https:\/\/7thclass.deltapublications.in\/index.php\/j-10-solve-proportions\/","title":{"rendered":"J.10 Solve proportions"},"content":{"rendered":"\n<h2 class=\"wp-block-heading has-text-align-center has-text-color\" style=\"color:#00056d;text-transform:uppercase\"><strong>Solve proportions<\/strong><\/h2>\n\n\n\n<p class=\"has-text-color has-link-color has-huge-font-size wp-elements-28d136ae4331e7eb05ec8e1cb71ebcde\" style=\"color:#74008b\">key notes :<\/p>\n\n\n\n<h3 class=\"wp-block-heading has-large-font-size\">\ud83d\udd22 <strong>What is a Proportion?<\/strong><\/h3>\n\n\n\n<p>\ud83d\udc49 A <strong>proportion<\/strong> shows that <strong>two ratios are equal<\/strong>.<br>\u2728 Example: <\/p>\n\n\n\n<p>2\/4 = 4\/8<\/p>\n\n\n\n<p>Both ratios mean the same thing \u2714\ufe0f<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">\u2696\ufe0f <strong>Parts of a Proportion<\/strong><\/h3>\n\n\n\n<p>In a proportion: <\/p>\n\n\n\n<p>a\/b = c\/d<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>a and d<\/strong> are called <strong>extremes<\/strong> \ud83d\udfe1<\/li>\n\n\n\n<li><strong>b and c<\/strong> are called <strong>means<\/strong> \ud83d\udd35<\/li>\n<\/ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading has-large-font-size\">\u2716\ufe0f <strong>Cross Multiplication Rule<\/strong><\/h3>\n\n\n\n<p>\ud83d\udccc To solve a proportion, <strong>cross multiply<\/strong>: <\/p>\n\n\n\n<p>a\/b = c\/d \u21d2 a\u00d7d = b\u00d7c<\/p>\n\n\n\n<p>\ud83e\udde0 This helps find the <strong>missing value<\/strong> easily!<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading has-large-font-size\">\ud83e\udde9 <strong>Solving a Proportion with a Variable<\/strong><\/h3>\n\n\n\n<p>Example: <\/p>\n\n\n\n<p>3\/5 = x\/10<\/p>\n\n\n\n<p>\ud83d\udc49 Cross multiply: <\/p>\n\n\n\n<p>3\u00d710=5\u00d7x<\/p>\n\n\n\n<p>30 x 10 = 5x<\/p>\n\n\n\n<p>x = 6 \ud83c\udf89<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading has-large-font-size\">\u2705 <strong>Check Your Answer<\/strong><\/h3>\n\n\n\n<p>\ud83d\udd0d Always substitute the value back to see if both ratios are equal.<br>\u2714\ufe0f If they match, your answer is correct!<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading has-large-font-size\">\ud83c\udf1f <strong>Real-Life Examples of Proportions<\/strong><\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\ud83c\udf55 Recipes (ingredients ratio)<\/li>\n\n\n\n<li>\ud83d\udccf Maps and scale drawings<\/li>\n\n\n\n<li>\ud83d\udcb0 Money exchange<\/li>\n\n\n\n<li>\ud83d\udd52 Speed and time problems<\/li>\n<\/ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading has-large-font-size\">\ud83e\udde0 <strong>Helpful Tips<\/strong><\/h3>\n\n\n\n<p>\u2728 Keep fractions <strong>simplified<\/strong><br>\u2728 Cross multiply carefully<br>\u2728 Units on both sides should match \ud83d\udcd0<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading has-large-font-size\">\ud83c\udfaf <strong>Remember!<\/strong><\/h3>\n\n\n\n<p>\ud83d\udc49 Proportions help compare quantities <strong>fairly and accurately<\/strong>.<br>\ud83d\udc49 Cross multiplication is the <strong>key tool<\/strong> \ud83d\udd11<\/p>\n\n\n\n<p class=\"has-text-align-center has-text-color has-large-font-size\" style=\"color:#105000\"><strong>Learn with an example<\/strong><\/p>\n\n\n\n<div class=\"wp-block-group has-large-font-size\"><div class=\"wp-block-group__inner-container is-layout-constrained wp-block-group-is-layout-constrained\">\n<div class=\"wp-block-group has-background\" style=\"background-color:#f8fccc\"><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\" style=\"color:#b00012\">\u270f\ufe0f <strong>Solve for&nbsp;<em>g<\/em>&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 )          <em>Multiply both sides by 16<\/em>g <\/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\" style=\"background-color:#ebfdd3\"><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\" style=\"color:#b00012\">\u270f\ufe0f<strong> 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 )            <em>Multiply both sides by 32 \u00b7 36<\/em><\/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\" style=\"background-color:#fecbcb\"><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\" style=\"color:#b00012\">\u270f\ufe0f <strong>Solve for&nbsp;<em>d<\/em>&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 )           <em>Multiply both sides by 26 \u00b7 12<\/em><\/p>\n\n\n\n<p>12d = 18 \u00b7 26                     Simplify<\/p>\n\n\n\n<p>12<em>d<\/em>&nbsp;=&nbsp;468                        <em>Simplify<\/em><\/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<\/div><\/div>\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\/85930\/887\/999\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/7thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-2-303.png\" alt=\"\" class=\"wp-image-7534\" srcset=\"https:\/\/7thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-2-303.png 500w, https:\/\/7thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-2-303-300x300.png 300w, https:\/\/7thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-2-303-150x150.png 150w, https:\/\/7thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-2-303-400x400.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\/31241\/392\/517\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/7thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-1-313.png\" alt=\"\" class=\"wp-image-7535\" srcset=\"https:\/\/7thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-1-313.png 500w, https:\/\/7thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-1-313-300x300.png 300w, https:\/\/7thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-1-313-150x150.png 150w, https:\/\/7thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-1-313-400x400.png 400w\" sizes=\"auto, (max-width: 500px) 100vw, 500px\" \/><\/a><\/figure>\n<\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>Solve proportions key notes : \ud83d\udd22 What is a Proportion? \ud83d\udc49 A proportion shows that two ratios are equal.\u2728 Example: 2\/4 = 4\/8 Both ratios mean the same thing \u2714\ufe0f \u2696\ufe0f Parts of a Proportion In a proportion: a\/b = c\/d \u2716\ufe0f Cross Multiplication Rule \ud83d\udccc To solve a proportion, cross multiply: a\/b = c\/d<a class=\"more-link\" href=\"https:\/\/7thclass.deltapublications.in\/index.php\/j-10-solve-proportions\/\">Continue reading <span class=\"screen-reader-text\">&#8220;J.10 Solve proportions&#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,"footnotes":""},"class_list":["post-210","page","type-page","status-publish","hentry","entry"],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/7thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/210","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/7thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/7thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/7thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/7thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/comments?post=210"}],"version-history":[{"count":11,"href":"https:\/\/7thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/210\/revisions"}],"predecessor-version":[{"id":17663,"href":"https:\/\/7thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/210\/revisions\/17663"}],"wp:attachment":[{"href":"https:\/\/7thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/media?parent=210"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}