{"id":162,"date":"2022-04-12T12:16:48","date_gmt":"2022-04-12T12:16:48","guid":{"rendered":"http:\/\/8thclass.deltapublications.in\/?page_id=162"},"modified":"2024-11-28T07:17:33","modified_gmt":"2024-11-28T07:17:33","slug":"h-10-solve-proportions","status":"publish","type":"page","link":"https:\/\/8thclass.deltapublications.in\/index.php\/h-10-solve-proportions\/","title":{"rendered":"H.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-1f2881d6f0121e520e2eb79642f35520\" style=\"color:#74008b\"><strong>key notes :-<\/strong><\/p>\n\n\n\n<h3 class=\"wp-block-heading has-text-color has-link-color has-large-font-size wp-elements-314aab5fe310c0292b474e8951fb9f58\" style=\"color:#000060\">1. <strong>Definition of Proportions<\/strong><\/h3>\n\n\n\n<ul class=\"has-large-font-size wp-block-list\">\n<li>A proportion is an equation that states that two ratios or fractions are equal.<\/li>\n\n\n\n<li>It is expressed in the form: <\/li>\n<\/ul>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"91\" height=\"65\" src=\"https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2024\/11\/image-199.png\" alt=\"\" class=\"wp-image-19125\"\/><\/figure><\/div>\n\n\n<ul class=\"has-large-font-size wp-block-list\">\n<li>The numbers a, b, c, and d are called <strong>terms<\/strong> of the proportion. a and d are called <strong>extremes<\/strong>, and b and c are called <strong>means<\/strong>.<\/li>\n<\/ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity is-style-wide\"\/>\n\n\n\n<h3 class=\"wp-block-heading has-text-color has-link-color has-large-font-size wp-elements-85f5824affb5eb65f3ec2031f9ea4138\" style=\"color:#000060\">2. <strong>Cross Multiplication Method<\/strong><\/h3>\n\n\n\n<ul class=\"has-large-font-size wp-block-list\">\n<li>To solve proportions, we can use the <strong>cross-multiplication<\/strong> method.<\/li>\n\n\n\n<li>Cross-multiply the extremes and the means:     a\u00d7d=b\u00d7c<\/li>\n\n\n\n<li>Then, solve for the unknown term.<\/li>\n<\/ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity is-style-wide\"\/>\n\n\n\n<h3 class=\"wp-block-heading has-text-color has-link-color has-large-font-size wp-elements-083a38100ec297be60ee3c3d4abbbc5f\" style=\"color:#000060\">3. <strong>Example of Solving Proportions<\/strong><\/h3>\n\n\n\n<ul class=\"has-large-font-size wp-block-list\">\n<li><strong>Problem<\/strong>: Solve the proportion <\/li>\n<\/ul>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"83\" height=\"47\" src=\"https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2024\/11\/image-200.png\" alt=\"\" class=\"wp-image-19127\" style=\"width:93px;height:auto\"\/><\/figure><\/div>\n\n\n<ul class=\"has-large-font-size wp-block-list\">\n<li><strong>Step 1<\/strong>: Cross-multiply: 3\u00d78 = 4\u00d7x.<\/li>\n\n\n\n<li><strong>Step 2<\/strong>: Simplify: 24 = 4x.<\/li>\n\n\n\n<li><strong>Step 3<\/strong>: Solve for x:<\/li>\n<\/ul>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"166\" height=\"82\" src=\"https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2024\/11\/image-201.png\" alt=\"\" class=\"wp-image-19128\"\/><\/figure><\/div>\n\n\n<ul class=\"has-large-font-size wp-block-list\">\n<li>So, x=6.<\/li>\n<\/ul>\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-primary-color has-text-color has-background has-link-color has-large-font-size wp-elements-07d12a0209bd69683791c839985182d4\" style=\"background-color:#a3e9ff\"><div class=\"wp-block-group__inner-container is-layout-flow wp-block-group-is-layout-flow\">\n<div class=\"wp-block-group has-primary-color has-background-background-color has-text-color has-background has-link-color wp-elements-b25feb576026c252763f80e85762644b\"><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-81cad7bfc68ec55c0ef06e903c4d1d09\" style=\"color:#b00012\"><strong>\u2708\ufe0f  Solve for&nbsp;w&nbsp;in the proportion.<\/strong><\/p>\n\n\n\n<p><strong>4\/6 = 6\/w<\/strong><\/p>\n\n\n\n<p><em>w<\/em>&nbsp;=&nbsp;____<\/p>\n<\/div><\/div>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Solve for&nbsp;<em>w<\/em>&nbsp;in the proportion.<\/li>\n\n\n\n<li>4\/6 = 6\/w<\/li>\n\n\n\n<li>4\/6 ( 6w ) = 6\/w ( 6w ) &#8212;&#8212;-&gt; Multiply both sides by 6w<\/li>\n\n\n\n<li>4w = 6 \u00b7 6 &#8212;&#8212;&#8211;&gt;Simplify<\/li>\n\n\n\n<li>4w&nbsp;=&nbsp;36 &#8212;&#8212;-&gt; Simplify<\/li>\n\n\n\n<li>w&nbsp;=&nbsp;9 &#8212;&#8211;&gt;Divide both sides by 4<\/li>\n<\/ul>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-group has-primary-color has-text-color has-background has-link-color has-large-font-size wp-elements-cf7aa1c1501da7e78375568f6697f1da\" style=\"background-color:#f9efa1\"><div class=\"wp-block-group__inner-container is-layout-flow wp-block-group-is-layout-flow\">\n<div class=\"wp-block-group has-primary-color has-background-background-color has-text-color has-background has-link-color wp-elements-daf6ec9b9777a9fd7e10187f89870789\"><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-2f73ac0c2e6a75b36ab0ea87e6e70306\" style=\"color:#b00012\"><strong>\u2708\ufe0f Solve for&nbsp;d&nbsp;in the proportion.<\/strong><\/p>\n\n\n\n<p><strong>1\/4 = 2\/d<\/strong><\/p>\n\n\n\n<p><em>d<\/em>&nbsp;= ____<\/p>\n<\/div><\/div>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Solve for&nbsp;d&nbsp;in the proportion.<\/li>\n\n\n\n<li>1\/4 = 2\/d<\/li>\n\n\n\n<li>1\/4 ( 4d ) = 2\/d ( 4d ) &#8212;&#8212;-&gt;Multiply both sides by 4d<\/li>\n\n\n\n<li>d&nbsp;=&nbsp;4 \u00b7 2 &#8212;&#8212;&gt; Simplify<\/li>\n\n\n\n<li>d&nbsp;=&nbsp;8 &#8212;&#8212;-&gt; Simplify<\/li>\n<\/ul>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-group has-primary-color has-text-color has-background has-link-color has-large-font-size wp-elements-62c46a2891bef3666148b5685035cbb3\" style=\"background-color:#f7b8ef\"><div class=\"wp-block-group__inner-container is-layout-flow wp-block-group-is-layout-flow\">\n<div class=\"wp-block-group has-primary-color has-tertiary-background-color has-text-color has-background has-link-color wp-elements-bd612953280ba751ad579860c6ed3194\"><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-8c6ed1549e9943f696b6e90d86574d81\" style=\"color:#b00012\"><strong>\u2708\ufe0f Solve for&nbsp;t&nbsp;in the proportion.<\/strong><\/p>\n\n\n\n<p><strong>10\/t = 8\/12<\/strong><\/p>\n\n\n\n<p>t= __<\/p>\n<\/div><\/div>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Solve for&nbsp;<em>t<\/em>&nbsp;in the proportion.<\/li>\n\n\n\n<li>10\/t = 8\/12<\/li>\n\n\n\n<li>10\/t ( 12t ) = 8\/12 ( 12t ) &#8212;&#8212;&gt; Multiply both sides by 12t<\/li>\n\n\n\n<li>12 \u00b7 10&nbsp;=&nbsp;8t &#8212;&#8212;&gt; Simplify<\/li>\n\n\n\n<li>120&nbsp;=&nbsp;8t &#8212;&#8212;&gt; Simplify<\/li>\n\n\n\n<li>15&nbsp;=&nbsp;t &#8212;&#8212;&gt; Divide both sides by 8<\/li>\n<\/ul>\n<\/div><\/div>\n\n\n\n<p class=\"has-text-color has-large-font-size\" style=\"color:#d90000\"><strong>Let&#8217;s practice! \ud83d\udd8a\ufe0f<\/strong><\/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\/81271\/722\/290\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-321.png\" alt=\"\" class=\"wp-image-9681\" srcset=\"https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-321.png 500w, https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-321-300x300.png 300w, https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-321-150x150.png 150w\" 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\/81430\/773\/136\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-329.png\" alt=\"\" class=\"wp-image-9682\" srcset=\"https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-329.png 500w, https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-329-300x300.png 300w, https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-329-150x150.png 150w\" sizes=\"auto, (max-width: 500px) 100vw, 500px\" \/><\/a><\/figure>\n<\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>Solve proportions key notes :- 1. Definition of Proportions 2. Cross Multiplication Method 3. Example of Solving Proportions Learn with an example \u2708\ufe0f Solve for&nbsp;w&nbsp;in the proportion. 4\/6 = 6\/w w&nbsp;=&nbsp;____ \u2708\ufe0f Solve for&nbsp;d&nbsp;in the proportion. 1\/4 = 2\/d d&nbsp;= ____ \u2708\ufe0f Solve for&nbsp;t&nbsp;in the proportion. 10\/t = 8\/12 t= __ Let&#8217;s practice! \ud83d\udd8a\ufe0f<\/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,"_monsterinsights_skip_tracking":false,"_monsterinsights_sitenote_active":false,"_monsterinsights_sitenote_note":"","_monsterinsights_sitenote_category":0,"footnotes":""},"class_list":["post-162","page","type-page","status-publish","hentry","entry"],"aioseo_notices":[],"_hostinger_reach_plugin_has_subscription_block":false,"_hostinger_reach_plugin_is_elementor":false,"_links":{"self":[{"href":"https:\/\/8thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/162","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/8thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/8thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/8thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/8thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/comments?post=162"}],"version-history":[{"count":18,"href":"https:\/\/8thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/162\/revisions"}],"predecessor-version":[{"id":19285,"href":"https:\/\/8thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/162\/revisions\/19285"}],"wp:attachment":[{"href":"https:\/\/8thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/media?parent=162"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}