{"id":160,"date":"2022-04-12T12:16:30","date_gmt":"2022-04-12T12:16:30","guid":{"rendered":"http:\/\/8thclass.deltapublications.in\/?page_id=160"},"modified":"2024-11-28T05:33:05","modified_gmt":"2024-11-28T05:33:05","slug":"h-9-do-the-ratios-form-a-proportion-word-problems","status":"publish","type":"page","link":"https:\/\/8thclass.deltapublications.in\/index.php\/h-9-do-the-ratios-form-a-proportion-word-problems\/","title":{"rendered":"H.9 Do the ratios form a proportion: word problems"},"content":{"rendered":"\n<div class=\"wp-block-group\"><div class=\"wp-block-group__inner-container is-layout-flow wp-block-group-is-layout-flow\">\n<h2 class=\"wp-block-heading has-text-align-center has-text-color\" style=\"color:#00056d;text-transform:uppercase\"><strong>do the ratios form a proportion: word problems<\/strong><\/h2>\n\n\n\n<p class=\"has-text-color has-link-color has-huge-font-size wp-elements-aae0d72b0df05b1a7d05750bd97517d2\" style=\"color:#74008b\"><strong>Key Notes :<\/strong><\/p>\n\n\n\n<h4 class=\"wp-block-heading has-large-font-size\"><strong>Understanding Ratios and Proportions<\/strong><\/h4>\n\n\n\n<ul class=\"has-large-font-size wp-block-list\">\n<li><strong>Ratio<\/strong>: A comparison of two quantities using division. For example, the ratio of 4 to 8 is written as 4:8 or 4\/8.<\/li>\n\n\n\n<li><strong>Proportion<\/strong>: An equation stating that two ratios are equal. For example, 4\/8=1\/2.<\/li>\n<\/ul>\n\n\n\n<h4 class=\"wp-block-heading has-large-font-size\"><strong>Steps to Check if Ratios Form a Proportion<\/strong><\/h4>\n\n\n\n<ol class=\"has-large-font-size wp-block-list\">\n<li><strong>Simplify Ratios<\/strong>: Reduce each ratio to its simplest form by dividing both terms by their greatest common factor (GCF).\n<ul class=\"wp-block-list\">\n<li><strong>Example<\/strong>: 6:9 simplifies to 2:3.<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li><strong>Cross-Multiply<\/strong>: Compare two ratios by cross-multiplying.\n<ul class=\"wp-block-list\">\n<li>If a\/b=c\/d, then a\u22c5d=b\u22c5ca .<\/li>\n\n\n\n<li><strong>Example<\/strong>: Are 3:4 and 6:8 proportional? 3\u00d78=24 and 4\u00d76=24. Since the products are equal, the ratios are proportional.<\/li>\n<\/ul>\n<\/li>\n<\/ol>\n\n\n\n<h4 class=\"wp-block-heading\"><strong>Word Problems Involving Ratios and Proportions<\/strong><\/h4>\n\n\n\n<ol class=\"has-large-font-size wp-block-list\">\n<li><strong>Identify the Ratios<\/strong>: Extract the two ratios from the problem statement.<\/li>\n\n\n\n<li><strong>Simplify or Cross-Multiply<\/strong>: Use either simplification or cross-multiplication to determine if the ratios form a proportion.<\/li>\n\n\n\n<li><strong>Interpret the Result<\/strong>:\n<ul class=\"wp-block-list\">\n<li>If the products of cross-multiplication are equal, the ratios form a proportion.<\/li>\n\n\n\n<li>If they are not equal, the ratios do not form a proportion.<\/li>\n<\/ul>\n<\/li>\n<\/ol>\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-20dad7df8d130d9255b540870045b663\" style=\"background-color:#ffe083\"><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-52ea873c87b4fe3ddb633416dd15c79a\"><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-28b28eeb12e0d397406ab51da3229664\" style=\"color:#b00012\"><strong>\u2708\ufe0f  Do these ratios form a proportion?<\/strong><\/p>\n\n\n\n<p><strong>30 large blankets: 35 medium blankets<\/strong><\/p>\n\n\n\n<p><strong>6 large blankets: 7 medium blankets<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>yes<\/li>\n\n\n\n<li>no<\/li>\n<\/ul>\n<\/div><\/div>\n\n\n\n<p>Write the ratios as fractions.<\/p>\n\n\n\n<p>30\/35 and&nbsp; 6\/7 <\/p>\n\n\n\n<p>Compare the two fractions to see if they are equivalent.<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2022\/12\/Untitled_design__60_-removebg-preview.png\" alt=\"\" class=\"wp-image-3467\" style=\"width:104px;height:auto\" srcset=\"https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2022\/12\/Untitled_design__60_-removebg-preview.png 500w, https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2022\/12\/Untitled_design__60_-removebg-preview-300x300.png 300w, https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2022\/12\/Untitled_design__60_-removebg-preview-150x150.png 150w\" sizes=\"auto, (max-width: 500px) 100vw, 500px\" \/><\/figure><\/div>\n\n\n<p>30 \u00d7 7 = 35 \u00d7 6 &#8212;&#8212;-&gt; Multiply both sides by 35 \u00d7 7<\/p>\n\n\n\n<p>210 = 210 &#8212;&#8212;-&gt; <em>Simplify<\/em><\/p>\n\n\n\n<p>The cross-products are equal, so the ratios form a proportion.<\/p>\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-ada881807987a3285cfcea86d16007c5\" style=\"background-color:#9cf0fa\"><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-84408646db90a40e4aba30e285765e71\"><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-946b6e792e98767acbde7a231372ecf4\" style=\"color:#b00012\"><strong>\u2708\ufe0f Do these ratios form a proportion?<\/strong><\/p>\n\n\n\n<p><strong>9 large cars: 2 medium cars<\/strong><\/p>\n\n\n\n<p><strong>19 large cars: 7 medium cars<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>yes<\/li>\n\n\n\n<li>no<\/li>\n<\/ul>\n<\/div><\/div>\n\n\n\n<p>Write the ratios as fractions.<\/p>\n\n\n\n<p>9\/2 and 19\/7<\/p>\n\n\n\n<p>Compare the two fractions to see if they are equivalent.<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2022\/12\/Untitled_design__61_-removebg-preview.png\" alt=\"\" class=\"wp-image-3470\" style=\"width:129px;height:auto\" srcset=\"https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2022\/12\/Untitled_design__61_-removebg-preview.png 500w, https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2022\/12\/Untitled_design__61_-removebg-preview-300x300.png 300w, https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2022\/12\/Untitled_design__61_-removebg-preview-150x150.png 150w\" sizes=\"auto, (max-width: 500px) 100vw, 500px\" \/><\/figure><\/div>\n\n\n<p>9 \u00d7 7 = 2 \u00d7 19 &#8212;&#8212;&gt; Multiply both sides by 2 \u00d7 7<\/p>\n\n\n\n<p>63 \u2260 38 &#8212;&#8212;&gt; <em>Simplify<\/em><\/p>\n\n\n\n<p>The cross-products are not equal, so the ratios do not form a proportion.<\/p>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-group\"><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-text-color has-background has-link-color has-large-font-size wp-elements-bb7f5a5eeedd4edeea2a6c03db4c98df\" style=\"background-color:#c8fc9a\"><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-3a97d226ae8b76223a69161e64673637\"><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-28b28eeb12e0d397406ab51da3229664\" style=\"color:#b00012\"><strong>\u2708\ufe0f  Do these ratios form a proportion?<\/strong><\/p>\n\n\n\n<p><strong>5 items every 40&nbsp;days<\/strong><\/p>\n\n\n\n<p><strong>3 items every 31&nbsp;days<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>yes<\/li>\n\n\n\n<li>no<\/li>\n<\/ul>\n<\/div><\/div>\n\n\n\n<p>Write the ratios as fractions.<\/p>\n\n\n\n<p>5\/40 and&nbsp; 3\/31 <\/p>\n\n\n\n<p>Compare the two fractions to see if they are equivalent.<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2022\/12\/Untitled_design__62_-removebg-preview.png\" alt=\"\" class=\"wp-image-3473\" style=\"width:105px;height:auto\" srcset=\"https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2022\/12\/Untitled_design__62_-removebg-preview.png 500w, https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2022\/12\/Untitled_design__62_-removebg-preview-300x300.png 300w, https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2022\/12\/Untitled_design__62_-removebg-preview-150x150.png 150w\" sizes=\"auto, (max-width: 500px) 100vw, 500px\" \/><\/figure><\/div>\n\n\n<p>5 \u00d7 31 = 40 \u00d7 3 &#8212;&#8212;-&gt; Multiply both sides by 40 \u00d7 31<\/p>\n\n\n\n<p>155 \u2260 120 &#8212;&#8212;&gt; Simplify<\/p>\n\n\n\n<p>The cross-products are not equal, so the ratios do not form a proportion.<\/p>\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<\/div><\/div>\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\/81271\/508\/354\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-322.png\" alt=\"\" class=\"wp-image-9684\" srcset=\"https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-322.png 500w, https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-322-300x300.png 300w, https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-322-150x150.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\/681\/840\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-330.png\" alt=\"\" class=\"wp-image-9687\" srcset=\"https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-330.png 500w, https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-330-300x300.png 300w, https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-330-150x150.png 150w\" sizes=\"auto, (max-width: 500px) 100vw, 500px\" \/><\/a><\/figure>\n<\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>do the ratios form a proportion: word problems Key Notes : Understanding Ratios and Proportions Steps to Check if Ratios Form a Proportion Word Problems Involving Ratios and Proportions Learn with an example \u2708\ufe0f Do these ratios form a proportion? 30 large blankets: 35 medium blankets 6 large blankets: 7 medium blankets Write the ratios<a class=\"more-link\" href=\"https:\/\/8thclass.deltapublications.in\/index.php\/h-9-do-the-ratios-form-a-proportion-word-problems\/\">Continue reading <span class=\"screen-reader-text\">&#8220;H.9 Do the ratios form a proportion: word problems&#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,"_monsterinsights_skip_tracking":false,"_monsterinsights_sitenote_active":false,"_monsterinsights_sitenote_note":"","_monsterinsights_sitenote_category":0,"footnotes":""},"class_list":["post-160","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\/160","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=160"}],"version-history":[{"count":21,"href":"https:\/\/8thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/160\/revisions"}],"predecessor-version":[{"id":19118,"href":"https:\/\/8thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/160\/revisions\/19118"}],"wp:attachment":[{"href":"https:\/\/8thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/media?parent=160"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}