{"id":150,"date":"2022-04-12T12:14:53","date_gmt":"2022-04-12T12:14:53","guid":{"rendered":"http:\/\/8thclass.deltapublications.in\/?page_id=150"},"modified":"2024-11-27T07:09:18","modified_gmt":"2024-11-27T07:09:18","slug":"h-4-equivalent-ratios-word-problems","status":"publish","type":"page","link":"https:\/\/8thclass.deltapublications.in\/index.php\/h-4-equivalent-ratios-word-problems\/","title":{"rendered":"H.4 Equivalent ratios: word problems"},"content":{"rendered":"\n<h2 class=\"wp-block-heading has-text-align-center has-text-color\" style=\"color:#00056d;text-transform:uppercase\"><strong> Equivalent ratios: 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<h3 class=\"wp-block-heading has-text-color has-link-color has-large-font-size wp-elements-68f29114ab89772c6cb9017d916c7799\" style=\"color:#000060\">1. <strong>Understanding Equivalent Ratios<\/strong><\/h3>\n\n\n\n<ul class=\"has-large-font-size wp-block-list\">\n<li>Two ratios are considered <strong>equivalent<\/strong> if they represent the same relationship between the two quantities.<\/li>\n\n\n\n<li><strong>Equivalent ratios<\/strong> can be found by multiplying or dividing both terms of a ratio by the same non-zero number.<\/li>\n<\/ul>\n\n\n\n<p class=\"has-large-font-size\"><strong>Example:<\/strong><\/p>\n\n\n\n<ul class=\"has-large-font-size wp-block-list\">\n<li>Ratio 1: 4:6<\/li>\n\n\n\n<li>Ratio 2: 8:12<\/li>\n\n\n\n<li>These are equivalent because both ratios simplify to 2:3.<\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading has-text-color has-link-color has-large-font-size wp-elements-032f554fb6947a38d8106765593b20a5\" style=\"color:#000060\">2. <strong>Simplifying Ratios to Find Equivalent Ratios<\/strong><\/h3>\n\n\n\n<ul class=\"has-large-font-size wp-block-list\">\n<li>To find equivalent ratios, <strong>simplify<\/strong> the given ratio by dividing both terms by their greatest common factor (GCF).<\/li>\n\n\n\n<li><strong>Example:<br><\/strong>For the ratio 12:18, the GCF is 6. Divide both terms by 6: <\/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=\"262\" height=\"88\" src=\"https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2024\/11\/image-194.png\" alt=\"\" class=\"wp-image-19068\" style=\"width:226px;height:auto\"\/><\/figure><\/div>\n\n\n<ul class=\"wp-block-list\">\n<li class=\"has-large-font-size\">Therefore, 12:18 is equivalent to 2:3.<\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading has-text-color has-link-color has-large-font-size wp-elements-3997f6fc56bac6052ff0038aef24ee17\" style=\"color:#000060\">3. <strong>Multiplying to Find Equivalent Ratios<\/strong><\/h3>\n\n\n\n<ul class=\"has-large-font-size wp-block-list\">\n<li>Alternatively, you can multiply both terms of a ratio by the same number to generate an equivalent ratio.<\/li>\n\n\n\n<li><strong>Example<\/strong>: If the ratio is 2:3 and you multiply both parts by 4, you get 8:12, which is equivalent to 2:3.<\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading has-text-color has-link-color has-large-font-size wp-elements-6e9f7e7efc319debb1c7df718f81e879\" style=\"color:#000060\">4. <strong>Setting Up Word Problems<\/strong><\/h3>\n\n\n\n<ul class=\"has-large-font-size wp-block-list\">\n<li><strong>Identify the ratio<\/strong> described in the word problem.<\/li>\n\n\n\n<li><strong>Set up a proportion<\/strong> if the problem involves finding an unknown value.<\/li>\n\n\n\n<li>Use the property of equivalent ratios to solve for the unknown.<\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading has-text-color has-link-color has-large-font-size wp-elements-33aeef2acb1ea8980ecdb6cc95b34b56\" style=\"color:#000060\">5. <strong>Solving Word Problems<\/strong><\/h3>\n\n\n\n<ul class=\"has-large-font-size wp-block-list\">\n<li><strong>Step 1:<\/strong> Write the given ratios.<\/li>\n\n\n\n<li><strong>Step 2:<\/strong> Set up a proportion (an equation where two ratios are equal).<\/li>\n\n\n\n<li><strong>Step 3:<\/strong> Solve for the unknown variable.<\/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-a428111a2ad242733adf9953e7664c05\" style=\"background-color:#f691a9\"><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-d2ca616ddbb7f547dd2974e69e0dc2c4\" style=\"color:#b00012\"><strong>\u2708\ufe0f Are these ratios equivalent?<\/strong><\/p>\n\n\n\n<p class=\"has-primary-color has-text-color has-link-color wp-elements-0a44d95f686e4dc9597f5b0ca9990ede\"><strong>\u2708\ufe0f 12 medium rugs to 4 small rugs<\/strong><\/p>\n\n\n\n<p class=\"has-primary-color has-text-color has-link-color wp-elements-17b6797af43ac1241cec5c1032ec5fe4\"><strong>\u2708\ufe0f 23 medium rugs to 9 small rugs<\/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>12\/4 and 23\/9<\/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__57_-removebg-preview.png\" alt=\"\" class=\"wp-image-3411\" style=\"width:139px;height:auto\" srcset=\"https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2022\/12\/Untitled_design__57_-removebg-preview.png 500w, https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2022\/12\/Untitled_design__57_-removebg-preview-300x300.png 300w, https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2022\/12\/Untitled_design__57_-removebg-preview-150x150.png 150w\" sizes=\"auto, (max-width: 500px) 100vw, 500px\" \/><\/figure><\/div>\n\n\n<p>12 \u00d7 9 = 4 \u00d7 23 &#8212;&#8211;&gt;Multiply both sides by 4 \u00d7 9<\/p>\n\n\n\n<p>108 \u2260 92 &#8212;&#8212;&gt;<em>Simplify<\/em><\/p>\n\n\n\n<p>The cross products are not equal, so the ratios are not equivalent.<\/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-7fca9d83520df22cd84a5c8ec3588b64\" style=\"background-color:#f9e5b3\"><div class=\"wp-block-group__inner-container is-layout-flow wp-block-group-is-layout-flow\">\n<div class=\"wp-block-group has-tertiary-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-166fd0d23c3733ca30ec3ece7744595c\" style=\"color:#b00012\"><strong>\u2708\ufe0f  Are these ratios equivalent?<\/strong><\/p>\n\n\n\n<p class=\"has-primary-color has-text-color has-link-color wp-elements-759159be87ea1c7f59f356b19e05db90\"><strong>\u2708\ufe0f  18 crossword puzzles to 20 word searches<\/strong><\/p>\n\n\n\n<p class=\"has-primary-color has-text-color has-link-color wp-elements-6fa67008dbf85339fcb13a1792a74d2a\"><strong>\u2708\ufe0f  9 crossword puzzles to 10-word searches<\/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>18\/20 and&nbsp; 9\/10<\/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__58_-removebg-preview.png\" alt=\"\" class=\"wp-image-3417\" style=\"width:127px;height:auto\" srcset=\"https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2022\/12\/Untitled_design__58_-removebg-preview.png 500w, https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2022\/12\/Untitled_design__58_-removebg-preview-300x300.png 300w, https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2022\/12\/Untitled_design__58_-removebg-preview-150x150.png 150w\" sizes=\"auto, (max-width: 500px) 100vw, 500px\" \/><\/figure><\/div>\n\n\n<p>18 \u00d7 10 = 20 \u00d7 9 &#8212;&#8212;-&gt;Multiply both sides by 20 \u00d7 10<\/p>\n\n\n\n<p>180 = 180 &#8212;&#8212;>Simplify<\/p>\n\n\n\n<p>The fractions are equivalent, so the ratios are equivalent.<\/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-7f37d0d73661c67b2923932de2d3bd5e\" style=\"background-color:#7bc8ee\"><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-d2ca616ddbb7f547dd2974e69e0dc2c4\" style=\"color:#b00012\"><strong>\u2708\ufe0f Are these ratios equivalent?<\/strong><\/p>\n\n\n\n<p class=\"has-primary-color has-text-color has-link-color wp-elements-482157e0b5c988128b4ca1f7da9312c8\"><strong>\u2708\ufe0f 42 teachers: 32 students<\/strong><\/p>\n\n\n\n<p class=\"has-primary-color has-text-color has-link-color wp-elements-5123721234c0e4718e0fca76d552df65\"><strong>\u2708\ufe0f 22 teachers: 19 students<\/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>42 \/ 32 and&nbsp; 22 \/ 19<\/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__59_-removebg-preview.png\" alt=\"\" class=\"wp-image-3424\" style=\"width:108px;height:auto\" srcset=\"https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2022\/12\/Untitled_design__59_-removebg-preview.png 500w, https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2022\/12\/Untitled_design__59_-removebg-preview-300x300.png 300w, https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2022\/12\/Untitled_design__59_-removebg-preview-150x150.png 150w\" sizes=\"auto, (max-width: 500px) 100vw, 500px\" \/><\/figure><\/div>\n\n\n<p>42 \u00d7 19 = 32 \u00d7 22 &#8212;&#8212;&gt;Multiply both sides by 32 \u00d7 19<\/p>\n\n\n\n<p>798 \u2260 704 &#8212;&#8211;&gt;<em>Simplify<\/em><\/p>\n\n\n\n<p>The cross-products are not equal, so the ratios are not equivalent.<\/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\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\/81267\/773\/722\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-318.png\" alt=\"\" class=\"wp-image-9666\" srcset=\"https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-318.png 500w, https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-318-300x300.png 300w, https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-318-150x150.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\/81428\/505\/202\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-326.png\" alt=\"\" class=\"wp-image-9667\" srcset=\"https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-326.png 500w, https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-326-300x300.png 300w, https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-326-150x150.png 150w\" sizes=\"auto, (max-width: 500px) 100vw, 500px\" \/><\/a><\/figure>\n<\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>Equivalent ratios: word problems Key Notes : 1. Understanding Equivalent Ratios Example: 2. Simplifying Ratios to Find Equivalent Ratios 3. Multiplying to Find Equivalent Ratios 4. Setting Up Word Problems 5. Solving Word Problems Learn with an example \u2708\ufe0f Are these ratios equivalent? \u2708\ufe0f 12 medium rugs to 4 small rugs \u2708\ufe0f 23 medium rugs<a class=\"more-link\" href=\"https:\/\/8thclass.deltapublications.in\/index.php\/h-4-equivalent-ratios-word-problems\/\">Continue reading <span class=\"screen-reader-text\">&#8220;H.4 Equivalent ratios: 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-150","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\/150","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=150"}],"version-history":[{"count":34,"href":"https:\/\/8thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/150\/revisions"}],"predecessor-version":[{"id":19074,"href":"https:\/\/8thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/150\/revisions\/19074"}],"wp:attachment":[{"href":"https:\/\/8thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/media?parent=150"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}