{"id":208,"date":"2022-04-12T09:53:38","date_gmt":"2022-04-12T09:53:38","guid":{"rendered":"http:\/\/7thclass.deltapublications.in\/?page_id=208"},"modified":"2025-12-19T05:31:12","modified_gmt":"2025-12-19T05:31:12","slug":"j-9-do-the-ratios-form-a-proportion-word-problems","status":"publish","type":"page","link":"https:\/\/7thclass.deltapublications.in\/index.php\/j-9-do-the-ratios-form-a-proportion-word-problems\/","title":{"rendered":"J.9 Do the ratios form a proportion: word problems"},"content":{"rendered":"\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-huge-font-size\" style=\"color:#74008b\">Key notes:<\/p>\n\n\n\n<h3 class=\"wp-block-heading has-large-font-size\">\ud83d\udd22 What is a Ratio?<\/h3>\n\n\n\n<p>\u27a1\ufe0f A <strong>ratio<\/strong> compares two quantities using:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Colon<\/strong> \ud83d\udc49 3 : 5<\/li>\n\n\n\n<li><strong>Fraction<\/strong> \ud83d\udc49 3\/5<\/li>\n\n\n\n<li><strong>Words<\/strong> \ud83d\udc49 3 to 5<\/li>\n<\/ul>\n\n\n\n<p>\u2728 Example:<br>\ud83d\udd8d\ufe0f Red pencils : Blue pencils = <strong>4 : 6<\/strong><\/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\">\u2696\ufe0f What is a Proportion?<\/h3>\n\n\n\n<p>\u27a1\ufe0f A <strong>proportion<\/strong> says <strong>two ratios are equal<\/strong>.<\/p>\n\n\n\n<p>\ud83d\udccc Written as:<br>\ud83d\udc49 a : b = c : d<br>\ud83d\udc49 a\/b = c\/d<\/p>\n\n\n\n<p>\u2728 Example:<br>\ud83c\udf4e 2 apples : 4 apples = 4 apples : 8 apples \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 has-large-font-size\">\u2705 How to Check if Ratios Form a Proportion<\/h3>\n\n\n\n<p>\ud83d\udd01 <strong>Cross Multiply!<\/strong><\/p>\n\n\n\n<p>\ud83d\udc49 If <strong>a \u00d7 d = b \u00d7 c<\/strong>, then it <strong>IS a proportion<\/strong> \ud83c\udf89<\/p>\n\n\n\n<p>\ud83e\uddee Example:<br>3 : 5 and 6 : 10<br>\u27a1\ufe0f 3 \u00d7 10 = 30<br>\u27a1\ufe0f 5 \u00d7 6 = 30<br>\u2714\ufe0f Yes! They form a proportion \ud83d\udc4d<\/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\">\u274c When Do Ratios NOT Form a Proportion?<\/h3>\n\n\n\n<p>\ud83d\udeab If cross products are <strong>not equal<\/strong>, it is <strong>NOT a proportion<\/strong>.<\/p>\n\n\n\n<p>\ud83e\uddee Example:<br>4 : 7 and 8 : 15<br>\u27a1\ufe0f 4 \u00d7 15 = 60<br>\u27a1\ufe0f 7 \u00d7 8 = 56<br>\u274c Not equal \u2192 Not a proportion<\/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\">\ud83d\udcd6 Proportion Word Problems \u2013 Key Clues<\/h3>\n\n\n\n<p>\ud83d\udd0d Look for words like:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>per<\/strong><\/li>\n\n\n\n<li><strong>for every<\/strong><\/li>\n\n\n\n<li><strong>same rate<\/strong><\/li>\n\n\n\n<li><strong>same speed<\/strong><\/li>\n\n\n\n<li><strong>same cost<\/strong><\/li>\n<\/ul>\n\n\n\n<p>\u2728 Example:<br>\ud83d\ude97 A car travels 60 km in 2 hours and 90 km in 3 hours.<br>\u27a1\ufe0f 60 : 2 = 30<br>\u27a1\ufe0f 90 : 3 = 30<br>\u2714\ufe0f Same ratio \u2192 Proportion \ud83d\ude80<\/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\udde0 6. Real-Life Examples<\/h3>\n\n\n\n<p>\ud83c\udfeb Class strength<br>\ud83d\udcb0 Money &amp; shopping<br>\u23f1\ufe0f Speed &amp; time<br>\ud83d\udce6 Cost per item<\/p>\n\n\n\n<p>\u2728 Example:<br>\ud83d\uded2 5 notebooks cost \u20b9100<br>\ud83d\uded2 10 notebooks cost \u20b9200<br>\u27a1\ufe0f 5 : 100 = 10 : 200 \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 has-large-font-size\">\ud83d\udcdd 7. Steps to Solve Word Problems<\/h3>\n\n\n\n<p>1\ufe0f\u20e3 Write the <strong>two ratios<\/strong><br>2\ufe0f\u20e3 Convert them to <strong>fractions<\/strong><br>3\ufe0f\u20e3 <strong>Cross multiply<\/strong><br>4\ufe0f\u20e3 Compare the results<br>5\ufe0f\u20e3 Decide \u2714\ufe0f or \u274c<\/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 8. Remember!<\/h3>\n\n\n\n<p>\ud83d\udca1 Equal ratios = <strong>Proportion<\/strong><br>\ud83d\udca1 Unequal ratios = <strong>Not a proportion<\/strong><br>\ud83d\udca1 Cross multiplication is the <strong>key<\/strong> \ud83d\udd11<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<p>\ud83c\udf89\ud83d\udcda <strong>Learning Tip:<\/strong><br>\ud83d\udc49 Always check the <strong>units<\/strong> (km, hours, rupees, items) before comparing ratios!<\/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<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-background\" style=\"background-color:#f0fddb\"><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>Do these ratios form a proportion?<\/strong><\/p>\n\n\n\n<p>8 large paper clips to 12 small paper clips<\/p>\n\n\n\n<p>12 large paper clips to 18 small paper clips<\/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>8\/12 and 12\/18<\/p>\n\n\n\n<p>Compare the two fractions to see if they are equivalent.<\/p>\n\n\n\n<p>8\/12 = 12\/18<\/p>\n\n\n\n<p>8 \u00d7 18 = 12 \u00d7 12           Multiply both sides by 12 \u00d7 18<\/p>\n\n\n\n<p>144 = 144            Simplify<\/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-background\" style=\"background-color:#ffdbd4\"><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> Do these ratios form a proportion?<\/strong><\/p>\n\n\n\n<p>9 large rugs to 18 small rugs<\/p>\n\n\n\n<p>1 large rug to 2 small rugs<\/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\/18 and 1\/2<\/p>\n\n\n\n<p>Compare the two fractions to see if they are equivalent.<\/p>\n\n\n\n<p>9\/18 = 1\/2<\/p>\n\n\n\n<p>9 \u00d7 2 = 18 \u00d7 1           Multiply both sides by 18 \u00d7 2<\/p>\n\n\n\n<p>18 = 18            Simplify<\/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-background\" style=\"background-color:#f4f6d0\"><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>Do these ratios form a proportion?<\/strong><\/p>\n\n\n\n<p>16 biscuits to 10 brownies<\/p>\n\n\n\n<p>8 biscuits to 5 brownies<\/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>16\/10 and 8\/5<\/p>\n\n\n\n<p>Compare the two fractions to see if they are equivalent.<\/p>\n\n\n\n<p>16\/10 = 8\/5<\/p>\n\n\n\n<p>16 \u00d7 5 = 10 \u00d7 8           Multiply both sides by 10 \u00d7 5<\/p>\n\n\n\n<p>80 = 80            Simplify<\/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<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\/081\/589\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/7thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-2-315.png\" alt=\"\" class=\"wp-image-7571\" srcset=\"https:\/\/7thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-2-315.png 500w, https:\/\/7thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-2-315-300x300.png 300w, https:\/\/7thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-2-315-150x150.png 150w, https:\/\/7thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-2-315-400x400.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\/299\/404\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/7thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-1-325.png\" alt=\"\" class=\"wp-image-7572\" srcset=\"https:\/\/7thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-1-325.png 500w, https:\/\/7thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-1-325-300x300.png 300w, https:\/\/7thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-1-325-150x150.png 150w, https:\/\/7thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-1-325-400x400.png 400w\" 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: \ud83d\udd22 What is a Ratio? \u27a1\ufe0f A ratio compares two quantities using: \u2728 Example:\ud83d\udd8d\ufe0f Red pencils : Blue pencils = 4 : 6 \u2696\ufe0f What is a Proportion? \u27a1\ufe0f A proportion says two ratios are equal. \ud83d\udccc Written as:\ud83d\udc49 a : b = c :<a class=\"more-link\" href=\"https:\/\/7thclass.deltapublications.in\/index.php\/j-9-do-the-ratios-form-a-proportion-word-problems\/\">Continue reading <span class=\"screen-reader-text\">&#8220;J.9 Do the ratios form a proportion: word 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