{"id":212,"date":"2022-04-12T09:54:17","date_gmt":"2022-04-12T09:54:17","guid":{"rendered":"http:\/\/7thclass.deltapublications.in\/?page_id=212"},"modified":"2025-12-19T05:31:36","modified_gmt":"2025-12-19T05:31:36","slug":"j-11-solve-proportions-word-problems","status":"publish","type":"page","link":"https:\/\/7thclass.deltapublications.in\/index.php\/j-11-solve-proportions-word-problems\/","title":{"rendered":"J.11 Solve proportions: word problems"},"content":{"rendered":"\n<h2 class=\"wp-block-heading has-text-align-center has-text-color\" style=\"color:#00056d;text-transform:uppercase\"><strong> Solve proportions: word problems<\/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\udd0d What is a Proportion?<\/h3>\n\n\n\n<p>\ud83d\udc49 A <strong>proportion<\/strong> shows that <strong>two ratios are equal<\/strong>.<br>\ud83e\uddee Example: <\/p>\n\n\n\n<p>2\/3 = 4\/6<\/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 Key Parts of a Proportion<\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\ud83d\udd22 <strong>Ratio<\/strong>: A comparison of two numbers (like 3:5 or 3\/5)<\/li>\n\n\n\n<li>\u2696\ufe0f <strong>Proportion<\/strong>: Two equal ratios<\/li>\n\n\n\n<li>\u2716\ufe0f <strong>Cross products<\/strong>: Multiply across to solve<\/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 Steps to Solve Proportion Word Problems<\/h3>\n\n\n\n<p>1\ufe0f\u20e3 <strong>Read carefully<\/strong> \ud83d\udcd6<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Find what is <strong>given<\/strong> and what is <strong>unknown<\/strong><\/li>\n<\/ul>\n\n\n\n<p>2\ufe0f\u20e3 <strong>Write the ratio<\/strong> \u270d\ufe0f<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Use fractions or \u201c:\u201d symbols<\/li>\n<\/ul>\n\n\n\n<p>3\ufe0f\u20e3 <strong>Set up a proportion<\/strong> \u2696\ufe0f<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Make two ratios equal<\/li>\n<\/ul>\n\n\n\n<p>4\ufe0f\u20e3 <strong>Cross multiply<\/strong> \u2716\ufe0f<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Multiply diagonally<\/li>\n<\/ul>\n\n\n\n<p>5\ufe0f\u20e3 <strong>Solve for the unknown<\/strong> \ud83d\udd0d<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Divide to find the answer<\/li>\n<\/ul>\n\n\n\n<p>6\ufe0f\u20e3 <strong>Check your answer<\/strong> \u2705<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Substitute back to see if it works<\/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\">\ud83d\udcdd Example<\/h3>\n\n\n\n<p>\ud83e\uddc3 <em>If 3 bottles of juice cost \u20b960, how much do 5 bottles cost?<\/em><\/p>\n\n\n\n<p>Step 1\ufe0f\u20e3 Write the proportion <\/p>\n\n\n\n<p>3\/60 = 5\/x<\/p>\n\n\n\n<p>Step 2\ufe0f\u20e3 Cross multiply <\/p>\n\n\n\n<p>3\/x = 300<\/p>\n\n\n\n<p>Step 3\ufe0f\u20e3 Solve <\/p>\n\n\n\n<p>x=100<\/p>\n\n\n\n<p>\u2705 <strong>Answer: 5 bottles cost \u20b9100<\/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\">\ud83c\udf0d Where Do We Use Proportions?<\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\ud83d\uded2 Shopping (price comparison)<\/li>\n\n\n\n<li>\ud83c\udf55 Recipes (scaling ingredients)<\/li>\n\n\n\n<li>\ud83d\ude97 Speed &amp; distance<\/li>\n\n\n\n<li>\ud83d\udcd0 Maps and scale drawings<\/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\">\u26a0\ufe0f Common Mistakes to Avoid<\/h3>\n\n\n\n<p>\u274c Mixing up numbers in ratios<br>\u274c Forgetting to cross multiply<br>\u274c Not checking the final answer<\/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 Quick Tip<\/h3>\n\n\n\n<p>\ud83d\udca1 <strong>Always keep units the same<\/strong> (rupees with rupees, km with km)<\/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:#e7d1f4\"><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> Shelley took a total of 10 pages of notes during 5 hours of class. After attending 6 hours of class, how many total pages of notes will Shelley have in her notebook? Assume the relationship is directly proportional.<\/strong><\/p>\n\n\n\n<p>______ pages<\/p>\n<\/div><\/div>\n\n\n\n<p>Set up a proportion and solve for&nbsp;<em>n<\/em>.<\/p>\n\n\n\n<p>10 pages \/ 5 hours = n pages \/ 6 hours<\/p>\n\n\n\n<p>10 \/ 5 ( 5 . 6 ) = n \/6  ( 5 . 6 )              Multiply both sides by 5 \u00b7 6<\/p>\n\n\n\n<p>10 \u00b7 6 = 5n               Simplify<\/p>\n\n\n\n<p>60 = 5n                 Multiply<\/p>\n\n\n\n<p>12 = n                 Divide both sides by 5<\/p>\n\n\n\n<p>After attending 6 hours of class, Shelley will have a total of 12 pages of notes in her notebook.<\/p>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-group has-background\" style=\"background-color:#fcf0d2\"><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> Rob jarred 4 litres of jam after 2 days. How many days does Rob need to spend making jam if he wants to jar 6 litres of jam in all? Assume the relationship is directly proportional.<\/strong><\/p>\n\n\n\n<p>_____ days<\/p>\n<\/div><\/div>\n\n\n\n<p>Set up a proportion and solve for&nbsp;<em>n<\/em>.<\/p>\n\n\n\n<p>4 litres \/ 2 days = 6 litres \/ n days<\/p>\n\n\n\n<p>4\/2 ( 2n ) = 6\/n ( 2n )                  <em>Multiply both sides by 2<\/em>n<\/p>\n\n\n\n<p>4n = 6 \u00b7 2                         Simplify<\/p>\n\n\n\n<p>4n = 12                          Multiply<\/p>\n\n\n\n<p>n = 3                          Divide both sides by 4<\/p>\n\n\n\n<p>If Rob wants to jar 6 litres of jam, he will need to spend 3 days making jam.<\/p>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-group has-background\" style=\"background-color:#f6caf0\"><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> Cameron prepared 16 kilograms of dough after working 2 hours. How much dough did Cameron prepare if he worked for 6 hours? Assume the relationship is directly proportional.<\/strong><\/p>\n\n\n\n<p>______&nbsp;kilograms<\/p>\n<\/div><\/div>\n\n\n\n<p>Set up a proportion and solve for&nbsp;<em>n<\/em>.<\/p>\n\n\n\n<p>16 kilograms \/ 2 hours = n kilograms \/ 6 hours<\/p>\n\n\n\n<p>16\/2 ( 2 . 6 ) = n\/6 ( 2 . 6 )                       <em>Multiply both sides by 2 \u00b7 6<\/em><\/p>\n\n\n\n<p>16 \u00b7 6 = 2n                        Simplify<\/p>\n\n\n\n<p>96 = 2n                           Multiply<\/p>\n\n\n\n<p>48 = n                           Divide both sides by 2<\/p>\n\n\n\n<p>If Cameron worked for 6 hours, he prepared 48 kilograms of dough.<\/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\/85931\/504\/523\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/7thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-2-304.png\" alt=\"\" class=\"wp-image-7537\" srcset=\"https:\/\/7thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-2-304.png 500w, https:\/\/7thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-2-304-300x300.png 300w, https:\/\/7thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-2-304-150x150.png 150w, https:\/\/7thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-2-304-400x400.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\/557\/879\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/7thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-1-314.png\" alt=\"\" class=\"wp-image-7538\" srcset=\"https:\/\/7thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-1-314.png 500w, https:\/\/7thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-1-314-300x300.png 300w, https:\/\/7thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-1-314-150x150.png 150w, https:\/\/7thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-1-314-400x400.png 400w\" sizes=\"auto, (max-width: 500px) 100vw, 500px\" \/><\/a><\/figure>\n<\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>Solve proportions: word problems key notes : \ud83d\udd0d What is a Proportion? \ud83d\udc49 A proportion shows that two ratios are equal.\ud83e\uddee Example: 2\/3 = 4\/6 \ud83e\udde9 Key Parts of a Proportion \ud83e\udde0 Steps to Solve Proportion Word Problems 1\ufe0f\u20e3 Read carefully \ud83d\udcd6 2\ufe0f\u20e3 Write the ratio \u270d\ufe0f 3\ufe0f\u20e3 Set up a proportion \u2696\ufe0f 4\ufe0f\u20e3 Cross<a class=\"more-link\" href=\"https:\/\/7thclass.deltapublications.in\/index.php\/j-11-solve-proportions-word-problems\/\">Continue reading <span class=\"screen-reader-text\">&#8220;J.11 Solve proportions: 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,"footnotes":""},"class_list":["post-212","page","type-page","status-publish","hentry","entry"],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/7thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/212","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=212"}],"version-history":[{"count":12,"href":"https:\/\/7thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/212\/revisions"}],"predecessor-version":[{"id":17662,"href":"https:\/\/7thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/212\/revisions\/17662"}],"wp:attachment":[{"href":"https:\/\/7thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/media?parent=212"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}