{"id":52,"date":"2022-04-13T06:12:35","date_gmt":"2022-04-13T06:12:35","guid":{"rendered":"http:\/\/9thclass.deltapublications.in\/?page_id=52"},"modified":"2025-11-21T07:28:13","modified_gmt":"2025-11-21T07:28:13","slug":"c-6-solve-proportions-word-problems","status":"publish","type":"page","link":"https:\/\/9thclass.deltapublications.in\/index.php\/c-6-solve-proportions-word-problems\/","title":{"rendered":"C.6 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<figure class=\"wp-block-video\"><video controls src=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/08\/Class-9-C.6-Solve-proportions_-word-problems.mp4\"><\/video><\/figure>\n\n\n\n<p class=\"has-text-color has-link-color has-large-font-size wp-elements-101e71c1795ccf1255759850f5f76b85\" style=\"color:#74008b\"><strong>Key notes :-<\/strong><\/p>\n\n\n\n<h3 class=\"wp-block-heading has-large-font-size\"><strong>1\ufe0f\u20e3 What is a Proportion?<\/strong><\/h3>\n\n\n\n<p>A <strong>proportion<\/strong> is an equation that shows <strong>two ratios are equal<\/strong>.<br>\ud83d\udd39 Example: <\/p>\n\n\n\n<p class=\"has-text-align-center\"><strong>a\/b = c\/d<\/strong><\/p>\n\n\n\n<p>\u2705 Means: a:b = c:d<\/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\"><strong>2\ufe0f\u20e3 How to Solve Proportions<\/strong><\/h3>\n\n\n\n<p><strong>Set up the proportion<\/strong> from the word problem \ud83d\udcdd<\/p>\n\n\n\n<p><strong>Use cross-multiplication<\/strong> to find the unknown \ud83d\udd04<\/p>\n\n\n\n<p class=\"has-text-align-center\"><strong> a:b = c:x\u2005\u200a\u27f9\u2005\u200aa\u22c5x = b\u22c5c<\/strong><\/p>\n\n\n\n<p><strong>Solve for the unknown<\/strong> number \u270f\ufe0f<\/p>\n\n\n\n<p><strong>Check your answer<\/strong> by substituting it back \u2705<\/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\"><strong>3\ufe0f\u20e3 Steps for Word Problems<\/strong><\/h3>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>Read carefully<\/strong> \ud83d\udcd6 \u2013 Identify what is known and what you need.<\/li>\n\n\n\n<li><strong>Assign variables<\/strong> \u270d\ufe0f \u2013 Let xxx be the unknown.<\/li>\n\n\n\n<li><strong>Write a ratio or fraction<\/strong> \ud83d\udd22 \u2013 Match quantities correctly.<\/li>\n\n\n\n<li><strong>Set up the proportion<\/strong> \u2696\ufe0f \u2013 Make the ratios equal.<\/li>\n\n\n\n<li><strong>Solve using cross-multiplication<\/strong> \u2716\ufe0f\u2797<\/li>\n\n\n\n<li><strong>Answer with correct units<\/strong> \ud83c\udff7\ufe0f<\/li>\n<\/ol>\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\"><strong>4\ufe0f\u20e3 Tips &amp; Tricks<\/strong><\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Keep units <strong>consistent<\/strong> (kg, m, liters\u2026) \u2696\ufe0f<\/li>\n\n\n\n<li>Check if the proportion makes <strong>logical sense<\/strong> \ud83d\udca1<\/li>\n\n\n\n<li>For <strong>percent problems<\/strong>, convert % to <strong>fractions<\/strong> first \ud83d\udd22<\/li>\n\n\n\n<li>Always <strong>simplify fractions<\/strong> if possible \u2728<\/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\"><strong>5\ufe0f\u20e3 Example Problem<\/strong><\/h3>\n\n\n\n<p><strong>Problem:<\/strong><br>A recipe needs 3 cups of sugar for 4 cups of flour. How much sugar is needed for 10 cups of flour? \ud83c\udf70<\/p>\n\n\n\n<p><strong>Solution:<\/strong> <\/p>\n\n\n\n<p>3\/4 = x\/10<\/p>\n\n\n\n<p>Cross multiply: <\/p>\n\n\n\n<p>4x = 30\u2005\u200a\u27f9\u2005\u200ax = 7.5<\/p>\n\n\n\n<p>\u2705 <strong>Answer:<\/strong> 7.5 cups of sugar<\/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\"><strong>6\ufe0f\u20e3 Fun Emoji Reminder<\/strong><\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Ratios:<\/strong> \ud83d\udd39\ud83d\udd38<\/li>\n\n\n\n<li><strong>Unknown:<\/strong> \u2753<\/li>\n\n\n\n<li><strong>Cross Multiply:<\/strong> \u2716\ufe0f<\/li>\n\n\n\n<li><strong>Check Answer:<\/strong> \u2705<\/li>\n\n\n\n<li><strong>Units:<\/strong> \ud83c\udff7\ufe0f<\/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-872b3678293f3da3e330afd3140cb460\" style=\"background-color:#f3bcbc\"><div class=\"wp-block-group__inner-container is-layout-constrained wp-block-group-is-layout-constrained\">\n<div class=\"wp-block-group has-background-background-color has-background\"><div class=\"wp-block-group__inner-container is-layout-constrained wp-block-group-is-layout-constrained\">\n<p class=\"has-text-color\" style=\"color:#b00012\"><strong>\ud83d\udd14 Jonah prepared 4 kilograms of dough after working 2 hours. How much dough did Jonah prepare if he worked for 7 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>4 kilograms \/ 2 hours = n kilograms \/ 7 hours<\/p>\n\n\n\n<p>4\/2 ( 2 . 7 ) = n\/7  ( 2 . 7 )            <em>Multiply both sides by 2 \u00b7 7<\/em><\/p>\n\n\n\n<p>4 \u00b7 7 = 2n                                  Simplify<\/p>\n\n\n\n<p>28 = 2n                                 Multiply<\/p>\n\n\n\n<p>14 = n                               Divide both sides by 2<\/p>\n\n\n\n<p>If Jonah worked for 7 hours, he prepared 14 kilograms of dough.<\/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-819e08dce2e8881a08be48406f9c1597\" style=\"background-color:#c0d7f6\"><div class=\"wp-block-group__inner-container is-layout-constrained wp-block-group-is-layout-constrained\">\n<div class=\"wp-block-group has-background-background-color has-background\"><div class=\"wp-block-group__inner-container is-layout-constrained wp-block-group-is-layout-constrained\">\n<p class=\"has-text-color\" style=\"color:#b00012\"><strong>\ud83d\udd14 Ronald spent 8 minutes on the phone while routeing 4 phone calls. In all, how many phone calls does Ronald have to route to spend a total of 14 minutes on the phone? Assume the relationship is directly proportional.<\/strong><\/p>\n\n\n\n<p>______&nbsp;phone calls<\/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>8 minutes \/ 4 phone calls = 14 minutes \/ n phone calls<\/p>\n\n\n\n<p>8\/4 ( 4n ) = 14\/n ( 4n )                   <em>Multiply both sides by 4<\/em>n<\/p>\n\n\n\n<p>8n = 14 \u00b7 4                                  Simplify<\/p>\n\n\n\n<p>8n = 56                                   Multiply<\/p>\n\n\n\n<p>n = 7                                   Divide both sides by 8<\/p>\n\n\n\n<p>To spend a total of 14 minutes on the phone, Ronald has to route 7 phone calls.<\/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-e87e01a6f13dc5afa6e9ac97bdc2061b\" style=\"background-color:#e8f9c9\"><div class=\"wp-block-group__inner-container is-layout-constrained wp-block-group-is-layout-constrained\">\n<div class=\"wp-block-group has-background-background-color has-background\"><div class=\"wp-block-group__inner-container is-layout-constrained wp-block-group-is-layout-constrained\">\n<p class=\"has-text-color\" style=\"color:#b00012\"><strong>\ud83d\udd14 Rodrigo prepared 4 kilograms of dough after working 2 hours. How much dough did Rodrigo prepare if he worked for 8 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>4 kilograms \/ 2 hours = n kilograms \/ 8hours <\/p>\n\n\n\n<p>4\/2 (2 . 8) = n\/8 (2 . 8)             Multiply both sides by 2 \u00b7 8<\/p>\n\n\n\n<p>4 \u00b7 8 = 2n                            Simplify<\/p>\n\n\n\n<p>32 = 2n                          Multiply<\/p>\n\n\n\n<p>16 = n                       Divide both sides by 2<\/p>\n\n\n\n<p>If Rodrigo worked for 8 hours, he prepared 16 kilograms of dough.<\/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!<\/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\/76289\/102\/850\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-14.png\" alt=\"\" class=\"wp-image-7306\" srcset=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-14.png 500w, https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-14-300x300.png 300w, https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-14-150x150.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\/76327\/504\/235\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-15.png\" alt=\"\" class=\"wp-image-7307\" srcset=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-15.png 500w, https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-15-300x300.png 300w, https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-15-150x150.png 150w\" 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 :- 1\ufe0f\u20e3 What is a Proportion? A proportion is an equation that shows two ratios are equal.\ud83d\udd39 Example: a\/b = c\/d \u2705 Means: a:b = c:d 2\ufe0f\u20e3 How to Solve Proportions Set up the proportion from the word problem \ud83d\udcdd Use cross-multiplication to find the unknown \ud83d\udd04 a:b =<a class=\"more-link\" href=\"https:\/\/9thclass.deltapublications.in\/index.php\/c-6-solve-proportions-word-problems\/\">Continue reading <span class=\"screen-reader-text\">&#8220;C.6 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,"_monsterinsights_skip_tracking":false,"_monsterinsights_sitenote_active":false,"_monsterinsights_sitenote_note":"","_monsterinsights_sitenote_category":0,"footnotes":""},"class_list":["post-52","page","type-page","status-publish","hentry","entry"],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/9thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/52","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/9thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/9thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/9thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/9thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/comments?post=52"}],"version-history":[{"count":18,"href":"https:\/\/9thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/52\/revisions"}],"predecessor-version":[{"id":18265,"href":"https:\/\/9thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/52\/revisions\/18265"}],"wp:attachment":[{"href":"https:\/\/9thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/media?parent=52"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}