{"id":80,"date":"2022-04-12T12:02:40","date_gmt":"2022-04-12T12:02:40","guid":{"rendered":"http:\/\/8thclass.deltapublications.in\/?page_id=80"},"modified":"2025-02-22T15:48:02","modified_gmt":"2025-02-22T15:48:02","slug":"e-6-multiply-and-divide-rational-numbers-word-problems","status":"publish","type":"page","link":"https:\/\/8thclass.deltapublications.in\/index.php\/e-6-multiply-and-divide-rational-numbers-word-problems\/","title":{"rendered":"E.6 Multiply and divide rational numbers: word problems"},"content":{"rendered":"\n<h2 class=\"wp-block-heading has-text-align-center has-text-color\" style=\"color:#00056d;text-transform:uppercase\"><strong>Multiply and divide rational numbers: word problems<\/strong><\/h2>\n\n\n\n<p class=\"has-text-color has-link-color has-huge-font-size wp-elements-ab4cbed01f2dc53453f6fa9edffd950d\" style=\"color:#74008b;text-transform:capitalize\"><strong>Key notes:<\/strong><\/p>\n\n\n\n<p class=\"has-text-color has-link-color has-large-font-size wp-elements-1e1d4ba2bc7e7a07a3e8947106f9bec3\" style=\"color:#000060\"><strong>Understanding Rational Numbers<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list has-large-font-size\">\n<li>Rational numbers include integers, fractions, and decimals that can be written as a ratio of two integers (e.g., 3\/4\u200b, -5, 0.75).<\/li>\n\n\n\n<li>They follow the same multiplication and division rules as whole numbers.<\/li>\n<\/ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity is-style-wide\"\/>\n\n\n\n<p class=\"has-text-color has-link-color has-large-font-size wp-elements-b49d7e8c19e29d33e41f90aac49a07be\" style=\"color:#000060\"><strong>Multiplication of Rational Numbers<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list has-large-font-size\">\n<li>Multiply the numerators and denominators when dealing with fractions.<\/li>\n\n\n\n<li>Apply integer sign rules:\n<ul class=\"wp-block-list\">\n<li>Positive \u00d7 Positive = Positive<\/li>\n\n\n\n<li>Negative \u00d7 Negative = Positive<\/li>\n\n\n\n<li>Positive \u00d7 Negative = Negative<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity is-style-wide\"\/>\n\n\n\n<p class=\"has-text-color has-link-color has-large-font-size wp-elements-4fb9c38aef5dadef8b860556c7b2b0aa\" style=\"color:#000060\"><strong>Division of Rational Numbers<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list has-large-font-size\">\n<li>To divide fractions, multiply by the reciprocal (e.g., 2\/3 \u00f7 5\/4 = 2\/3 \u00d7 4\/5\u200b).<\/li>\n\n\n\n<li>Follow the integer sign rules for division (same as multiplication).<\/li>\n<\/ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity is-style-wide\"\/>\n\n\n\n<p class=\"has-text-color has-link-color has-large-font-size wp-elements-3086ffb7be3834102d81b9ef77c97d8c\" style=\"color:#000060\"><strong>Word Problems Strategy<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list has-large-font-size\">\n<li><strong>Identify<\/strong> what is given and what is being asked.<\/li>\n\n\n\n<li><strong>Determine<\/strong> whether to multiply or divide based on the context.<\/li>\n\n\n\n<li><strong>Convert<\/strong> any decimals to fractions if needed for easier calculation.<\/li>\n\n\n\n<li><strong>Simplify<\/strong> your answer and check for reasonableness.<\/li>\n<\/ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity is-style-wide\"\/>\n\n\n\n<p class=\"has-text-color has-link-color has-large-font-size wp-elements-cd54cd2cf2ce066fb71dce688af1d871\" style=\"color:#000060\"><strong>Common Word Problem Scenarios<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list has-large-font-size\">\n<li><strong>Proportional reasoning<\/strong>: &#8220;A rope is 5.5 meters long. Each piece is 3\/4\u200b meters. How many pieces can be cut?&#8221; \u2192 Use division.<\/li>\n\n\n\n<li><strong>Rate problems<\/strong>: &#8220;A car travels 3\/2\u200b miles per minute. How far does it travel in 6 minutes?&#8221; \u2192 Use multiplication.<\/li>\n\n\n\n<li><strong>Scaling recipes<\/strong>: &#8220;A recipe calls for 2\/3\u200b cup of sugar per cake. How much sugar is needed for 4 cakes?&#8221; \u2192 Use multiplication.<\/li>\n<\/ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity is-style-wide\"\/>\n\n\n\n<p class=\"has-text-color has-link-color has-large-font-size wp-elements-5f2a1c55076ba157419eb04926947c6f\" style=\"color:#000060\"><strong>Real-Life Applications<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list has-large-font-size\">\n<li>Finance (calculating discounts, tax, or interest).<\/li>\n\n\n\n<li>Science (density, speed, and conversion problems).<\/li>\n\n\n\n<li>Construction (measuring and cutting materials).<\/li>\n<\/ul>\n\n\n\n<p class=\"has-text-align-center has-text-color has-link-color has-huge-font-size wp-elements-b9a4d2dbd2b5893137fb321e43f2d55d\" 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-63b47f60ef275d93fdb65f198dff1008\" style=\"background-color:#e2d1fe\"><div class=\"wp-block-group__inner-container is-layout-constrained wp-block-group-is-layout-constrained\">\n<div class=\"wp-block-group has-primary-color has-background-background-color has-text-color has-background has-link-color wp-elements-6b0fd491e43d78555d48373286064204\"><div class=\"wp-block-group__inner-container is-layout-constrained wp-block-group-is-layout-constrained\">\n<p class=\"has-text-color has-link-color wp-elements-d52bed15b578627e6e64997589e37875\" style=\"color:#b00012\"><strong>Carly collected 1\/2 of a bin of glass bottles to recycle. Erin collected 9 times as many bins as Carly. How many bins of bottles did Erin collect?<\/strong><\/p>\n\n\n\n<p>Write your answer as a fraction or as a whole or mixed number.<\/p>\n\n\n\n<p>_____&nbsp;bins<\/p>\n<\/div><\/div>\n\n\n\n<p>Erin collected 9 times 1\/2 of a bin of bottles.<\/p>\n\n\n\n<p>Multiply:<\/p>\n\n\n\n<p>9 x 1\/2 = ?<\/p>\n\n\n\n<p>Write 9 as an improper fraction.<\/p>\n\n\n\n<p>9 = 1\/9<\/p>\n\n\n\n<p>Multiply the numerators and multiply the denominators.<\/p>\n\n\n\n<p>9\/1 x 1\/2 = 9 x 1 \/ 1 x 2 = 9\/2<\/p>\n\n\n\n<p>Simplify the product.<\/p>\n\n\n\n<p>9\/2 = 4 1\/2<\/p>\n\n\n\n<p>Erin collected 4 1\/2 bins of bottles.<\/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-2fbbb40f277e1e4698321fa917382f8f\" style=\"background-color:#f7c8c8\"><div class=\"wp-block-group__inner-container is-layout-constrained wp-block-group-is-layout-constrained\">\n<div class=\"wp-block-group has-primary-color has-background-background-color has-text-color has-background has-link-color wp-elements-5caf4a49402ae1353302749191f708f7\"><div class=\"wp-block-group__inner-container is-layout-constrained wp-block-group-is-layout-constrained\">\n<p class=\"has-text-color has-link-color wp-elements-fda2df951aedb36ee890dc003044ab2f\" style=\"color:#b00012\"><strong>Warren bought 5 rolls of paper towels. He got 86 meters of paper towels in all. How many meters of paper towels were on each roll?<\/strong><\/p>\n\n\n\n<p>Write your answer as a decimal.<\/p>\n\n\n\n<p>____&nbsp;metres<\/p>\n<\/div><\/div>\n\n\n\n<p>Add zeroes after the decimal point in the number you are dividing. Divide until there is no remainder.<\/p>\n\n\n<div class=\"wp-block-image is-resized\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"499\" height=\"500\" src=\"https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Untitled_design__4_-removebg-preview-2.png\" alt=\"\" class=\"wp-image-10030\" style=\"width:287px;height:auto\" srcset=\"https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Untitled_design__4_-removebg-preview-2.png 499w, https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Untitled_design__4_-removebg-preview-2-300x300.png 300w, https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Untitled_design__4_-removebg-preview-2-150x150.png 150w\" sizes=\"auto, (max-width: 499px) 100vw, 499px\" \/><\/figure><\/div>\n\n\n<p>There were 17.2 meters of paper towels on each roll.<\/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-3e3c1a8ce083136821d67f9200703b6d\" style=\"background-color:#b3daf2\"><div class=\"wp-block-group__inner-container is-layout-constrained wp-block-group-is-layout-constrained\">\n<p class=\"has-background-background-color has-text-color has-background has-link-color wp-elements-1e8a5d89a235e0cad620a34ea3f30889\" style=\"color:#b00012\"><strong>A construction company transported 3 stones that weighed a total of 7.2 kilograms. How much did each stone weigh? _______kilograms<\/strong><\/p>\n\n\n\n<p>Divide until there is no remainder.<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"296\" height=\"215\" src=\"https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/06\/81-removebg-preview.png\" alt=\"\" class=\"wp-image-10253\" style=\"width:373px;height:auto\"\/><\/figure><\/div>\n\n\n<p>Each stone weighed 2.4 kilograms.<\/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\/80682\/267\/608\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-282.png\" alt=\"\" class=\"wp-image-9519\" srcset=\"https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-282.png 500w, https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-282-300x300.png 300w, https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-282-150x150.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\/85124\/442\/710\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-289.png\" alt=\"\" class=\"wp-image-9520\" srcset=\"https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-289.png 500w, https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-289-300x300.png 300w, https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-289-150x150.png 150w\" sizes=\"auto, (max-width: 500px) 100vw, 500px\" \/><\/a><\/figure>\n<\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>Multiply and divide rational numbers: word problems Key notes: Understanding Rational Numbers Multiplication of Rational Numbers Division of Rational Numbers Word Problems Strategy Common Word Problem Scenarios Real-Life Applications Learn with an example Carly collected 1\/2 of a bin of glass bottles to recycle. Erin collected 9 times as many bins as Carly. How many<a class=\"more-link\" href=\"https:\/\/8thclass.deltapublications.in\/index.php\/e-6-multiply-and-divide-rational-numbers-word-problems\/\">Continue reading <span class=\"screen-reader-text\">&#8220;E.6 Multiply and divide rational numbers: 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-80","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\/80","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=80"}],"version-history":[{"count":23,"href":"https:\/\/8thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/80\/revisions"}],"predecessor-version":[{"id":19912,"href":"https:\/\/8thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/80\/revisions\/19912"}],"wp:attachment":[{"href":"https:\/\/8thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/media?parent=80"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}