{"id":74,"date":"2022-04-12T12:01:56","date_gmt":"2022-04-12T12:01:56","guid":{"rendered":"http:\/\/8thclass.deltapublications.in\/?page_id=74"},"modified":"2025-02-22T15:44:50","modified_gmt":"2025-02-22T15:44:50","slug":"e-3-add-and-subtract-rational-numbers-word-problems","status":"publish","type":"page","link":"https:\/\/8thclass.deltapublications.in\/index.php\/e-3-add-and-subtract-rational-numbers-word-problems\/","title":{"rendered":"E.3 Add and subtract rational numbers: word problems"},"content":{"rendered":"\n<h2 class=\"wp-block-heading has-text-align-center has-text-color has-huge-font-size\" style=\"color:#00056d;text-transform:uppercase\"><strong>Add and subtract rational numbers: word problems<\/strong><\/h2>\n\n\n\n<p class=\"has-text-color has-link-color has-huge-font-size wp-elements-ab8376a8ebfb22772ef7356f8b60e696\" style=\"color:#74008b\"><strong>Key notes:<\/strong><\/p>\n\n\n\n<p class=\"has-text-color has-link-color has-large-font-size wp-elements-dc08ce210399c68fd5b8f73c88f305ad\" 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 fractions, decimals, and integers.<\/li>\n\n\n\n<li>They can be positive or negative.<\/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-78bb45eef6aed103b89bf1513a416c91\" style=\"color:#000060\"><strong>Addition of Rational Numbers<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list has-large-font-size\">\n<li>When adding numbers with the same sign, add their absolute values and keep the sign.<\/li>\n\n\n\n<li>When adding numbers with different signs, subtract the smaller absolute value from the larger one and keep the sign of the larger number.<\/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-9f76f31151ef509737ba8d358367f61d\" style=\"color:#000060\"><strong>Subtraction of Rational Numbers<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list has-large-font-size\">\n<li>Change the subtraction into addition by using the rule: <strong>a &#8211; b = a + (-b)<\/strong>.<\/li>\n\n\n\n<li>Follow the rules for adding rational numbers after changing the sign.<\/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-4902e75e2fd248ff431530ce3ca40236\" style=\"color:#000060\"><strong>Finding Common Denominators for Fractions<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list has-large-font-size\">\n<li>Convert fractions to have the same denominator before adding or subtracting.<\/li>\n\n\n\n<li>Perform operations on numerators while keeping the denominator unchanged.<\/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-4b8c51fab0fde8af2511aa3ac64269a7\" style=\"color:#000060\"><strong>Working with Decimals<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list has-large-font-size\">\n<li>Align the decimal points before performing addition or subtraction.<\/li>\n\n\n\n<li>Add zeros if necessary for proper alignment.<\/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-12927feca430a262d4d7f2c27afb400a\" style=\"color:#000060\"><strong>Word Problem Strategies<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list has-large-font-size\">\n<li><strong>Identify<\/strong> key information: numbers, operation keywords (sum, difference, increase, decrease).<\/li>\n\n\n\n<li><strong>Write<\/strong> an equation based on the problem statement.<\/li>\n\n\n\n<li><strong>Solve<\/strong> using the correct addition or subtraction rules.<\/li>\n\n\n\n<li><strong>Check<\/strong> the answer by substituting it back into the problem context.<\/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-50d9183909ae1db6e789d5a39ad2c5a5\" style=\"color:#000060\"><strong>Common Keywords in Word Problems<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list has-large-font-size\">\n<li><strong>Addition:<\/strong> sum, total, increase, gain, combined, together<\/li>\n\n\n\n<li><strong>Subtraction:<\/strong> difference, decrease, loss, less than, remaining<\/li>\n<\/ul>\n\n\n\n<p class=\"has-text-align-center has-text-color has-huge-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-0f1b2b8dd08fb6c986a2c1f702ecb4c4\" style=\"background-color:#f9f7cf\"><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 has-link-color wp-elements-ff818eadfa5736dfe1f79f3020543a8e\" style=\"color:#b00012\"><strong>\ud83c\udfaf Over the weekend, Darren drank 9\/10 of a bottle of soda and Tori drank 2\/5 of a bottle. How much more soda did Darren drink than Tori?<\/strong><\/p>\n\n\n\n<p>Simplify your answer and write it as a fraction or as a whole or mixed number.<\/p>\n\n\n\n<p>_____&nbsp;bottles<\/p>\n<\/div><\/div>\n\n\n\n<p>Find how much more soda Darren drank by subtracting 2\/5 from 9\/10.<\/p>\n\n\n\n<p>You can use 10 as the common denominator.<\/p>\n\n\n\n<p>Multiply the numerator and the denominator of&nbsp;2\/5 &nbsp;by 2 to find an equivalent fraction.<\/p>\n\n\n\n<p>2 x 2 \/ 5 x 2 = 4\/10<\/p>\n\n\n\n<p>Now subtract the fractions. Subtract the numerators and keep the denominators the same.<\/p>\n\n\n\n<p>9\/10 &#8211; 4\/10 = 5\/10<\/p>\n\n\n\n<p>Write the answer in simplest form. Divide both the numerator and the denominator by 5.<\/p>\n\n\n\n<p>5 \u00f7&nbsp;5 \/ 10 \u00f7 5 = 1\/2<\/p>\n\n\n\n<p>Now write the answer.<\/p>\n\n\n\n<p>9\/10 &#8211; 2\/5 = 1\/2<\/p>\n\n\n\n<p>Darren drank 1\/2 of a bottle more soda than Tori.<\/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-efb49fcc47208a49cb598ad2676da7ef\" style=\"background-color:#ead6fe\"><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 has-link-color wp-elements-abf3e6940f96fb09716bdd0257624492\" style=\"color:#b00012\"><strong>\ud83c\udfaf On a school trip, a class travels 4.7 kilometres by train and 9.9 kilometres by bus. How far did the class travel?<\/strong><\/p>\n\n\n\n<p>\u200b______&nbsp;kilometres<\/p>\n<\/div><\/div>\n\n\n\n<p>Add the numbers of kilometres. Remember to line up the decimal points.<\/p>\n\n\n\n<p>      1<\/p>\n\n\n\n<p>     4.7<\/p>\n\n\n\n<p>     +9.9<\/p>\n\n\n\n<p>    = 14.6<\/p>\n\n\n\n<p>The class travelled 14.6 kilometres.<\/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-b3fa82d893bc831dfecbcf4a9f6e33d7\" style=\"background-color:#c9e2f8\"><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 has-link-color wp-elements-8d556041fe17cfc15b121625225eed09\" style=\"color:#b00012\"><strong>\ud83c\udfaf At a pizza party, Duncan and his friends drank 3&nbsp;3\/8 bottles of lemon-lime soda and 2 bottles of cola. How much soda did they drink in all?<\/strong><\/p>\n\n\n\n<p>Simplify your answer and write it as a fraction or as a whole or mixed number.<\/p>\n\n\n\n<p>_______&nbsp;bottles<\/p>\n<\/div><\/div>\n\n\n\n<p>Find how much soda they drank in all by adding 3&nbsp;3\/8 and 2.<\/p>\n\n\n\n<p>Add. Remember to add whole numbers to whole numbers and fractions to fractions.<\/p>\n\n\n\n<p>3 3\/8 + 2 = 5 3\/8<\/p>\n\n\n\n<p>This answer is in simplest form.<\/p>\n\n\n\n<p>Duncan and his friends drank 5 3\/8 bottles in all.<\/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\/80681\/670\/490\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-285.png\" alt=\"\" class=\"wp-image-9533\" srcset=\"https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-285.png 500w, https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-285-300x300.png 300w, https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-285-150x150.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\/85076\/559\/531\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-292.png\" alt=\"\" class=\"wp-image-9534\" srcset=\"https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-292.png 500w, https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-292-300x300.png 300w, https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-292-150x150.png 150w\" sizes=\"auto, (max-width: 500px) 100vw, 500px\" \/><\/a><\/figure>\n<\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>Add and subtract rational numbers: word problems Key notes: Understanding Rational Numbers Addition of Rational Numbers Subtraction of Rational Numbers Finding Common Denominators for Fractions Working with Decimals Word Problem Strategies Common Keywords in Word Problems Learn with an example \ud83c\udfaf Over the weekend, Darren drank 9\/10 of a bottle of soda and Tori drank<a class=\"more-link\" href=\"https:\/\/8thclass.deltapublications.in\/index.php\/e-3-add-and-subtract-rational-numbers-word-problems\/\">Continue reading <span class=\"screen-reader-text\">&#8220;E.3 Add and subtract 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-74","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\/74","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=74"}],"version-history":[{"count":22,"href":"https:\/\/8thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/74\/revisions"}],"predecessor-version":[{"id":19907,"href":"https:\/\/8thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/74\/revisions\/19907"}],"wp:attachment":[{"href":"https:\/\/8thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/media?parent=74"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}