{"id":72,"date":"2022-04-12T12:01:32","date_gmt":"2022-04-12T12:01:32","guid":{"rendered":"http:\/\/8thclass.deltapublications.in\/?page_id=72"},"modified":"2025-02-22T15:38:34","modified_gmt":"2025-02-22T15:38:34","slug":"e-2-add-and-subtract-rational-numbers","status":"publish","type":"page","link":"https:\/\/8thclass.deltapublications.in\/index.php\/e-2-add-and-subtract-rational-numbers\/","title":{"rendered":"E.2 Add and subtract rational numbers"},"content":{"rendered":"\n<h2 class=\"wp-block-heading has-text-align-center has-text-color\" style=\"color:#00056d;text-transform:uppercase\"><strong>Add and subtract rational numbers<\/strong><\/h2>\n\n\n\n<p class=\"has-text-color has-link-color has-huge-font-size wp-elements-36dce3b5d8a769fca29ca1d6990a0e17\" 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-caad2abb6e97042a82d024cda87c5f61\" style=\"color:#000060\"><strong>Definition of Rational Numbers<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list has-large-font-size\">\n<li>A rational number is any number that can be expressed as a fraction a\/b\u200b, where aaa and b are integers and b\u22600.<\/li>\n\n\n\n<li><strong>Examples:<\/strong> 3\/4, \u2212 5,0.75, \u2212 2\/3 ,1.25.<\/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><strong>Same Denominator<\/strong>: Add the numerators and keep the denominator the same.<\/li>\n<\/ul>\n\n\n\n<p class=\"has-large-font-size\"><strong>Example: <\/strong>3 \/ 8 + 5 \/ 8 = 3+5 \/ 8 = 8 \/ 8 = 1.<\/p>\n\n\n\n<ul class=\"wp-block-list has-large-font-size\">\n<li><strong>Different Denominators<\/strong>: Find the Least Common Denominator (LCD), convert the fractions, and then add.<\/li>\n<\/ul>\n\n\n\n<p class=\"has-large-font-size\"><strong>Example:<\/strong> 1\/3 + 2\/5\u200b<\/p>\n\n\n\n<p class=\"has-large-font-size\">LCD of 3 and 5 = 15<\/p>\n\n\n\n<p class=\"has-large-font-size\">Convert: 1\/3 = 5\/15 , 2\/5 = 6\/156\u200b<\/p>\n\n\n\n<p class=\"has-large-font-size\">Add: 5\/15 + 6\/15 = 11\/15\u200b.<\/p>\n\n\n\n<ul class=\"wp-block-list has-large-font-size\">\n<li><strong>Adding Decimals<\/strong>: Align decimal points and add normally.<\/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><strong>Same Denominator<\/strong>: Subtract the numerators and keep the denominator the same.<\/li>\n<\/ul>\n\n\n\n<p class=\"has-large-font-size\"><strong>Example:<\/strong> 7\/9 \u2212 2\/9 = 7\u22122 \/ 9 = 5\/9\u200b.<\/p>\n\n\n\n<ul class=\"wp-block-list has-large-font-size\">\n<li><strong>Different Denominators<\/strong>: Find the LCD, convert the fractions, and subtract.<\/li>\n<\/ul>\n\n\n\n<p class=\"has-large-font-size\"><strong>Example:<\/strong> 5 6 \u2212 1 4\u200b<\/p>\n\n\n\n<p class=\"has-large-font-size\">LCD of 6 and 4 = 12<\/p>\n\n\n\n<p class=\"has-large-font-size\">Convert: 5\/6 = 10\/12 , 1\/4 = 3\/12\u200b<\/p>\n\n\n\n<p class=\"has-large-font-size\">Subtract: 10\/12 \u2212 3\/12 = 7\/12\u200b.<\/p>\n\n\n\n<ul class=\"wp-block-list has-large-font-size\">\n<li><strong>Subtracting Decimals<\/strong>: Align decimal points and subtract normally.<\/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-b1702cd542a181fd9efe34c8ea5170a1\" style=\"color:#000060\"><strong>Adding and Subtracting Negative Rational Numbers<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list has-large-font-size\">\n<li><strong>Adding a Negative Number<\/strong>: This is the same as subtraction.<\/li>\n<\/ul>\n\n\n\n<p class=\"has-large-font-size\"><strong>Example:<\/strong> 4\/5 + (\u22122\/5) = 4\/5 \u2212 2\/5 = 2\/5\u200b.<\/p>\n\n\n\n<ul class=\"wp-block-list has-large-font-size\">\n<li><strong>Subtracting a Negative Number<\/strong>: This is the same as addition.<\/li>\n<\/ul>\n\n\n\n<p class=\"has-large-font-size\"><strong>Example<\/strong>: 3\/7 \u2212 (\u22122\/7) = 3\/7 + 2\/7 = 5\/7\u200b.<\/p>\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-522fe6fc7ee8d2bcfd8c1cfdd4ae1986\" style=\"color:#000060\"><strong>Using a Number Line for Addition and Subtraction<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list has-large-font-size\">\n<li>Start at the first number and move right for addition or left for subtraction.<\/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-339d05a6f547e936d2dd86850e73d08e\" style=\"color:#000060\"><strong>Word Problems with Rational Numbers<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list has-large-font-size\">\n<li>Identify key information and decide whether to add or subtract.<\/li>\n\n\n\n<li>Convert mixed numbers to improper fractions if necessary.<\/li>\n<\/ul>\n\n\n\n<p class=\"has-text-align-center has-text-color has-link-color has-large-font-size wp-elements-3fefd20f8ce119a518e5f53333ab5486\" 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-dcd0a1ebfe02d5a8bd97b2ae252aaed1\" style=\"background-color:#bde7fc\"><div class=\"wp-block-group__inner-container is-layout-flow wp-block-group-is-layout-flow\">\n<p class=\"has-text-align-center has-background-background-color has-text-color has-background has-link-color has-large-font-size wp-elements-121cf3af3c7cb25e2d0573f072fa5bc7\" style=\"color:#b00012\">\ud83c\udfaf 1\/5 + 1\/5 = ?<\/p>\n\n\n\n<p>Add:<\/p>\n\n\n\n<p>1\/5 + 1\/5 = 2\/5<\/p>\n\n\n\n<p>Since the numbers being added are positive, the result must also be positive.<\/p>\n\n\n\n<p>So:<\/p>\n\n\n\n<p class=\"has-large-font-size\">1\/5 + 1\/5 = 2\/5<\/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-73f26dd7e48dc16a45e19723b288f322\" style=\"background-color:#dff9ca\"><div class=\"wp-block-group__inner-container is-layout-flow wp-block-group-is-layout-flow\">\n<p class=\"has-text-align-center has-background-background-color has-text-color has-background has-link-color has-large-font-size wp-elements-2fdccee00f3a257bbf8f423bf362cff9\" style=\"color:#b00012\"><strong>\ud83c\udfaf 3\/4 + 1\/2 = ?<\/strong><\/p>\n\n\n\n<p>Add:<\/p>\n\n\n\n<p>3\/4 + 1\/2 = 3\/4 + 2\/4<\/p>\n\n\n\n<p>                = 1 1\/4<\/p>\n\n\n\n<p>Since the numbers being added are positive, the result must also be positive.<\/p>\n\n\n\n<p>So:<\/p>\n\n\n\n<p class=\"has-large-font-size\">3\/4 + 1\/2 = 1 1\/4<\/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-8bfbbbaa53fd1fddd70ee46a8f41bd03\" style=\"background-color:#e8d0f8\"><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>\ud83c\udfaf Add.<\/p>\n\n\n\n<p class=\"has-text-color has-link-color wp-elements-1b7fa6f87f2addc8ea0e74880b7fe774\" style=\"color:#b00012\">1\/4 + 1\/2 = ____<\/p>\n<\/div><\/div>\n\n\n\n<p>Add:<\/p>\n\n\n\n<p>1\/4 + 1\/2 <\/p>\n\n\n\n<p>= 1\/4 + 2\/4<\/p>\n\n\n\n<p>= 3\/4<\/p>\n\n\n\n<p>Since the numbers being added are positive, the result must also be positive.<\/p>\n\n\n\n<p>So:<\/p>\n\n\n\n<p>1\/4 + 1\/2 = 3\/4<\/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\/76092\/531\/776\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-286.png\" alt=\"\" class=\"wp-image-9536\" srcset=\"https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-286.png 500w, https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-286-300x300.png 300w, https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-286-150x150.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\/85062\/501\/268\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-293.png\" alt=\"\" class=\"wp-image-9537\" srcset=\"https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-293.png 500w, https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-293-300x300.png 300w, https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-293-150x150.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 Key Notes Definition of Rational Numbers Addition of Rational Numbers Example: 3 \/ 8 + 5 \/ 8 = 3+5 \/ 8 = 8 \/ 8 = 1. Example: 1\/3 + 2\/5\u200b LCD of 3 and 5 = 15 Convert: 1\/3 = 5\/15 , 2\/5 = 6\/156\u200b Add: 5\/15 +<a class=\"more-link\" href=\"https:\/\/8thclass.deltapublications.in\/index.php\/e-2-add-and-subtract-rational-numbers\/\">Continue reading <span class=\"screen-reader-text\">&#8220;E.2 Add and subtract rational numbers&#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-72","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\/72","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=72"}],"version-history":[{"count":21,"href":"https:\/\/8thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/72\/revisions"}],"predecessor-version":[{"id":19906,"href":"https:\/\/8thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/72\/revisions\/19906"}],"wp:attachment":[{"href":"https:\/\/8thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/media?parent=72"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}