{"id":33,"date":"2022-04-13T09:48:21","date_gmt":"2022-04-13T09:48:21","guid":{"rendered":"http:\/\/10thclass.deltapublications.in\/?page_id=33"},"modified":"2025-03-05T06:46:24","modified_gmt":"2025-03-05T06:46:24","slug":"b-4-add-and-subtract-rational-numbers","status":"publish","type":"page","link":"https:\/\/10thclass.deltapublications.in\/index.php\/b-4-add-and-subtract-rational-numbers\/","title":{"rendered":"B.4 Add and subtract rational numbers"},"content":{"rendered":"\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<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<\/strong><\/h2>\n\n\n\n<p class=\"has-text-color has-link-color has-huge-font-size wp-elements-4dde4300b7763c9a2a860fe18546dfe2\" style=\"color:#74008b;text-transform:uppercase\">key notes:<\/p>\n\n\n\n<h4 class=\"wp-block-heading\"><strong>Understanding Rational Numbers<\/strong><\/h4>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>Definition:<\/strong><\/li>\n<\/ol>\n\n\n\n<figure class=\"wp-block-image size-full is-resized\"><img decoding=\"async\" src=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2024\/08\/image-24.png\" alt=\"\" class=\"wp-image-14629\" style=\"width:634px;height:auto\"\/><\/figure>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>Examples:<\/strong><\/li>\n<\/ol>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full is-resized\"><img decoding=\"async\" src=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2024\/08\/image-23.png\" alt=\"\" class=\"wp-image-14626\" style=\"width:604px;height:auto\"\/><\/figure><\/div>\n\n\n<h4 class=\"wp-block-heading\"><strong>Addition of Rational Numbers<\/strong><\/h4>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>Same Denominator:<\/strong>\n<ul class=\"wp-block-list\">\n<li>When adding rational numbers with the same denominator, add the numerators and keep the denominator the same.<\/li>\n<\/ul>\n<\/li>\n<\/ol>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full is-resized\"><img decoding=\"async\" src=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2024\/08\/image-22.png\" alt=\"\" class=\"wp-image-14622\" style=\"width:355px;height:auto\"\/><\/figure><\/div>\n\n\n<ol class=\"wp-block-list\">\n<li><strong>Different Denominators:<\/strong><ul><li>Find a common denominator by finding the least common multiple (LCM) of the denominators.Convert each fraction to an equivalent fraction with the common denominator.Add the numerators of the equivalent fractions and keep the common denominator.<\/li><\/ul><strong>Example:<\/strong><\/li>\n<\/ol>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full is-resized\"><img decoding=\"async\" src=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2024\/08\/image-21.png\" alt=\"\" class=\"wp-image-14621\" style=\"width:447px;height:auto\"\/><\/figure><\/div>\n\n\n<h4 class=\"wp-block-heading\"><strong>Addition of Positive and Negative Rational Numbers<\/strong><\/h4>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>Same Sign:<\/strong>\n<ul class=\"wp-block-list\">\n<li>When adding rational numbers with the same sign, add their absolute values and keep the common sign.<\/li>\n<\/ul>\n<\/li>\n<\/ol>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full is-resized\"><img decoding=\"async\" src=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2024\/08\/image-20.png\" alt=\"\" class=\"wp-image-14618\" style=\"width:440px;height:auto\"\/><\/figure><\/div>\n\n\n<ol class=\"wp-block-list\">\n<li><strong>Diffearent Signs:<\/strong>\n<ul class=\"wp-block-list\">\n<li>When adding rational numbers with different signs, subtract the smaller absolute value from the larger absolute value and keep the sign of the number with the larger absolute value.<\/li>\n<\/ul>\n<\/li>\n<\/ol>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full is-resized\"><img decoding=\"async\" src=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2024\/08\/image-19.png\" alt=\"\" class=\"wp-image-14617\" style=\"width:416px;height:auto\"\/><\/figure><\/div>\n\n\n<h4 class=\"wp-block-heading\"><strong>Simplifying Rational Numbers<\/strong><\/h4>\n\n\n\n<ul class=\"wp-block-list\">\n<li>After adding the rational numbers, simplify the result if possible by dividing the numerator and the denominator by their greatest common divisor (GCD).<strong>Example:<\/strong><\/li>\n<\/ul>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full is-resized\"><img decoding=\"async\" src=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2024\/08\/image-18.png\" alt=\"\" class=\"wp-image-14613\" style=\"width:803px;height:auto\"\/><\/figure><\/div>\n\n\n<h3 class=\"wp-block-heading\"><strong>Practice Problems<\/strong><\/h3>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>Same Denominator:<\/strong><\/li>\n<\/ol>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full is-resized\"><img decoding=\"async\" src=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2024\/08\/image-13.png\" alt=\"\" class=\"wp-image-14606\" style=\"width:238px;height:auto\"\/><\/figure><\/div>\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Different Denominators:<\/strong><\/li>\n<\/ul>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full is-resized\"><img decoding=\"async\" src=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2024\/08\/image-14.png\" alt=\"\" class=\"wp-image-14608\" style=\"width:219px;height:auto\"\/><\/figure><\/div>\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Mixed Numbers:<\/strong><\/li>\n<\/ul>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full is-resized\"><img decoding=\"async\" src=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2024\/08\/image-15.png\" alt=\"\" class=\"wp-image-14609\" style=\"width:256px;height:auto\"\/><\/figure><\/div>\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Positive and Negative Rational Numbers:<\/strong><\/li>\n<\/ul>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full is-resized\"><img decoding=\"async\" src=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2024\/08\/image-16.png\" alt=\"\" class=\"wp-image-14610\" style=\"width:254px;height:auto\"\/><\/figure><\/div>\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-background has-large-font-size\" style=\"background-color:#edf7ac\"><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-015226c910843d70dc49ac4dde6e9e90\" style=\"color:#b00012\">Add.<\/p>\n\n\n\n<p class=\"has-text-color has-link-color wp-elements-436020f3648cf3e708720c8e754a5cc1\" style=\"color:#b00012\">1\/10 + 1\/2 =<\/p>\n<\/div><\/div>\n\n\n\n<p>Add:<\/p>\n\n\n\n<p>1\/10 + 1\/2<\/p>\n\n\n\n<p>= 1\/10 + 5\/10<\/p>\n\n\n\n<p>= 6\/10 <\/p>\n\n\n\n<p>= 3\/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>1\/10 + 1\/2 = 3\/5<\/p>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-group has-background has-large-font-size\" style=\"background-color:#f8ace5\"><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-b7e7e958f4a6dc6428ba84b43b64a5ac\" style=\"color:#b00012\">Subtract.<\/p>\n\n\n\n<p class=\"has-text-color has-link-color wp-elements-6172edc40d5481780b32d87d94f0b8a7\" style=\"color:#b00012\">7\/10 &#8211; 1\/10 =<\/p>\n<\/div><\/div>\n\n\n\n<p>Subtract:<\/p>\n\n\n\n<p>7\/10 + 1\/10 <\/p>\n\n\n\n<p>= 6\/10<\/p>\n\n\n\n<p>= 3\/5<\/p>\n\n\n\n<p>Since you are subtracting a smaller number from a larger number, the result must be positive.<\/p>\n\n\n\n<p>So:<\/p>\n\n\n\n<p>7\/10 &#8211; 1\/10 = 3\/5<\/p>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-group has-background has-large-font-size\" style=\"background-color:#d4aff4\"><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-015226c910843d70dc49ac4dde6e9e90\" style=\"color:#b00012\">Add.<\/p>\n\n\n\n<p class=\"has-text-color has-link-color wp-elements-655b77681658556ae80807f1581dcb5e\" style=\"color:#b00012\">1\/5 + 4\/5 = <\/p>\n<\/div><\/div>\n\n\n\n<p>Add:<\/p>\n\n\n\n<p>1\/5 + 4\/5 <\/p>\n\n\n\n<p>= 1<\/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\/5 + 4\/5 = 1<\/p>\n<\/div><\/div>\n\n\n\n<p class=\"has-text-color has-large-font-size\" style=\"color:#d90000\">Let&#8217;s Practice!<\/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\/934\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-7.png\" alt=\"\" class=\"wp-image-6443\" srcset=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-7.png 500w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-7-300x300.png 300w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-7-150x150.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\/76168\/490\/783\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-7.png\" alt=\"\" class=\"wp-image-6444\" srcset=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-7.png 500w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-7-300x300.png 300w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-7-150x150.png 150w\" sizes=\"auto, (max-width: 500px) 100vw, 500px\" \/><\/a><\/figure>\n<\/div>\n<\/div>\n<\/div><\/div>\n","protected":false},"excerpt":{"rendered":"<p>Add and subtract rational numbers key notes: Understanding Rational Numbers Addition of Rational Numbers Addition of Positive and Negative Rational Numbers Simplifying Rational Numbers Practice Problems Learn with an example Add. 1\/10 + 1\/2 = Add: 1\/10 + 1\/2 = 1\/10 + 5\/10 = 6\/10 = 3\/5 Since the numbers being added are positive, the<a class=\"more-link\" href=\"https:\/\/10thclass.deltapublications.in\/index.php\/b-4-add-and-subtract-rational-numbers\/\">Continue reading <span class=\"screen-reader-text\">&#8220;B.4 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-33","page","type-page","status-publish","hentry","entry"],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/10thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/33","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/10thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/10thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/10thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/10thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/comments?post=33"}],"version-history":[{"count":17,"href":"https:\/\/10thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/33\/revisions"}],"predecessor-version":[{"id":17572,"href":"https:\/\/10thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/33\/revisions\/17572"}],"wp:attachment":[{"href":"https:\/\/10thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/media?parent=33"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}