{"id":168,"date":"2022-04-12T09:45:23","date_gmt":"2022-04-12T09:45:23","guid":{"rendered":"http:\/\/7thclass.deltapublications.in\/?page_id=168"},"modified":"2025-12-03T11:48:13","modified_gmt":"2025-12-03T11:48:13","slug":"h-5-add-and-subtract-rational-numbers","status":"publish","type":"page","link":"https:\/\/7thclass.deltapublications.in\/index.php\/h-5-add-and-subtract-rational-numbers\/","title":{"rendered":"H.5 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-huge-font-size\" style=\"color:#74008b\"><strong>Key notes:<\/strong><\/p>\n\n\n\n<h3 class=\"wp-block-heading has-large-font-size\">\ud83d\udd22 <strong>What Are Rational Numbers?<\/strong><\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Rational numbers are numbers that can be written as a <strong>fraction<\/strong> \ud83e\udd67<\/li>\n\n\n\n<li>Example: <strong>1\/2, -3\/4, 5, -8<\/strong>, <strong>0.25 ( = 1\/4 )<\/strong><\/li>\n\n\n\n<li>They include <strong>positive<\/strong>, <strong>negative<\/strong>, <strong>fractions<\/strong>, and <strong>decimals<\/strong>! \ud83c\udf1f<\/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\">\u2795 <strong>Adding Rational Numbers with the Same Sign<\/strong><\/h3>\n\n\n\n<p>Add normally and keep the <strong>same sign<\/strong> \u2714\ufe0f<\/p>\n\n\n\n<p>Example:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>3\/5 + 2\/5 = 5\/5 = 1<\/strong> \ud83d\ude04<\/li>\n\n\n\n<li><strong>-4 + -2 = -6<\/strong><\/li>\n<\/ul>\n\n\n\n<p>\ud83d\udca1 <em>Same side = team up!<\/em> \ud83e\udd1d<\/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\">\ud83d\udd04 <strong>Adding Rational Numbers with Different Signs<\/strong><\/h3>\n\n\n\n<p>Subtract the smaller value from the bigger value<\/p>\n\n\n\n<p>Keep the <strong>sign of the larger number<\/strong><\/p>\n\n\n\n<p>Example:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>7 &#8211; 10 = -3<\/strong><\/li>\n\n\n\n<li><strong>-5 + 12 = 7<\/strong><\/li>\n<\/ul>\n\n\n\n<p>\ud83d\udca1 <em>Opposites try to cancel each other!<\/em> \u26a1\u26a1<\/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\">\u2796 <strong>Subtracting Rational Numbers<\/strong><\/h3>\n\n\n\n<p>Change subtraction to <strong>addition of the opposite<\/strong> \u2728<\/p>\n\n\n\n<p>Example:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>4 &#8211; 7 = 4 + (-7) = -3<\/strong><\/li>\n\n\n\n<li><strong>-3 &#8211; 5 = -3 + (-5) = -8<\/strong><\/li>\n<\/ul>\n\n\n\n<p>\ud83d\udca1 <em>Subtracting becomes adding the opposite!<\/em> \ud83d\udd01<\/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\">\ud83c\udf70 <strong>Adding &amp; Subtracting Fractions<\/strong><\/h3>\n\n\n\n<h4 class=\"wp-block-heading\">\ud83d\udccc If denominators are the same:<\/h4>\n\n\n\n<p>Add\/subtract numerators only!<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>3\/8 + 2\/8 = 5\/8<\/strong><\/li>\n\n\n\n<li><strong>7\/9 &#8211; 4\/9 = 3\/9 = 1\/3<\/strong><\/li>\n<\/ul>\n\n\n\n<h4 class=\"wp-block-heading\">\ud83d\udccc If denominators are different:<\/h4>\n\n\n\n<p>Find <strong>LCM<\/strong> (Least Common Multiple) \ud83c\udfaf<\/p>\n\n\n\n<p>Convert to <strong>equivalent fractions<\/strong><\/p>\n\n\n\n<p>Add\/subtract numerators<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>1\/4 + 1\/6 \u2192 LCM = 12<\/strong><\/li>\n\n\n\n<li><strong>3\/12 + 2\/12 = 5\/12<\/strong><\/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\">\ud83e\uddca <strong>Adding &amp; Subtracting Decimals<\/strong><\/h3>\n\n\n\n<p>Line up the <strong>decimal points<\/strong><\/p>\n\n\n\n<p>Add or subtract normally<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>3.75 + 2.1 = 5.85<\/strong><\/li>\n\n\n\n<li><strong>6.4 &#8211; 3.25 = 3.15<\/strong><\/li>\n<\/ul>\n\n\n\n<p>\ud83d\udd8a\ufe0f <em>Keep decimals in the right place!<\/em> \ud83d\udccd<\/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\">\ud83c\udfaf <strong>Opposites and Zero Pair<\/strong><\/h3>\n\n\n\n<p>A number and its opposite always add to <strong>0<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>5 + (-5) = 0<\/strong><\/li>\n\n\n\n<li><strong>-8 + 8 = 0<\/strong><\/li>\n<\/ul>\n\n\n\n<p>\ud83d\udca5 <em>They cancel each other!<\/em> \ud83d\udeab<\/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\">\ud83e\uddee <strong>Key Rule to Remember<\/strong><\/h3>\n\n\n\n<blockquote class=\"wp-block-quote is-layout-flow wp-block-quote-is-layout-flow\">\n<p>\u2714\ufe0f <strong>Addition \u2192 Follow sign rules<\/strong><br>\u2714\ufe0f <strong>Subtraction \u2192 Add the opposite<\/strong><br>\u2714\ufe0f <strong>Fractions \u2192 Use LCM<\/strong><br>\u2714\ufe0f <strong>Decimals \u2192 Align decimal points<\/strong><\/p>\n<\/blockquote>\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\">\ud83c\udf1f <strong>Real-life Examples<\/strong><\/h3>\n\n\n\n<p>Temperature changes \ud83c\udf21\ufe0f<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>-3\u00b0C + 7\u00b0C = 4\u00b0C<\/strong><\/li>\n<\/ul>\n\n\n\n<p>Money profit &amp; loss \ud83d\udcb0<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>\u20b9500 &#8211; \u20b9800 = -\u20b9300<\/strong><\/li>\n<\/ul>\n\n\n\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<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\" style=\"background-color:#f6cef5\"><div class=\"wp-block-group__inner-container is-layout-flow wp-block-group-is-layout-flow\">\n<div class=\"wp-block-group has-background-background-color has-background\"><div class=\"wp-block-group__inner-container is-layout-flow wp-block-group-is-layout-flow\">\n<p class=\"has-text-color\" style=\"color:#b00012\">\ud83c\udfaf <strong>Add. 3 1\/2 + -1\/2 = _________<\/strong><\/p>\n<\/div><\/div>\n\n\n\n<ul class=\"wp-block-list\">\n<li>You are adding two numbers with different signs, so subtract the lesser absolute value from the greater absolute value:<\/li>\n<\/ul>\n\n\n\n<ul class=\"wp-block-list\">\n<li>3 1\/2 &#8211; 1\/2 = 3<\/li>\n<\/ul>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Since the number with the greater absolute value is positive, the result must also be positive.<\/li>\n<\/ul>\n\n\n\n<ul class=\"wp-block-list\">\n<li>So: <strong>3 1\/2 + &#8211; 1\/2 = 3<\/strong><\/li>\n<\/ul>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-group has-primary-color has-text-color has-background\" style=\"background-color:#fde6d4\"><div class=\"wp-block-group__inner-container is-layout-flow wp-block-group-is-layout-flow\">\n<div class=\"wp-block-group has-background-background-color has-background\"><div class=\"wp-block-group__inner-container is-layout-flow wp-block-group-is-layout-flow\">\n<p class=\"has-text-color\" style=\"color:#b00012\">\ud83d\udc49 <strong>Add. -4 + 1\/2 = _____<\/strong><\/p>\n<\/div><\/div>\n\n\n\n<ul class=\"wp-block-list\">\n<li>You are adding two numbers with different signs, so subtract the lesser absolute value from the greater absolute value:<\/li>\n\n\n\n<li>4 &#8211; 1\/2<\/li>\n\n\n\n<li>3 1\/2<\/li>\n<\/ul>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Since the number with the greater absolute value is negative, the result must also be negative:<\/li>\n\n\n\n<li>3 1\/2 &#8212;-&gt; &#8211; 3 1\/2<\/li>\n\n\n\n<li>So: <strong>&#8211; 4 + 1\/2 = -3 1\/2<\/strong><\/li>\n<\/ul>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-group has-primary-color has-text-color has-background\" style=\"background-color:#edd6f8\"><div class=\"wp-block-group__inner-container is-layout-flow wp-block-group-is-layout-flow\">\n<div class=\"wp-block-group has-background-background-color has-background\"><div class=\"wp-block-group__inner-container is-layout-flow wp-block-group-is-layout-flow\">\n<p class=\"has-text-color\" style=\"color:#b00012\">\ud83c\udfaf <strong>Add.  &#8211; 8 + 9 \/ 10 ____<\/strong><\/p>\n<\/div><\/div>\n\n\n\n<ul class=\"wp-block-list\">\n<li>You are adding two numbers with different signs, so subtract the lesser absolute value from the greater absolute value:<\/li>\n\n\n\n<li>8 &#8211; 9\/10 = 7 1\/10<\/li>\n\n\n\n<li>Since the number with the greater absolute value is negative, the result must also be negative:<\/li>\n\n\n\n<li>7  1\/10 &#8212;-&gt; &#8211; 7 1\/10<\/li>\n\n\n\n<li>So: <strong>&#8211; 8 + 9\/10 = &#8211; 7  1\/10<\/strong><\/li>\n<\/ul>\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<\/div><\/div>\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\/787\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/7thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-2-270.png\" alt=\"\" class=\"wp-image-7423\" srcset=\"https:\/\/7thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-2-270.png 500w, https:\/\/7thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-2-270-300x300.png 300w, https:\/\/7thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-2-270-150x150.png 150w, https:\/\/7thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-2-270-400x400.png 400w\" 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\/81271\/363\/912\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/7thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-1-278.png\" alt=\"\" class=\"wp-image-7424\" srcset=\"https:\/\/7thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-1-278.png 500w, https:\/\/7thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-1-278-300x300.png 300w, https:\/\/7thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-1-278-150x150.png 150w, https:\/\/7thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-1-278-400x400.png 400w\" 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: \ud83d\udd22 What Are Rational Numbers? \u2795 Adding Rational Numbers with the Same Sign Add normally and keep the same sign \u2714\ufe0f Example: \ud83d\udca1 Same side = team up! \ud83e\udd1d \ud83d\udd04 Adding Rational Numbers with Different Signs Subtract the smaller value from the bigger value Keep the sign of<a class=\"more-link\" href=\"https:\/\/7thclass.deltapublications.in\/index.php\/h-5-add-and-subtract-rational-numbers\/\">Continue reading <span class=\"screen-reader-text\">&#8220;H.5 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,"footnotes":""},"class_list":["post-168","page","type-page","status-publish","hentry","entry"],"aioseo_notices":[],"aioseo_head":"\n\t\t<!-- All in One SEO 5.0.1.1 - aioseo.com -->\n\t<meta name=\"description\" content=\"Add and subtract rational numbers Key notes: \ud83d\udd22 What Are Rational Numbers? 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