{"id":62,"date":"2022-04-12T09:26:24","date_gmt":"2022-04-12T09:26:24","guid":{"rendered":"http:\/\/7thclass.deltapublications.in\/?page_id=62"},"modified":"2025-11-21T05:52:27","modified_gmt":"2025-11-21T05:52:27","slug":"c-9-evaluate-numerical-expressions-involving-integers","status":"publish","type":"page","link":"https:\/\/7thclass.deltapublications.in\/index.php\/c-9-evaluate-numerical-expressions-involving-integers\/","title":{"rendered":"C.9 Evaluate numerical expressions involving integers"},"content":{"rendered":"\n<h2 class=\"wp-block-heading has-text-align-center has-text-color\" style=\"color:#00056d;text-transform:uppercase\"><strong>Evaluate numerical expressions involving integers<\/strong><\/h2>\n\n\n\n<figure class=\"wp-block-video\"><video controls src=\"https:\/\/7thclass.deltapublications.in\/wp-content\/uploads\/2023\/08\/C.8-Evaluate-numerical-expressions-involving-integers.mp4\"><\/video><\/figure>\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\">1\ufe0f\u20e3 Understand Integers<\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Integers are <strong>whole numbers<\/strong> including <strong>positive (+)<\/strong>, <strong>negative (-)<\/strong>, and <strong>zero (0)<\/strong>.<\/li>\n\n\n\n<li>Examples: \u2026, -3, -2, -1, 0, 1, 2, 3, \u2026<\/li>\n\n\n\n<li>\ud83d\udd39 Positive \u2795<\/li>\n\n\n\n<li>\ud83d\udd39 Negative \u2796<\/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\">2\ufe0f\u20e3 Order of Operations (BODMAS \/ PEMDAS) \ud83e\uddee<\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Always follow this order:<br><strong>B<\/strong> \u2013 Brackets ( )<br><strong>O<\/strong> \u2013 Orders (powers and roots, e.g., 2\u00b2)<br><strong>D<\/strong> \u2013 Division \u00f7<br><strong>M<\/strong> \u2013 Multiplication \u00d7<br><strong>A<\/strong> \u2013 Addition +<br><strong>S<\/strong> \u2013 Subtraction &#8211;<\/li>\n<\/ul>\n\n\n\n<blockquote class=\"wp-block-quote is-layout-flow wp-block-quote-is-layout-flow\">\n<p>Example: 5+2\u00d7(3\u22121)=?5 + 2 \\times (3 &#8211; 1) = ?5+2\u00d7(3\u22121)=?<br>Step 1: Brackets \u2192 3 &#8211; 1 = 2<br>Step 2: Multiplication \u2192 2 \u00d7 2 = 4<br>Step 3: Addition \u2192 5 + 4 = 9 \u2705<\/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\">3\ufe0f\u20e3 Adding Integers \u2795<\/h3>\n\n\n\n<p><strong>Same signs:<\/strong> Add and keep the sign<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>5 + 3 = 8<\/li>\n\n\n\n<li>-5 + -3 = -8<\/li>\n<\/ul>\n\n\n\n<p><strong>Different signs:<\/strong> Subtract smaller from larger, keep <strong>larger number\u2019s sign<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>7 + (-4) \u2192 7 &#8211; 4 = 3 \u2705<\/li>\n\n\n\n<li>-7 + 4 \u2192 7 &#8211; 4 = 3, sign = &#8211; \u2705<\/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\">4\ufe0f\u20e3 Subtracting Integers \u2796<\/h3>\n\n\n\n<p>Change subtraction to addition of the <strong>opposite<\/strong><\/p>\n\n\n\n<p>a &#8211; b = a + (-b)<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Example: 5 &#8211; (-3) = 5 + 3 = 8 \u2705<\/li>\n\n\n\n<li>Example: -4 &#8211; 6 = -4 + (-6) = -10 \u2705<\/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\">5\ufe0f\u20e3 Multiplying Integers \u2716\ufe0f<\/h3>\n\n\n\n<p><strong>Same signs<\/strong> \u2192 Positive<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>3 \u00d7 4 = 12 \u2705<\/li>\n\n\n\n<li>-3 \u00d7 -4 = 12 \u2705<\/li>\n<\/ul>\n\n\n\n<p><strong>Different signs<\/strong> \u2192 Negative<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>-3 \u00d7 4 = -12 \u2705<\/li>\n\n\n\n<li>3 \u00d7 -4 = -12 \u2705<\/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\">6\ufe0f\u20e3 Dividing Integers \u2797<\/h3>\n\n\n\n<p>Rules same as multiplication:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Same signs \u2192 Positive<\/li>\n\n\n\n<li>Different signs \u2192 Negative<\/li>\n<\/ul>\n\n\n\n<p>Example:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>-12 \u00f7 3 = -4 \u2705<\/li>\n\n\n\n<li>12 \u00f7 -3 = -4 \u2705<\/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\">7\ufe0f\u20e3 Practice Tips \u270f\ufe0f<\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Always <strong>simplify inside brackets first<\/strong> \ud83c\udff7\ufe0f<\/li>\n\n\n\n<li>Use <strong>number lines<\/strong> for visual help \ud83d\udfe2\ud83d\udd34<\/li>\n\n\n\n<li>Check <strong>sign rules<\/strong> carefully \u2705<\/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\">8\ufe0f\u20e3 Quick Tricks \u26a1<\/h3>\n\n\n\n<p><strong>Double negative \u2192 positive<\/strong>: -(-5) = 5<\/p>\n\n\n\n<p><strong>Zero rules<\/strong>:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>0 + any number = number<\/li>\n\n\n\n<li>0 \u00d7 any number = 0<\/li>\n\n\n\n<li>Any number \u00f7 0 \u2192 Not allowed \u274c<\/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\">9\ufe0f\u20e3 Fun Example \ud83c\udf89<\/h3>\n\n\n\n<p>Evaluate: \u22123+2\u00d7(4\u22127)-3 + 2 \\times (4 &#8211; 7)\u22123+2\u00d7(4\u22127)<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Step 1: Brackets \u2192 4 &#8211; 7 = -3<\/li>\n\n\n\n<li>Step 2: Multiply \u2192 2 \u00d7 -3 = -6<\/li>\n\n\n\n<li>Step 3: Add \u2192 -3 + -6 = -9 \u2705<\/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 has-link-color wp-elements-01ef442c5894f852d02fc5d929c4def2\" style=\"background-color:#d1fbe3\"><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-constrained wp-block-group-is-layout-constrained\">\n<p class=\"has-text-color has-large-font-size\" style=\"color:#b00012\"><strong>Evaluate&nbsp;the&nbsp;expression.<\/strong><\/p>\n\n\n\n<p class=\"has-text-align-center has-text-color has-large-font-size\" style=\"color:#b00012\"> <strong>2+4\u00f72<\/strong><\/p>\n<\/div><\/div>\n\n\n\n<p>First,&nbsp;identify the operations in the&nbsp;expression.<\/p>\n\n\n\n<p>2+4\u00f72 This&nbsp;expression has addition and division.<\/p>\n\n\n\n<p> The order of operations says to divide before&nbsp;adding.<\/p>\n\n\n\n<p>2+4\u00f72=2+<strong>2<\/strong><\/p>\n\n\n\n<p>Now,&nbsp;add.2+2=<strong>4<\/strong>.<\/p>\n\n\n\n<p>The&nbsp;value of the expression is&nbsp;<strong>4<\/strong>.<\/p>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-group has-primary-color has-text-color has-background has-link-color wp-elements-1511352091b85c408138fb9f53aafff4\" style=\"background-color:#d2edf6\"><div class=\"wp-block-group__inner-container is-layout-flow wp-block-group-is-layout-flow\">\n<p>Example 2 :<\/p>\n\n\n\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\">\u27a1\ufe0f <strong>Evaluate the expression for x = 5, y = 8 and z = 6.<\/strong><\/p>\n\n\n\n<p>(y<sup>2<\/sup>&nbsp;+ z) \u00f7 x<\/p>\n<\/div><\/div>\n\n\n\n<p>Solution :<\/p>\n\n\n\n<p>= (y<sup>2<\/sup>&nbsp;+ x) \u00f7 x<\/p>\n\n\n\n<p>Substitute&nbsp;x = 5, y = 8 and z = 6.<\/p>\n\n\n\n<p>= (8<sup>2<\/sup>&nbsp;+ 6) \u00f7 5<\/p>\n\n\n\n<p>= (64&nbsp;+ 6) \u00f7 5<\/p>\n\n\n\n<p>= 70 \u00f7 5<\/p>\n\n\n\n<p>= 14<\/p>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-group has-primary-color has-text-color has-background has-link-color wp-elements-40a1612a5448ad96399ee646c0a415ad\" style=\"background-color:#c8f7cc\"><div class=\"wp-block-group__inner-container is-layout-flow wp-block-group-is-layout-flow\">\n<div class=\"wp-block-group has-primary-color has-background-background-color has-text-color has-background has-link-color wp-elements-11d2176d52f07a28ef29ce5aed868d77\"><div class=\"wp-block-group__inner-container is-layout-flow wp-block-group-is-layout-flow\">\n<p>\u27a1\ufe0f Example 3 :<\/p>\n\n\n\n<p class=\"has-text-color\" style=\"color:#b00012\"><strong>Evaluate the expression for p = 6, q = 5 and r = 4.<\/strong><\/p>\n\n\n\n<p class=\"has-text-align-center has-large-font-size\">(pq &#8211; 28)<sup>2<\/sup>&nbsp;\u00f7 r<\/p>\n<\/div><\/div>\n\n\n\n<p>Solution :<\/p>\n\n\n\n<p>(pq &#8211; 28)<sup>2<\/sup>&nbsp;\u00f7 r<\/p>\n\n\n\n<p>Substitute&nbsp;p = 6, q = 5 and r = 4.<\/p>\n\n\n\n<p>= [(6)(5) &#8211; 28]<sup>2<\/sup>&nbsp;\u00f7 4<\/p>\n\n\n\n<p>= (30 &#8211; 28)<sup>2<\/sup>&nbsp;\u00f7 4<\/p>\n\n\n\n<p>= 2<sup>2<\/sup>&nbsp;\u00f7 4<\/p>\n\n\n\n<p>= 4 \u00f7 4<\/p>\n\n\n\n<p>= 1<\/p>\n<\/div><\/div>\n\n\n\n<p class=\"has-text-color has-large-font-size\" style=\"color:#d90000\"><strong>Try some practice problems!<\/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\/76370\/988\/685\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/7thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-2-197.png\" alt=\"\" class=\"wp-image-7159\" srcset=\"https:\/\/7thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-2-197.png 500w, https:\/\/7thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-2-197-300x300.png 300w, https:\/\/7thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-2-197-150x150.png 150w, https:\/\/7thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-2-197-400x400.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\/76375\/690\/612\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/7thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-1-200.png\" alt=\"\" class=\"wp-image-7160\" srcset=\"https:\/\/7thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-1-200.png 500w, https:\/\/7thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-1-200-300x300.png 300w, https:\/\/7thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-1-200-150x150.png 150w, https:\/\/7thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-1-200-400x400.png 400w\" sizes=\"auto, (max-width: 500px) 100vw, 500px\" \/><\/a><\/figure>\n<\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>Evaluate numerical expressions involving integers Key Notes: 1\ufe0f\u20e3 Understand Integers 2\ufe0f\u20e3 Order of Operations (BODMAS \/ PEMDAS) \ud83e\uddee Example: 5+2\u00d7(3\u22121)=?5 + 2 \\times (3 &#8211; 1) = ?5+2\u00d7(3\u22121)=?Step 1: Brackets \u2192 3 &#8211; 1 = 2Step 2: Multiplication \u2192 2 \u00d7 2 = 4Step 3: Addition \u2192 5 + 4 = 9 \u2705 3\ufe0f\u20e3 Adding<a class=\"more-link\" href=\"https:\/\/7thclass.deltapublications.in\/index.php\/c-9-evaluate-numerical-expressions-involving-integers\/\">Continue reading <span class=\"screen-reader-text\">&#8220;C.9 Evaluate numerical expressions involving integers&#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-62","page","type-page","status-publish","hentry","entry"],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/7thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/62","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/7thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/7thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/7thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/7thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/comments?post=62"}],"version-history":[{"count":17,"href":"https:\/\/7thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/62\/revisions"}],"predecessor-version":[{"id":17592,"href":"https:\/\/7thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/62\/revisions\/17592"}],"wp:attachment":[{"href":"https:\/\/7thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/media?parent=62"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}