{"id":50,"date":"2022-04-12T11:57:35","date_gmt":"2022-04-12T11:57:35","guid":{"rendered":"http:\/\/8thclass.deltapublications.in\/?page_id=50"},"modified":"2025-11-20T06:18:03","modified_gmt":"2025-11-20T06:18:03","slug":"c-8-evaluate-numerical-expressions-involving-integers","status":"publish","type":"page","link":"https:\/\/8thclass.deltapublications.in\/index.php\/c-8-evaluate-numerical-expressions-involving-integers\/","title":{"rendered":"C.8 Evaluate numerical expressions involving integers"},"content":{"rendered":"\n<div class=\"wp-block-group has-normal-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>Evaluate numerical expressions involving integers<\/strong><\/h2>\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\" style=\"flex-basis:100%\">\n<div style=\"position: relative; width: 100%; height: 0; padding-top: 56.2500%;\n padding-bottom: 0; box-shadow: 0 2px 8px 0 rgba(63,69,81,0.16); margin-top: 1.6em; margin-bottom: 0.9em; overflow: hidden;\n border-radius: 8px; will-change: transform;\">\n  <iframe loading=\"lazy\" style=\"position: absolute; width: 100%; height: 100%; top: 0; left: 0; border: none; padding: 0;margin: 0;\"\n    src=\"https:\/\/www.canva.com\/design\/DAGwfqt7dyE\/6QlovowW50nVTyDtf-nZ6g\/watch?embed\" allowfullscreen=\"allowfullscreen\" allow=\"fullscreen\">\n  <\/iframe>\n<\/div>\n<a href=\"https:&#x2F;&#x2F;www.canva.com&#x2F;design&#x2F;DAGwfqt7dyE&#x2F;6QlovowW50nVTyDtf-nZ6g&#x2F;watch?utm_content=DAGwfqt7dyE&amp;utm_campaign=designshare&amp;utm_medium=embeds&amp;utm_source=link\" target=\"_blank\" rel=\"noopener\">E.11 Evaluate Numerical Expressions Involving\u00a0Decimals<\/a> by Delta publications\n<\/div>\n<\/div>\n\n\n\n<p class=\"has-text-color has-link-color has-huge-font-size wp-elements-aae0d72b0df05b1a7d05750bd97517d2\" style=\"color:#74008b\"><strong>Key Notes :<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-table has-normal-font-size\"><table class=\"has-text-color has-link-color has-fixed-layout\" style=\"color:#000060\"><tbody><tr><td><strong>\ud83d\udd39  What are Integers?<\/strong><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<ul class=\"wp-block-list has-normal-font-size\">\n<li>Integers are <strong>whole numbers and their negatives<\/strong>.<\/li>\n\n\n\n<li>Examples: <strong>\u2026, -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5 \u2026<\/strong><\/li>\n<\/ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<figure class=\"wp-block-table has-normal-font-size\"><table class=\"has-text-color has-link-color has-fixed-layout\" style=\"color:#000060\"><tbody><tr><td><strong>\ud83d\udd39  What is a Numerical Expression?<\/strong><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<ul class=\"wp-block-list\">\n<li>A <strong>numerical expression<\/strong> is a combination of numbers and mathematical operations ( +, \u2212, \u00d7, \u00f7, brackets, exponents).<\/li>\n\n\n\n<li>Example: 3+(\u22125)\u00d72<\/li>\n<\/ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<figure class=\"wp-block-table has-normal-font-size\"><table class=\"has-text-color has-link-color has-fixed-layout\" style=\"color:#000060\"><tbody><tr><td><strong>\ud83d\udd39 Order of Operations (BODMAS Rule)<\/strong><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p>To evaluate expressions correctly, follow <strong>BODMAS<\/strong>:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>B \u2192 Brackets<\/strong> (first solve inside brackets)<\/li>\n\n\n\n<li><strong>O \u2192 Orders<\/strong> (powers, squares, roots, etc.)<\/li>\n\n\n\n<li><strong>D \u2192 Division<\/strong><\/li>\n\n\n\n<li><strong>M \u2192 Multiplication<\/strong><\/li>\n\n\n\n<li><strong>A \u2192 Addition<\/strong><\/li>\n\n\n\n<li><strong>S \u2192 Subtraction<\/strong><\/li>\n<\/ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<figure class=\"wp-block-table has-normal-font-size\"><table class=\"has-text-color has-link-color has-fixed-layout\" style=\"color:#000060\"><tbody><tr><td><strong>\ud83d\udd39  Rules of Integers<\/strong><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p><strong>Addition<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>(+) + (+) = +<\/li>\n\n\n\n<li>(\u2212) + (\u2212) = \u2212<\/li>\n\n\n\n<li>(\u2212) + (+) \u2192 subtract and keep the sign of bigger number<\/li>\n<\/ul>\n\n\n\n<p><strong>Subtraction<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>a\u2212b=a+(\u2212b)<\/li>\n<\/ul>\n\n\n\n<p><strong>Multiplication &amp; Division<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>(+) \u00d7 (+) = +<\/li>\n\n\n\n<li>(\u2212) \u00d7 (\u2212) = +<\/li>\n\n\n\n<li>(+) \u00d7 (\u2212) = \u2212<\/li>\n\n\n\n<li>(\u2212) \u00d7 (+) = \u2212<\/li>\n<\/ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<figure class=\"wp-block-table has-normal-font-size\"><table class=\"has-text-color has-link-color has-fixed-layout\" style=\"color:#000060\"><tbody><tr><td><strong>\ud83d\udd39  Examples<\/strong><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<h3 class=\"wp-block-heading has-normal-font-size\"><strong>Example 1:<\/strong><\/h3>\n\n\n\n<p>Evaluate: 5+(\u22123)<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\ud83d\udc49 5\u22123=2<\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading has-normal-font-size\"><strong>Example 2:<\/strong><\/h3>\n\n\n\n<p>Evaluate: (\u22126)\u2212(\u22128)<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\ud83d\udc49 \u22126+8=2<\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading has-normal-font-size\"><strong>Example 3:<\/strong><\/h3>\n\n\n\n<p>Evaluate: (\u22124)\u00d7(\u22127)<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\ud83d\udc49 +28<\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading has-normal-font-size\"><strong>Example 4:<\/strong><\/h3>\n\n\n\n<p>Evaluate: 12\u00f7(\u22123)<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\ud83d\udc49 \u22124<\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading has-normal-font-size\"><strong>Example 5:<\/strong><\/h3>\n\n\n\n<p>Evaluate: [3+(\u22122)]\u00d7(\u22124)<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\ud83d\udc49 Inside bracket: 3\u22122=1<\/li>\n\n\n\n<li>\ud83d\udc49 Multiply: 1\u00d7(\u22124)=\u22124<\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading has-normal-font-size\"><strong>Example 6:<\/strong><\/h3>\n\n\n\n<p>Evaluate: (\u22122)<sup>2<\/sup>+(\u22123)<sup>3<\/sup><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\ud83d\udc49 (\u22122)<sup>2<\/sup>=4<\/li>\n\n\n\n<li>\ud83d\udc49 (\u22123)<sup>3<\/sup>=\u221227<\/li>\n\n\n\n<li>\ud83d\udc49 4+(\u221227)=\u221223<\/li>\n<\/ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<figure class=\"wp-block-table has-normal-font-size\"><table class=\"has-text-color has-link-color has-fixed-layout\" style=\"color:#000060\"><tbody><tr><td><strong>\ud83d\udd39  Key Points to Remember<\/strong><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Always apply <strong>BODMAS<\/strong> when more than one operation is involved.<\/li>\n\n\n\n<li>Be careful with <strong>signs<\/strong> while adding, subtracting, multiplying, and dividing.<\/li>\n\n\n\n<li>Use brackets to simplify step by step.<\/li>\n\n\n\n<li>Negative \u00d7 Negative = Positive; Positive \u00d7 Negative = Negative.<\/li>\n<\/ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<figure class=\"wp-block-table has-normal-font-size\"><table class=\"has-text-color has-link-color has-fixed-layout\" style=\"color:#000060\"><tbody><tr><td><strong>\u2705 <strong>Practice Questions for Students<\/strong><\/strong><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<ol class=\"wp-block-list\">\n<li>Evaluate: (\u22125)+(\u22128)+12<\/li>\n\n\n\n<li>Evaluate: 15\u2212(\u22129)<\/li>\n\n\n\n<li>Evaluate: (\u22127)\u00d7(\u22126)\u00f7(\u22122)<\/li>\n\n\n\n<li>Evaluate: [10\u2212(\u22125)]\u00d7(\u22123)<\/li>\n\n\n\n<li>Evaluate: (\u22124)<sup>3<\/sup>+(2)<sup>2<\/sup><\/li>\n<\/ol>\n\n\n\n<p class=\"has-text-align-center has-text-color has-large-font-size\" style=\"color:#105000\"><strong>Learn with Example<\/strong><\/p>\n\n\n\n<div class=\"wp-block-group has-background has-normal-font-size\" style=\"background-color:#fbdcfb\"><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 has-normal-font-size\"><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-c1c4cd929c23403fb539ce083ec0663c\" style=\"color:#b00012\">\u27a1\ufe0f Example 1 :<\/p>\n\n\n\n<p class=\"has-text-align-left has-text-color has-link-color has-normal-font-size wp-elements-12fd7130fe22626a6b158d2f7d10d6df\" style=\"color:#b00012\">\u27a1\ufe0f Evaluate&nbsp;the&nbsp;expression. <\/p>\n\n\n\n<p class=\"has-text-align-left has-text-color has-link-color has-normal-font-size wp-elements-bd831ad9c863273f58dd5bdca2db39fa\" style=\"color:#b00012\">2+4\u00f72<\/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-background has-normal-font-size\" style=\"background-color:#aee3f4\"><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-text-color has-background has-link-color wp-elements-3df693342e0d1081a538a4903e00079e\" style=\"color:#b00012\"><div class=\"wp-block-group__inner-container is-layout-flow wp-block-group-is-layout-flow\">\n<p class=\"has-normal-font-size\">\u27a1\ufe0f Example 2 :<\/p>\n\n\n\n<p>Evaluate the expression for x = 5, y = 8 and z = 6.<\/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-background has-normal-font-size\" style=\"background-color:#b2f9e1\"><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-text-color has-background has-link-color wp-elements-a1ab1ac888a5284c0444ad1b54f67d38\" style=\"color:#b00012\"><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>Evaluate the expression for p = 6, q = 5 and r = 4.<\/p>\n\n\n\n<p class=\"has-text-align-left has-normal-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\">Let&#8217;s practice!\ud83d\udd8a\ufe0f <\/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\/76327\/331\/865\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-227.png\" alt=\"\" class=\"wp-image-9325\" srcset=\"https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-227.png 500w, https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-227-300x300.png 300w, https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-227-150x150.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\/33812\/134\/368\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-233.png\" alt=\"\" class=\"wp-image-9326\" srcset=\"https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-233.png 500w, https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-233-300x300.png 300w, https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-233-150x150.png 150w\" sizes=\"auto, (max-width: 500px) 100vw, 500px\" \/><\/a><\/figure>\n<\/div>\n<\/div>\n<\/div><\/div>\n","protected":false},"excerpt":{"rendered":"<p>Evaluate numerical expressions involving integers E.11 Evaluate Numerical Expressions Involving\u00a0Decimals by Delta publications Key Notes : \ud83d\udd39 What are Integers? \ud83d\udd39 What is a Numerical Expression? \ud83d\udd39 Order of Operations (BODMAS Rule) To evaluate expressions correctly, follow BODMAS: \ud83d\udd39 Rules of Integers Addition Subtraction Multiplication &amp; Division \ud83d\udd39 Examples Example 1: Evaluate: 5+(\u22123) Example 2:<a class=\"more-link\" href=\"https:\/\/8thclass.deltapublications.in\/index.php\/c-8-evaluate-numerical-expressions-involving-integers\/\">Continue reading <span class=\"screen-reader-text\">&#8220;C.8 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,"_monsterinsights_skip_tracking":false,"_monsterinsights_sitenote_active":false,"_monsterinsights_sitenote_note":"","_monsterinsights_sitenote_category":0,"footnotes":""},"class_list":["post-50","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\/50","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=50"}],"version-history":[{"count":32,"href":"https:\/\/8thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/50\/revisions"}],"predecessor-version":[{"id":22319,"href":"https:\/\/8thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/50\/revisions\/22319"}],"wp:attachment":[{"href":"https:\/\/8thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/media?parent=50"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}