{"id":28,"date":"2022-04-13T06:09:07","date_gmt":"2022-04-13T06:09:07","guid":{"rendered":"http:\/\/9thclass.deltapublications.in\/?page_id=28"},"modified":"2025-11-20T06:45:56","modified_gmt":"2025-11-20T06:45:56","slug":"b-2-evaluate-numerical-expressions-involving-integers","status":"publish","type":"page","link":"https:\/\/9thclass.deltapublications.in\/index.php\/b-2-evaluate-numerical-expressions-involving-integers\/","title":{"rendered":"B.2 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<h3 class=\"wp-block-heading has-text-align-center has-background-background-color has-text-color has-background\" style=\"color:#00056d;text-transform:uppercase\"><strong>Evaluate numerical expressions involving integers<\/strong><\/h3>\n\n\n\n<p class=\"has-text-color has-huge-font-size\" style=\"color:#74008b\">key notes :<\/p>\n\n\n\n<h3 class=\"wp-block-heading has-large-font-size\">\ud83d\udd22 <strong>Integers<\/strong><\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Integers include <strong>positive numbers<\/strong>, <strong>negative numbers<\/strong>, and <strong>zero<\/strong>.<br>Example: \u2026 \u22125, \u22122, 0, 3, 7 \u2026<\/li>\n<\/ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h1 class=\"wp-block-heading has-large-font-size\">\ud83e\uddee <strong>Order of Operations (BODMAS \/ PEMDAS)<\/strong><\/h1>\n\n\n\n<p>To evaluate any numerical expression, always follow the correct order:<\/p>\n\n\n\n<h3 class=\"wp-block-heading has-large-font-size\"><strong>B \u2192 Brackets<\/strong> \ud83d\udfe9<\/h3>\n\n\n\n<p>Evaluate inside <strong>()<\/strong>, <strong>{}<\/strong>, or <strong>[]<\/strong> first.<\/p>\n\n\n\n<h3 class=\"wp-block-heading has-large-font-size\"><strong>O \u2192 Orders<\/strong> (Powers\/Exponents)<\/h3>\n\n\n\n<p>Example: 3<sup>2<\/sup>=9<\/p>\n\n\n\n<h3 class=\"wp-block-heading has-large-font-size\"><strong>D\/M \u2192 Division &amp; Multiplication<\/strong> (Left to right)<\/h3>\n\n\n\n<h3 class=\"wp-block-heading has-large-font-size\"><strong>A\/S \u2192 Addition &amp; Subtraction<\/strong> (Left to right)<\/h3>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h1 class=\"wp-block-heading has-large-font-size\">\u2795\u2796\u2716\ufe0f\u2797 <strong>Adding Integers<\/strong><\/h1>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Same signs:<\/strong> Add the values, keep the sign.<br>Example: \u22123 + (\u22125) = \u22128<\/li>\n\n\n\n<li><strong>Different signs:<\/strong> Subtract the values, keep the sign of the larger number.<br>Example: \u22127 + 4 = \u22123<\/li>\n<\/ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h1 class=\"wp-block-heading has-large-font-size\">\u2796 <strong>Subtracting Integers<\/strong><\/h1>\n\n\n\n<p>Change subtraction to addition by adding the opposite:<br>\ud83d\udc49 a\u2212b=a+(\u2212b)<\/p>\n\n\n\n<p>Example: 8 \u2212 (\u22123) = 8 + 3 = <strong>11<\/strong><\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h1 class=\"wp-block-heading has-large-font-size\">\u2716\ufe0f <strong>Multiplying &amp; Dividing Integers<\/strong><\/h1>\n\n\n\n<figure class=\"wp-block-table\"><table class=\"has-fixed-layout\"><thead><tr><th>Operation<\/th><th>Result<\/th><\/tr><\/thead><tbody><tr><td>(+) \u00d7 (+)<\/td><td>+<\/td><\/tr><tr><td>(\u2212) \u00d7 (\u2212)<\/td><td>+<\/td><\/tr><tr><td>(+) \u00d7 (\u2212)<\/td><td>\u2212<\/td><\/tr><tr><td>(\u2212) \u00d7 (+)<\/td><td>\u2212<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p>Same rules apply for division.<\/p>\n\n\n\n<p>Example:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\u22126\u00d7\u22122=12<\/li>\n\n\n\n<li>15\u00f7\u22123=\u22125<\/li>\n<\/ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h1 class=\"wp-block-heading has-large-font-size\">\ud83e\udde0 <strong>Simplifying Expressions Step-by-Step<\/strong><\/h1>\n\n\n\n<p>Always:<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li>Apply <strong>BODMAS<\/strong>.<\/li>\n\n\n\n<li>Work <strong>left to right<\/strong>.<\/li>\n\n\n\n<li>Keep track of <strong>signs<\/strong>.<\/li>\n<\/ol>\n\n\n\n<p>Example:<br>Evaluate: 6\u2212[3\u2212(8\u221212)]<\/p>\n\n\n\n<p>Step 1: Inside inner bracket \u2192 8\u221212 = \u22124<br>Step 2: Next bracket \u2192 3\u2212(\u22124) = 3+4 = 7<br>Step 3: Final \u2192 6\u22127 = \u22121<\/p>\n\n\n\n<p>Answer: <strong>\u22121<\/strong><\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h1 class=\"wp-block-heading has-large-font-size\">\ud83d\udcd8 <strong>Common Mistakes to Avoid<\/strong><\/h1>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Ignoring <strong>minus signs<\/strong> near brackets.<\/li>\n\n\n\n<li>Forgetting to use <strong>left-to-right<\/strong> rules for multiplication\/division.<\/li>\n\n\n\n<li>Not converting subtraction to <strong>addition of the opposite<\/strong>.<\/li>\n<\/ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h1 class=\"wp-block-heading has-large-font-size\">\ud83d\udcdd <strong>Practice Examples<\/strong><\/h1>\n\n\n\n<ol class=\"wp-block-list\">\n<li>\u22125+12\u22127=?<\/li>\n\n\n\n<li>3\u00d7(\u22124)+8=?<\/li>\n\n\n\n<li>(15\u00f7\u22123)\u00d7(\u22122)=?<\/li>\n\n\n\n<li>[6\u2212(2\u22129)]\u00f77=?<\/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 an example<\/strong><\/p>\n\n\n\n<div class=\"wp-block-group has-background has-normal-font-size\" style=\"background-color:#facfef\"><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<div class=\"wp-block-group\"><div class=\"wp-block-group__inner-container is-layout-constrained wp-block-group-is-layout-constrained\">\n<p class=\"has-text-color has-normal-font-size\" style=\"color:#b00012\"><strong>Evaluate&nbsp;the&nbsp;expression.<\/strong><\/p>\n<\/div><\/div>\n\n\n\n<p class=\"has-text-align-center has-normal-font-size\"> 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:#c2eaf9\"><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\"><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-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-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\"><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-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!<\/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\/76089\/287\/396\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-24.png\" alt=\"\" class=\"wp-image-7340\" srcset=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-24.png 500w, https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-24-300x300.png 300w, https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-24-150x150.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\/76131\/905\/895\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-25.png\" alt=\"\" class=\"wp-image-7341\" srcset=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-25.png 500w, https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-25-300x300.png 300w, https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-25-150x150.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 key notes : \ud83d\udd22 Integers \ud83e\uddee Order of Operations (BODMAS \/ PEMDAS) To evaluate any numerical expression, always follow the correct order: B \u2192 Brackets \ud83d\udfe9 Evaluate inside (), {}, or [] first. O \u2192 Orders (Powers\/Exponents) Example: 32=9 D\/M \u2192 Division &amp; Multiplication (Left to right) A\/S \u2192 Addition<a class=\"more-link\" href=\"https:\/\/9thclass.deltapublications.in\/index.php\/b-2-evaluate-numerical-expressions-involving-integers\/\">Continue reading <span class=\"screen-reader-text\">&#8220;B.2 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-28","page","type-page","status-publish","hentry","entry"],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/9thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/28","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/9thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/9thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/9thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/9thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/comments?post=28"}],"version-history":[{"count":24,"href":"https:\/\/9thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/28\/revisions"}],"predecessor-version":[{"id":18249,"href":"https:\/\/9thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/28\/revisions\/18249"}],"wp:attachment":[{"href":"https:\/\/9thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/media?parent=28"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}