{"id":29,"date":"2022-04-13T09:47:51","date_gmt":"2022-04-13T09:47:51","guid":{"rendered":"http:\/\/10thclass.deltapublications.in\/?page_id=29"},"modified":"2025-07-31T09:36:22","modified_gmt":"2025-07-31T09:36:22","slug":"b-2-evaluate-numerical-expressions-involving-integers","status":"publish","type":"page","link":"https:\/\/10thclass.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-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-background-background-color has-text-color has-background has-link-color has-huge-font-size wp-elements-f6ff35dfa15167072a1322ba7799cdaf\" style=\"color:#00056d;text-transform:uppercase\"><strong>Evaluate numerical expressions involving integers<\/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<ol class=\"wp-block-list\">\n<li><strong>Definition:<\/strong>\n<ul class=\"wp-block-list\">\n<li>A numerical expression is a mathematical phrase that includes numbers and operations (such as addition, subtraction, multiplication, and division) but does not include an equals sign.<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li><strong>Order of Operations:<\/strong>\n<ul class=\"wp-block-list\">\n<li>To correctly evaluate numerical expressions, follow the order of operations, often remembered by the acronym PEMDAS:\n<ul class=\"wp-block-list\">\n<li><strong>P<\/strong>arentheses<\/li>\n\n\n\n<li><strong>E<\/strong>xponents (not typically covered in 6th grade, but it&#8217;s good to be aware)<\/li>\n\n\n\n<li><strong>M<\/strong>ultiplication and <strong>D<\/strong>ivision (from left to right)<\/li>\n\n\n\n<li><strong>A<\/strong>ddition and <strong>S<\/strong>ubtraction (from left to right)<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<\/li>\n<\/ol>\n\n\n\n<h4 class=\"wp-block-heading\">Steps to Evaluate Numerical Expressions<\/h4>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>Step 1: Parentheses<\/strong>\n<ul class=\"wp-block-list\">\n<li>Solve expressions inside parentheses first.<\/li>\n\n\n\n<li>Example: (3+4)\u00d72<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li><strong>Step 2: Multiplication and Division<\/strong>\n<ul class=\"wp-block-list\">\n<li>Perform all multiplication and division from left to right.<\/li>\n\n\n\n<li>Example: 3+4\u00d72<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li><strong>Step 3: Addition and Subtraction<\/strong>\n<ul class=\"wp-block-list\">\n<li>Perform all addition and subtraction from left to right.<\/li>\n\n\n\n<li>Example: 3+(4\u00d72)<\/li>\n<\/ul>\n<\/li>\n<\/ol>\n\n\n\n<h4 class=\"wp-block-heading\">Example Problems<\/h4>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>Simple Example:<\/strong>\n<ul class=\"wp-block-list\">\n<li>5+3\u00d72\n<ul class=\"wp-block-list\">\n<li>First, multiply: 3\u00d72=6<\/li>\n\n\n\n<li>Then, add: 5+6=11<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li><strong>With Parentheses:<\/strong>\n<ul class=\"wp-block-list\">\n<li>(2+3)\u00d74\n<ul class=\"wp-block-list\">\n<li>First, solve inside parentheses: 2+3=5<\/li>\n\n\n\n<li>Then, multiply: 5\u00d74=20<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li><strong>Multiple Operations:<\/strong>\n<ul class=\"wp-block-list\">\n<li>6\u22122\u00d73+4\u00f72\n<ul class=\"wp-block-list\">\n<li>First, multiply and divide from left to right:\n<ul class=\"wp-block-list\">\n<li>2\u00d73=6<\/li>\n\n\n\n<li>4\u00f72=2<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li>Then, add and subtract from left to right:\n<ul class=\"wp-block-list\">\n<li>6\u22126+2=0+2=2<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<\/li>\n<\/ol>\n\n\n\n<h4 class=\"wp-block-heading\">Tips for Students<\/h4>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Write Clearly:<\/strong>\n<ul class=\"wp-block-list\">\n<li>Write each step of your work to avoid mistakes.<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li><strong>Double-Check:<\/strong>\n<ul class=\"wp-block-list\">\n<li>Always double-check each operation to ensure accuracy.<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li><strong>Use Parentheses:<\/strong>\n<ul class=\"wp-block-list\">\n<li>When in doubt, use parentheses to clarify the order of operations.<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li><strong>Practice:<\/strong>\n<ul class=\"wp-block-list\">\n<li>Regular practice with different types of problems helps reinforce the rules.<\/li>\n<\/ul>\n<\/li>\n<\/ul>\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-large-font-size\" style=\"background-color:#a2f2ea\"><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\">\ud83d\udd2e Evaluate&nbsp;the&nbsp;expression.<\/p>\n\n\n\n<p class=\"has-text-align-center has-foreground-color has-text-color has-large-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-large-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 has-link-color wp-elements-d33b81cf5d7f072494a0684258f47be3\" style=\"color:#b00012\">\ud83d\udd2e 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-large-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 has-link-color wp-elements-71947937e81e2afdf2508b2aeface057\" style=\"color:#b00012\">\ud83d\udd2e Evaluate the expression for p = 6, q = 5 and r = 4.<\/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<div class=\"wp-block-group has-background has-large-font-size\" style=\"background-color:#f0f49c\"><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-afb4779a2022477b64ad85a34db8145e\" style=\"color:#b00012\">\ud83d\udd2e Evaluate the expression.<\/p>\n\n\n\n<p>2\u00f71\u20135<\/p>\n<\/div><\/div>\n\n\n\n<p>First, identify the operations in the expression.<\/p>\n\n\n\n<p>2\u00f71\u20135<\/p>\n\n\n\n<p>This&nbsp;expression has division and subtraction. The order of operations says to divide before&nbsp;subtracting.<\/p>\n\n\n\n<h5 class=\"wp-block-heading has-foreground-color has-text-color has-link-color wp-elements-bf9bcaf70fd12fc69f029220b2dd5016\"><strong>2\u00f71<\/strong>\u20135<\/h5>\n\n\n\n<p>= <strong>2<\/strong>\u20135<\/p>\n\n\n\n<p>Now,&nbsp;subtract.<\/p>\n\n\n\n<p><strong>2 &#8211; 5<\/strong><\/p>\n\n\n\n<p>=<strong> -3<\/strong> <\/p>\n\n\n\n<p>The&nbsp;value of the expression is&nbsp;-3<\/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\/365\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-9.png\" alt=\"\" class=\"wp-image-6449\" srcset=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-9.png 500w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-9-300x300.png 300w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-9-150x150.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\/76058\/579\/241\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-9.png\" alt=\"\" class=\"wp-image-6450\" srcset=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-9.png 500w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-9-300x300.png 300w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-9-150x150.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: Steps to Evaluate Numerical Expressions Example Problems Tips for Students Learn with an example \ud83d\udd2e Evaluate&nbsp;the&nbsp;expression. 2+4\u00f72 First,&nbsp;identify the operations in the&nbsp;expression. 2+4\u00f72 This&nbsp;expression has addition and division. The order of operations says to divide before&nbsp;adding. 2+4\u00f72=2+2 Now,&nbsp;add.2+2=4. The&nbsp;value of the expression is&nbsp;4. \ud83d\udd2e Evaluate the expression for<a class=\"more-link\" href=\"https:\/\/10thclass.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-29","page","type-page","status-publish","hentry","entry"],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/10thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/29","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=29"}],"version-history":[{"count":22,"href":"https:\/\/10thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/29\/revisions"}],"predecessor-version":[{"id":18161,"href":"https:\/\/10thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/29\/revisions\/18161"}],"wp:attachment":[{"href":"https:\/\/10thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/media?parent=29"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}