{"id":37,"date":"2022-04-13T09:48:57","date_gmt":"2022-04-13T09:48:57","guid":{"rendered":"http:\/\/10thclass.deltapublications.in\/?page_id=37"},"modified":"2025-03-05T06:48:26","modified_gmt":"2025-03-05T06:48:26","slug":"b-6-evaluate-numerical-expressions-involving-rational-numbers","status":"publish","type":"page","link":"https:\/\/10thclass.deltapublications.in\/index.php\/b-6-evaluate-numerical-expressions-involving-rational-numbers\/","title":{"rendered":"B.6 Evaluate numerical expressions involving rational numbers"},"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-text-color has-huge-font-size\" style=\"color:#00056d;text-transform:uppercase\"><strong>Evaluate numerical expressions involving rational numbers<\/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<h4 class=\"wp-block-heading\"><strong>Understanding Rational Numbers<\/strong><\/h4>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>Definition:<\/strong><\/li>\n<\/ol>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full is-resized\"><img decoding=\"async\" src=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2024\/08\/image-35.png\" alt=\"\" class=\"wp-image-14647\" style=\"width:837px;height:auto\"\/><\/figure><\/div>\n\n\n<ol class=\"wp-block-list\">\n<li><strong>Examples:<\/strong><\/li>\n<\/ol>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full is-resized\"><img decoding=\"async\" src=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2024\/08\/image-36.png\" alt=\"\" class=\"wp-image-14648\" style=\"width:744px;height:auto\"\/><\/figure><\/div>\n\n\n<h4 class=\"wp-block-heading\"><strong>Evaluating Numerical Expressions<\/strong><\/h4>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Order of Operations (PEMDAS\/BODMAS):<\/strong><\/li>\n<\/ul>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>P<\/strong>arentheses\/<strong>B<\/strong>rackets: Solve expressions inside parentheses\/brackets first.<\/li>\n\n\n\n<li><strong>E<\/strong>xponents\/<strong>O<\/strong>rders: Evaluate exponents or orders (powers and roots).<\/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<\/ol>\n\n\n\n<p><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Steps for Evaluating Expressions:<\/strong><\/li>\n<\/ul>\n\n\n\n<ol class=\"wp-block-list\">\n<li>Simplify inside parentheses or brackets first.<\/li>\n\n\n\n<li>Apply exponents or roots.<\/li>\n\n\n\n<li>Perform multiplication and division from left to right.<\/li>\n\n\n\n<li>Perform addition and subtraction from left to right.<\/li>\n<\/ol>\n\n\n\n<p><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Combining Rational Numbers:<\/strong><\/li>\n<\/ul>\n\n\n\n<ol class=\"wp-block-list\">\n<li>Addition\/Subtraction: Find a common denominator if needed.<\/li>\n\n\n\n<li>Multiplication: Multiply the numerators and the denominators.<\/li>\n\n\n\n<li>Division: Multiply by the reciprocal of the divisor.<\/li>\n<\/ol>\n\n\n\n<h4 class=\"wp-block-heading\">Examples<\/h4>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>Simple Addition:<\/strong><\/li>\n<\/ol>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full is-resized\"><img decoding=\"async\" src=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2024\/08\/image-37.png\" alt=\"\" class=\"wp-image-14653\" style=\"width:354px;height:auto\"\/><\/figure><\/div>\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Expression with Parentheses:<\/strong><\/li>\n<\/ul>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full is-resized\"><img decoding=\"async\" src=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2024\/08\/image-38.png\" alt=\"\" class=\"wp-image-14654\" style=\"width:511px;height:auto\"\/><\/figure><\/div>\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Expression with Exponents:<\/strong><\/li>\n<\/ul>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full is-resized\"><img decoding=\"async\" src=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2024\/08\/image-39.png\" alt=\"\" class=\"wp-image-14656\" style=\"width:409px;height:auto\"\/><\/figure><\/div>\n\n\n<ul class=\"wp-block-list\">\n<li><\/li>\n<\/ul>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Complex Expression:<\/strong><\/li>\n<\/ul>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full is-resized\"><img decoding=\"async\" src=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2024\/08\/image-40.png\" alt=\"\" class=\"wp-image-14657\" style=\"width:455px;height:auto\"\/><\/figure><\/div>\n\n\n<h4 class=\"wp-block-heading\">Practice Problems<\/h4>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>Addition and Subtraction:<\/strong><\/li>\n<\/ol>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full is-resized\"><img decoding=\"async\" src=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2024\/08\/image-41.png\" alt=\"\" class=\"wp-image-14659\" style=\"width:168px;height:auto\"\/><\/figure><\/div>\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Multiplication and Division:<\/strong><\/li>\n<\/ul>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full is-resized\"><img decoding=\"async\" src=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2024\/08\/image-42.png\" alt=\"\" class=\"wp-image-14661\" style=\"width:134px;height:auto\"\/><\/figure><\/div>\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Expressions with Parentheses:<\/strong><\/li>\n<\/ul>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full is-resized\"><img decoding=\"async\" src=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2024\/08\/image-43.png\" alt=\"\" class=\"wp-image-14662\" style=\"width:163px;height:auto\"\/><\/figure><\/div>\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Expressions with Exponents:<\/strong><\/li>\n<\/ul>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full is-resized\"><img decoding=\"async\" src=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2024\/08\/image-44.png\" alt=\"\" class=\"wp-image-14663\" style=\"width:153px;height:auto\"\/><\/figure><\/div>\n\n\n<h3 class=\"wp-block-heading\">Tips for Success<\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Follow Order of Operations:<\/strong><\/li>\n<\/ul>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Always follow the order of operations (PEMDAS\/BODMAS) to evaluate expressions correctly.<\/li>\n<\/ul>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Common Denominator:<\/strong><\/li>\n<\/ul>\n\n\n\n<ul class=\"wp-block-list\">\n<li>When adding or subtracting fractions, always find a common denominator.<\/li>\n<\/ul>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Simplify:<\/strong><\/li>\n<\/ul>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Simplify fractions whenever possible to make calculations easier.<\/li>\n<\/ul>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Check Work:<\/strong><\/li>\n<\/ul>\n\n\n\n<ul class=\"wp-block-list has-large-font-size\">\n<li>Double-check calculations to ensure accuracy, especially when dealing with complex expressions.<\/li>\n<\/ul>\n\n\n\n<p class=\"has-text-align-center has-text-color has-link-color has-huge-font-size wp-elements-b9a4d2dbd2b5893137fb321e43f2d55d\" 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:#8cd2f4\"><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-align-center has-foreground-color has-text-color has-link-color wp-elements-b707d59f1c49a35640084a8e924e7fba\">\ud83d\udd2e Evaluate&nbsp;the&nbsp;expression.<\/p>\n\n\n\n<p class=\"has-text-align-center\">0.2\u00f72+0.6<\/p>\n\n\n\n<p class=\"has-text-color has-link-color wp-elements-f6ad28abdf3dc551333588f786bb6d19\" style=\"color:#b00012\">Write&nbsp;your answer as an integer or a decimal. Do not&nbsp;round.<\/p>\n<\/div><\/div>\n\n\n\n<p>First,&nbsp;identify the operations in the&nbsp;expression.<\/p>\n\n\n\n<p>0.2\u00f72+0.6<\/p>\n\n\n\n<p>This&nbsp;expression has division and addition. The order of operations says to divide before&nbsp;adding.<\/p>\n\n\n\n<p>0.2\u00f72+0.6=<strong>0.1<\/strong>+0.6<\/p>\n\n\n\n<p>Now,&nbsp;add.0.1+0.6=<strong>0.7<\/strong><\/p>\n\n\n\n<p>The&nbsp;value of the expression is&nbsp;<strong>0.7<\/strong>.<\/p>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-group has-background has-large-font-size\" style=\"background-color:#f4a9a9\"><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-align-center has-foreground-color has-text-color has-link-color wp-elements-b707d59f1c49a35640084a8e924e7fba\">\ud83d\udd2e Evaluate&nbsp;the&nbsp;expression.<\/p>\n\n\n\n<p class=\"has-text-align-center\">0.3\u00f73\u00d70.2<\/p>\n\n\n\n<p class=\"has-text-color has-link-color wp-elements-f6ad28abdf3dc551333588f786bb6d19\" style=\"color:#b00012\">Write&nbsp;your answer as an integer or a decimal. Do not&nbsp;round.<\/p>\n<\/div><\/div>\n\n\n\n<p>First,&nbsp;identify the operations in the&nbsp;expression.<\/p>\n\n\n\n<p>0.3\u00f73<strong>\u00d7<\/strong>0.2<\/p>\n\n\n\n<p>This&nbsp;expression has division and multiplication. The order of operations says to multiply and divide from left to&nbsp;right.<\/p>\n\n\n\n<p>0.3\u00f73\u00d70.2<\/p>\n\n\n\n<p>=<strong>0.1<\/strong>\u00d70.2<\/p>\n\n\n\n<p>=0.1\u00d70.2<\/p>\n\n\n\n<p>=<strong>0.02<\/strong><\/p>\n\n\n\n<p>The&nbsp;value of the expression is&nbsp;<strong>0.02<\/strong>.<\/p>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-group has-background has-large-font-size\" style=\"background-color:#c0c0f2\"><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-foreground-color has-text-color has-link-color wp-elements-3754bf58c888eb77eec90f40a0508b2f\">\ud83d\udd2e Evaluate the expression.<\/p>\n\n\n\n<p>7+0.5\u00d72<\/p>\n\n\n\n<p class=\"has-text-color has-link-color wp-elements-48e1815c737c74b25c8f2ec873ce567b\" style=\"color:#b00012\">Write your answer as an integer or a decimal. Do not round.<\/p>\n<\/div><\/div>\n\n\n\n<p>First, identify the operations in the expression.<\/p>\n\n\n\n<p>7+0.5\u00d72<\/p>\n\n\n\n<p>This expression has addition and multiplication. The order of operations says to multiply before adding.<\/p>\n\n\n\n<h5 class=\"wp-block-heading\"><strong>7+0.5\u00d72<\/strong><\/h5>\n\n\n\n<p>= 7+1<\/p>\n\n\n\n<p>Now,&nbsp;add.<\/p>\n\n\n\n<p>7 + 1<\/p>\n\n\n\n<p>= 8<\/p>\n\n\n\n<p>The value of the expression is <strong>8<\/strong>.<\/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\/76137\/669\/215\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-12.png\" alt=\"\" class=\"wp-image-6511\" srcset=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-12.png 500w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-12-300x300.png 300w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-12-150x150.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\/76188\/791\/131\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-12.png\" alt=\"\" class=\"wp-image-6512\" srcset=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-12.png 500w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-12-300x300.png 300w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-12-150x150.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 rational numbers key notes: Understanding Rational Numbers Evaluating Numerical Expressions Examples Practice Problems Tips for Success Learn with an example \ud83d\udd2e Evaluate&nbsp;the&nbsp;expression. 0.2\u00f72+0.6 Write&nbsp;your answer as an integer or a decimal. Do not&nbsp;round. First,&nbsp;identify the operations in the&nbsp;expression. 0.2\u00f72+0.6 This&nbsp;expression has division and addition. The order of operations says to divide<a class=\"more-link\" href=\"https:\/\/10thclass.deltapublications.in\/index.php\/b-6-evaluate-numerical-expressions-involving-rational-numbers\/\">Continue reading <span class=\"screen-reader-text\">&#8220;B.6 Evaluate numerical expressions involving 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,"_monsterinsights_skip_tracking":false,"_monsterinsights_sitenote_active":false,"_monsterinsights_sitenote_note":"","_monsterinsights_sitenote_category":0,"footnotes":""},"class_list":["post-37","page","type-page","status-publish","hentry","entry"],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/10thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/37","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=37"}],"version-history":[{"count":17,"href":"https:\/\/10thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/37\/revisions"}],"predecessor-version":[{"id":17574,"href":"https:\/\/10thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/37\/revisions\/17574"}],"wp:attachment":[{"href":"https:\/\/10thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/media?parent=37"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}