{"id":36,"date":"2022-04-13T06:10:09","date_gmt":"2022-04-13T06:10:09","guid":{"rendered":"http:\/\/9thclass.deltapublications.in\/?page_id=36"},"modified":"2025-11-20T07:15:39","modified_gmt":"2025-11-20T07:15:39","slug":"b-6-evaluate-numerical-expressions-involving-rational-numbers","status":"publish","type":"page","link":"https:\/\/9thclass.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<h2 class=\"wp-block-heading has-text-align-center has-text-color\" style=\"color:#00056d;text-transform:uppercase\"><strong>Evaluate numerical expressions involving rational numbers<\/strong><\/h2>\n\n\n\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<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>Understanding Rational Numbers<\/strong><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p><strong>Definition:<\/strong><\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"619\" height=\"51\" src=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2024\/08\/image-35.png\" alt=\"\" class=\"wp-image-14647\" style=\"width:837px;height:auto\" srcset=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2024\/08\/image-35.png 619w, https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2024\/08\/image-35-300x25.png 300w\" sizes=\"auto, (max-width: 619px) 100vw, 619px\" \/><\/figure><\/div>\n\n\n<p><strong>Examples:<\/strong><\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"alignleft size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"458\" height=\"64\" src=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2024\/08\/image-36.png\" alt=\"\" class=\"wp-image-14648\" style=\"width:544px;height:auto\" srcset=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2024\/08\/image-36.png 458w, https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2024\/08\/image-36-300x42.png 300w\" sizes=\"auto, (max-width: 458px) 100vw, 458px\" \/><\/figure><\/div>\n\n\n<h4 class=\"wp-block-heading\"><\/h4>\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><strong>Evaluating Numerical Expressions<\/strong><\/strong><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p><strong>Order of Operations (PEMDAS\/BODMAS):<\/strong><\/p>\n\n\n\n<ul 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<\/ul>\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><strong>Steps for Evaluating Expressions:<\/strong><\/strong><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<ul 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<\/ul>\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><strong>Combining Rational Numbers:<\/strong><\/strong><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<ul 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<\/ul>\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>Examples<\/strong><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p><strong>Simple Addition:<\/strong><\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"297\" height=\"166\" 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<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><strong>Expression with Parentheses:<\/strong><\/strong><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"456\" height=\"199\" src=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2024\/08\/image-38.png\" alt=\"\" class=\"wp-image-14654\" style=\"width:511px;height:auto\" srcset=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2024\/08\/image-38.png 456w, https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2024\/08\/image-38-300x131.png 300w\" sizes=\"auto, (max-width: 456px) 100vw, 456px\" \/><\/figure><\/div>\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><strong>Expression with Exponents:<\/strong><\/strong><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"305\" height=\"205\" src=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2024\/08\/image-39.png\" alt=\"\" class=\"wp-image-14656\" style=\"width:409px;height:auto\" srcset=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2024\/08\/image-39.png 305w, https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2024\/08\/image-39-300x202.png 300w\" sizes=\"auto, (max-width: 305px) 100vw, 305px\" \/><\/figure><\/div>\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><strong>Complex Expression:<\/strong><\/strong><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"369\" height=\"231\" src=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2024\/08\/image-40.png\" alt=\"\" class=\"wp-image-14657\" style=\"width:455px;height:auto\" srcset=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2024\/08\/image-40.png 369w, https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2024\/08\/image-40-300x188.png 300w\" sizes=\"auto, (max-width: 369px) 100vw, 369px\" \/><\/figure><\/div>\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>Practice Problems<\/strong><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p><strong>Addition and Subtraction:<\/strong><\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"102\" height=\"68\" 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 loading=\"lazy\" decoding=\"async\" width=\"96\" height=\"66\" 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 loading=\"lazy\" decoding=\"async\" width=\"125\" height=\"66\" 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 loading=\"lazy\" decoding=\"async\" width=\"113\" height=\"71\" 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<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>Tips for Success<\/strong><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p><strong>Follow Order of Operations:<\/strong><\/p>\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<p><strong>Common Denominator:<\/strong><\/p>\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<p><strong>Simplify:<\/strong><\/p>\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<p><strong>Check Work:<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Double-check calculations to ensure accuracy, especially when dealing with complex expressions.<\/li>\n<\/ul>\n<\/div><\/div>\n\n\n\n<p class=\"has-text-align-center has-text-color has-normal-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:#c0e7fb\"><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-text-color\" style=\"color:#b00012\">\ud83c\udfaf Evaluate&nbsp;the&nbsp;expression.<\/p>\n\n\n\n<p class=\"has-text-align-center has-text-color\" style=\"color:#b00012\"><strong>0.2\u00f72+0.6<\/strong><\/p>\n\n\n\n<p><em>Write&nbsp;your answer as an integer or a decimal. Do not&nbsp;round.<\/em><\/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 class=\"has-normal-font-size\">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-normal-font-size\" style=\"background-color:#ecc7c7\"><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-text-color\" style=\"color:#b00012\">\ud83c\udfaf Evaluate&nbsp;the&nbsp;expression.<\/p>\n\n\n\n<p class=\"has-text-align-center has-text-color\" style=\"color:#b00012\"><strong>0.3\u00f73\u00d70.2<\/strong><\/p>\n\n\n\n<p><em>Write&nbsp;your answer as an integer or a decimal. Do not&nbsp;round.<\/em><\/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-normal-font-size\" style=\"background-color:#e0f7d1\"><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<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\" style=\"color:#b00012\">\ud83c\udfaf Evaluate the expression.<\/p>\n\n\n\n<p class=\"has-text-color\" style=\"color:#b00012\"><strong>0.6 + 0.4 \u00f7 4<\/strong><\/p>\n<\/div><\/div>\n\n\n\n<p>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>0.6 + 0.4 \u00f7 4<\/p>\n\n\n\n<p>This expression has addition and division. The order of operations says to divide before adding.<\/p>\n\n\n\n<h5 class=\"wp-block-heading has-normal-font-size\">0.6 + 0.4 \u00f7 4<\/h5>\n\n\n\n<p>0.6 + 0.1<\/p>\n\n\n\n<p>Now,&nbsp;add.<\/p>\n\n\n\n<h5 class=\"wp-block-heading has-normal-font-size\">0.6 + 0.1<\/h5>\n\n\n\n<p>0.7<\/p>\n\n\n\n<p>The value of the expression is 0.7.<\/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\/102512\/595\/978\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-20.png\" alt=\"\" class=\"wp-image-7326\" srcset=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-20.png 500w, https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-20-300x300.png 300w, https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-20-150x150.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\/76164\/278\/149\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-21.png\" alt=\"\" class=\"wp-image-7327\" srcset=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-21.png 500w, https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-21-300x300.png 300w, https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-21-150x150.png 150w\" sizes=\"auto, (max-width: 500px) 100vw, 500px\" \/><\/a><\/figure>\n<\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>Evaluate numerical expressions involving rational numbers Understanding Rational Numbers Definition: Examples: Evaluating Numerical Expressions Order of Operations (PEMDAS\/BODMAS): Steps for Evaluating Expressions: Combining Rational Numbers: Examples Simple Addition: Expression with Parentheses: Expression with Exponents: Complex Expression: Practice Problems Addition and Subtraction: Tips for Success Follow Order of Operations: Common Denominator: Simplify: Check Work: Learn with<a class=\"more-link\" href=\"https:\/\/9thclass.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-36","page","type-page","status-publish","hentry","entry"],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/9thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/36","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=36"}],"version-history":[{"count":34,"href":"https:\/\/9thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/36\/revisions"}],"predecessor-version":[{"id":18252,"href":"https:\/\/9thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/36\/revisions\/18252"}],"wp:attachment":[{"href":"https:\/\/9thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/media?parent=36"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}