{"id":86,"date":"2022-04-12T12:04:01","date_gmt":"2022-04-12T12:04:01","guid":{"rendered":"http:\/\/8thclass.deltapublications.in\/?page_id=86"},"modified":"2025-02-22T15:49:54","modified_gmt":"2025-02-22T15:49:54","slug":"e-9-evaluate-numerical-expressions-involving-rational-numbers","status":"publish","type":"page","link":"https:\/\/8thclass.deltapublications.in\/index.php\/e-9-evaluate-numerical-expressions-involving-rational-numbers\/","title":{"rendered":"E.9 Evaluate numerical expressions involving rational numbers"},"content":{"rendered":"\n<h2 class=\"wp-block-heading has-text-align-center has-text-color has-large-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-ab4cbed01f2dc53453f6fa9edffd950d\" style=\"color:#74008b;text-transform:capitalize\"><strong>Key notes:<\/strong><\/p>\n\n\n\n<p class=\"has-text-color has-link-color has-large-font-size wp-elements-8bcc390ed9ef54ad0d64e116677b522c\" style=\"color:#000060\"><strong>Definition of Rational Numbers<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list has-large-font-size\">\n<li>Rational numbers are numbers that can be expressed as a fraction p\/q\u200b, where p and q are integers, and q \u2260 0.<\/li>\n\n\n\n<li>Includes integers, fractions, terminating and repeating decimals.<\/li>\n<\/ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity is-style-wide\"\/>\n\n\n\n<p class=\"has-text-color has-link-color has-large-font-size wp-elements-236b2258eb4065fe287a089e5dafdd6d\" style=\"color:#000060\"><strong>Order of Operations (PEMDAS\/BODMAS)<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list has-large-font-size\">\n<li><strong>P<\/strong>arentheses \/ <strong>B<\/strong>rackets<\/li>\n\n\n\n<li><strong>E<\/strong>xponents \/ <strong>O<\/strong>rders (Squares, Cubes, etc.)<\/li>\n\n\n\n<li><strong>MD<\/strong> Multiplication and Division (Left to Right)<\/li>\n\n\n\n<li><strong>AS<\/strong> Addition and Subtraction (Left to Right)<\/li>\n<\/ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity is-style-wide\"\/>\n\n\n\n<p class=\"has-text-color has-link-color has-large-font-size wp-elements-69c8806fadfe1fe8c0aca73d39916e52\" style=\"color:#000060\"><strong>Operations with Rational Numbers<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list has-large-font-size\">\n<li><strong>Addition &amp; Subtraction<\/strong>: Convert to a common denominator if necessary.<\/li>\n\n\n\n<li><strong>Multiplication<\/strong>: Multiply numerators and denominators separately.<\/li>\n\n\n\n<li><strong>Division<\/strong>: Multiply by the reciprocal of the divisor.<\/li>\n<\/ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity is-style-wide\"\/>\n\n\n\n<p class=\"has-text-color has-link-color has-large-font-size wp-elements-4709d21a44536834015f314046ea0a06\" style=\"color:#000060\"><strong>Working with Decimals &amp; Fractions<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list has-large-font-size\">\n<li>Convert between fractions and decimals for ease of computation.<\/li>\n\n\n\n<li>Use long division to convert fractions to decimals.<\/li>\n<\/ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity is-style-wide\"\/>\n\n\n\n<p class=\"has-text-color has-link-color has-large-font-size wp-elements-ec206f17a90f9bc012811a6ad622e3ab\" style=\"color:#000060\"><strong>Using Negative Numbers<\/strong><\/p>\n\n\n\n<p class=\"has-large-font-size\">Follow sign rules:<\/p>\n\n\n\n<ul class=\"wp-block-list has-large-font-size\">\n<li><strong>Addition\/Subtraction<\/strong>: Same signs \u2192 Add &amp; keep sign, Different signs \u2192 Subtract &amp; use sign of the larger absolute value.<\/li>\n<\/ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity is-style-wide\"\/>\n\n\n\n<p class=\"has-text-color has-link-color has-large-font-size wp-elements-bc6822fb19622ee01d6a31e97b3532eb\" style=\"color:#000060\"><strong>Multiplication\/Division<\/strong>:<\/p>\n\n\n\n<ul class=\"wp-block-list has-large-font-size\">\n<li>Positive \u00d7 Positive = Positive<\/li>\n\n\n\n<li>Negative \u00d7 Negative = Positive<\/li>\n\n\n\n<li>Positive \u00d7 Negative = Negative<\/li>\n<\/ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity is-style-wide\"\/>\n\n\n\n<p class=\"has-text-color has-link-color has-large-font-size wp-elements-e7e0a33e8e7f535918e2bcfa28899c72\" style=\"color:#000060\"><strong>Evaluating Expressions with Exponents<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list has-large-font-size\">\n<li>Apply exponent rules (e.g., a<sup>m<\/sup> \u00d7 a<sup>n<\/sup> = a<sup>m + n<\/sup>).<\/li>\n\n\n\n<li>Square and cube rational numbers carefully.<\/li>\n<\/ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity is-style-wide\"\/>\n\n\n\n<p class=\"has-text-color has-link-color has-large-font-size wp-elements-1d065f71826cded05dd6196011ed86c3\" style=\"color:#000060\"><strong>Distributive Property<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list has-large-font-size\">\n<li>Use <strong>a (b + c) = ab + ac<\/strong> when simplifying expressions.<\/li>\n<\/ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity is-style-wide\"\/>\n\n\n\n<p class=\"has-text-color has-link-color has-large-font-size wp-elements-e49fb57d935556a879237e2c6fbd6dc9\" style=\"color:#000060\"><strong>Solving Word Problems<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list has-large-font-size\">\n<li>Identify rational number operations from the problem statement.<\/li>\n\n\n\n<li>Apply the correct order of operations and check for reasonableness.<\/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-fdfc903bcf42b04ba0650a8adc990ef0\" style=\"color:#105000\">Learn with an example<\/p>\n\n\n\n<div class=\"wp-block-group has-primary-color has-text-color has-background has-link-color has-large-font-size wp-elements-13531c2dce8c5244ba6030f365ca8382\" style=\"background-color:#bfe6f9\"><div class=\"wp-block-group__inner-container is-layout-flow wp-block-group-is-layout-flow\">\n<div class=\"wp-block-group has-primary-color has-background-background-color has-text-color has-background has-link-color wp-elements-06602ba1d805196badae16b8f735355d\"><div class=\"wp-block-group__inner-container is-layout-flow wp-block-group-is-layout-flow\">\n<p class=\"has-text-align-center\">Evaluate&nbsp;the&nbsp;expression.<\/p>\n\n\n\n<p class=\"has-text-align-center\">0.2 \u00f7 2 + 0.6<\/p>\n\n\n\n<p class=\"has-text-color has-link-color wp-elements-8981390a2ba2b71f8c7eff5e9e51e02d\" style=\"color:#b00012\"><strong>Write&nbsp;your answer as an integer or a decimal. Do not&nbsp;round.<\/strong><\/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 \u00f7 2 + 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 \u00f7 2 + 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-primary-color has-text-color has-background has-link-color has-large-font-size wp-elements-4fbcfb588c5b2c68b6262056b7200e36\" 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 has-link-color wp-elements-696f4134244b851f9c1447e3823fb19f\" style=\"color:#b00012\">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-8981390a2ba2b71f8c7eff5e9e51e02d\" style=\"color:#b00012\"><strong>Write&nbsp;your answer as an integer or a decimal. Do not&nbsp;round.<\/strong><\/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 \u00f7 3 <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 \u00f7 3 \u00d7 0.2<\/p>\n\n\n\n<p>=<strong>0.1<\/strong> \u00d7 0.2<\/p>\n\n\n\n<p>=0.1 \u00d7 0.2<\/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-primary-color has-text-color has-background has-link-color has-large-font-size wp-elements-3e688cd08f56efa5b4b7c24507b5f806\" style=\"background-color:#cffbde\"><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>Evaluate&nbsp;the&nbsp;expression.<\/p>\n\n\n\n<p class=\"has-text-color has-link-color wp-elements-16b25f50bcfc2d64cdc92ea7484a27c0\" style=\"color:#b00012\"><strong>1 \u00f7 2\/3 &#8211; 1\/2<\/strong><\/p>\n<\/div><\/div>\n\n\n\n<p>First,&nbsp;identify the operations in the&nbsp;expression.<\/p>\n\n\n\n<p>1 <strong>\u00f7 <\/strong>2\/3 &#8211; 1\/2<\/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<p><strong>1 \u00f7 2\/3<\/strong> &#8211; 1\/2<\/p>\n\n\n\n<p>= <strong>1 x 3\/2<\/strong> &#8211; 1\/2               To divide, multiply by the reciprocal<\/p>\n\n\n\n<p>= <strong>3\/2 <\/strong>&#8211; 1\/2<\/p>\n\n\n\n<p>Now,&nbsp;subtract.<\/p>\n\n\n\n<p><strong>3\/2 &#8211; 1\/2<\/strong><\/p>\n\n\n\n<p><strong>= 2\/2 <\/strong><\/p>\n\n\n\n<p><strong>= 1 <\/strong>        Reduce the fraction to lowest terms<\/p>\n\n\n\n<p>The value of the expression is <strong>1<\/strong>.<\/p>\n<\/div><\/div>\n\n\n\n<p class=\"has-text-color has-large-font-size\" style=\"color:#d90000\"><strong>Let&#8217;s practice!\ud83d\udd8a\ufe0f<\/strong><\/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\/751\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-288.png\" alt=\"\" class=\"wp-image-9543\" srcset=\"https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-288.png 500w, https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-288-300x300.png 300w, https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-288-150x150.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\/85166\/154\/237\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-295.png\" alt=\"\" class=\"wp-image-9544\" srcset=\"https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-295.png 500w, https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-295-300x300.png 300w, https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-295-150x150.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 Key notes: Definition of Rational Numbers Order of Operations (PEMDAS\/BODMAS) Operations with Rational Numbers Working with Decimals &amp; Fractions Using Negative Numbers Follow sign rules: Multiplication\/Division: Evaluating Expressions with Exponents Distributive Property Solving Word Problems Learn with an example Evaluate&nbsp;the&nbsp;expression. 0.2 \u00f7 2 + 0.6 Write&nbsp;your answer as an<a class=\"more-link\" href=\"https:\/\/8thclass.deltapublications.in\/index.php\/e-9-evaluate-numerical-expressions-involving-rational-numbers\/\">Continue reading <span class=\"screen-reader-text\">&#8220;E.9 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-86","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\/86","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=86"}],"version-history":[{"count":17,"href":"https:\/\/8thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/86\/revisions"}],"predecessor-version":[{"id":19916,"href":"https:\/\/8thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/86\/revisions\/19916"}],"wp:attachment":[{"href":"https:\/\/8thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/media?parent=86"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}