{"id":38,"date":"2022-04-13T06:10:26","date_gmt":"2022-04-13T06:10:26","guid":{"rendered":"http:\/\/9thclass.deltapublications.in\/?page_id=38"},"modified":"2025-11-20T07:18:58","modified_gmt":"2025-11-20T07:18:58","slug":"b-7-evaluate-variable-expressions-involving-rational-numbers","status":"publish","type":"page","link":"https:\/\/9thclass.deltapublications.in\/index.php\/b-7-evaluate-variable-expressions-involving-rational-numbers\/","title":{"rendered":"B.7 Evaluate variable expressions involving rational numbers"},"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<h2 class=\"wp-block-heading has-text-align-center has-text-color\" style=\"color:#00056d;text-transform:uppercase\">Evaluate variable expressions involving rational numbers<\/h2>\n\n\n\n<p class=\"has-text-color has-huge-font-size\" style=\"color:#74008b\">key notes :<\/p>\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>Understanding Variable Expressions<\/strong><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p><strong>Definition:<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>A variable expression is a mathematical phrase that includes numbers, variables (letters that represent numbers), and operations (addition, subtraction, multiplication, division).<\/li>\n<\/ul>\n\n\n\n<p><strong>Examples:<\/strong><\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"130\" height=\"103\" src=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2024\/08\/image-46.png\" alt=\"\" class=\"wp-image-14672\" style=\"width:120px;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>Evaluating Variable Expressions<\/strong><\/strong><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p><strong>Substitution:<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>To evaluate a variable expression, substitute the values of the variables into the expression and perform the operations according to the order of operations (PEMDAS\/BODMAS).<\/li>\n<\/ul>\n\n\n\n<p><strong>Order of Operations:<\/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 Evaluation<\/strong><\/strong><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p><strong>Substitute Values:<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Replace each variable in the expression with its given value.<\/li>\n<\/ul>\n\n\n\n<p><strong>Simplify Inside Parentheses:<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>If the expression contains parentheses, simplify the expression inside them first.<\/li>\n<\/ul>\n\n\n\n<p><strong>Apply Exponents:<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>If the expression contains exponents, apply them next.<\/li>\n<\/ul>\n\n\n\n<p><strong>Perform Multiplication and Division:<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Perform all multiplication and division from left to right.<\/li>\n<\/ul>\n\n\n\n<p><strong>Perform Addition and Subtraction:<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Perform all 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>Examples<\/strong><\/strong><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p><strong>Simple Variable Expression:<\/strong><\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"261\" height=\"128\" src=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2024\/08\/image-47.png\" alt=\"\" class=\"wp-image-14674\" style=\"width:319px;height:auto\"\/><\/figure><\/div>\n\n\n<p><strong>Expression with Multiple Variables:<\/strong><\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"275\" height=\"128\" src=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2024\/08\/image-48.png\" alt=\"\" class=\"wp-image-14675\" style=\"width:312px;height:auto\"\/><\/figure><\/div>\n\n\n<p><strong>Expression with Parentheses:<\/strong><\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"381\" height=\"168\" src=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2024\/08\/image-49.png\" alt=\"\" class=\"wp-image-14676\" style=\"width:436px;height:auto\" srcset=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2024\/08\/image-49.png 381w, https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2024\/08\/image-49-300x132.png 300w\" sizes=\"auto, (max-width: 381px) 100vw, 381px\" \/><\/figure><\/div>\n\n\n<p><strong>Complex Expression:<\/strong><\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"alignleft size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"447\" height=\"173\" src=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2024\/08\/image-50.png\" alt=\"\" class=\"wp-image-14677\" style=\"width:430px;height:auto\" srcset=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2024\/08\/image-50.png 447w, https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2024\/08\/image-50-300x116.png 300w\" sizes=\"auto, (max-width: 447px) 100vw, 447px\" \/><\/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>Practice Problems<\/strong><\/strong><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p><strong>Simple Expressions:<\/strong><\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"222\" height=\"62\" src=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2024\/08\/image-51.png\" alt=\"\" class=\"wp-image-14678\" style=\"width:323px;height:auto\"\/><\/figure><\/div>\n\n\n<p><strong>Expressions with Multiple Variables:<\/strong><\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"306\" height=\"64\" src=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2024\/08\/image-52.png\" alt=\"\" class=\"wp-image-14679\" style=\"width:412px;height:auto\" srcset=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2024\/08\/image-52.png 306w, https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2024\/08\/image-52-300x63.png 300w\" sizes=\"auto, (max-width: 306px) 100vw, 306px\" \/><\/figure><\/div>\n\n\n<p><strong>Expressions with Parentheses:<\/strong><\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"296\" height=\"71\" src=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2024\/08\/image-53.png\" alt=\"\" class=\"wp-image-14680\" style=\"width:428px;height:auto\"\/><\/figure><\/div>\n\n\n<p><strong>Complex Expressions:<\/strong><\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"362\" height=\"75\" src=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2024\/08\/image-54.png\" alt=\"\" class=\"wp-image-14681\" style=\"width:472px;height:auto\" srcset=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2024\/08\/image-54.png 362w, https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2024\/08\/image-54-300x62.png 300w\" sizes=\"auto, (max-width: 362px) 100vw, 362px\" \/><\/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>Tips for Success<\/strong><\/strong><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p><strong>Careful Substitution:<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Ensure that each variable is correctly substituted with its given value.<\/li>\n<\/ul>\n\n\n\n<p><strong>Follow Order of Operations:<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Adhere strictly to the order of operations to avoid mistakes.<\/li>\n<\/ul>\n\n\n\n<p><strong>Simplify Step-by-Step:<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Simplify the expression step-by-step to prevent errors.<\/li>\n<\/ul>\n\n\n\n<p><strong>Check Your Work:<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>After evaluating the expression, double-check each step to ensure accuracy.<\/li>\n<\/ul>\n\n\n\n<div class=\"wp-block-group has-background has-normal-font-size\" style=\"background-color:#faf4ab\"><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>Evaluate the expression for&nbsp;<em>t<\/em>&nbsp;=&nbsp;-0.7.<\/p>\n\n\n\n<p><em>Write your answer as a decimal or whole number.<\/em><\/p>\n\n\n\n<p class=\"has-normal-font-size\">-15<em>t<\/em>&nbsp;=_______<\/p>\n<\/div><\/div>\n\n\n\n<p>Plug in&nbsp;<em>t<\/em>&nbsp;=&nbsp;-0.7 and simplify.<\/p>\n\n\n\n<figure id=\"yui_3_18_1_1_1660570986757_309\" class=\"wp-block-table\"><table class=\"has-fixed-layout\"><tbody><tr><td class=\"has-text-align-left\" data-align=\"left\">-15<strong><em>t<\/em><\/strong><\/td><td><em><\/em><\/td><\/tr><tr><td class=\"has-text-align-left\" data-align=\"left\">-15(<strong><sup>\u2013<\/sup>0.7<\/strong>)<\/td><td><em>Plug in&nbsp;t&nbsp;=&nbsp;-0.7<\/em><\/td><\/tr><tr><td class=\"has-text-align-left\" data-align=\"left\">10.5<\/td><td><em>Multiply<\/em><\/td><\/tr><\/tbody><\/table><\/figure>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-group has-background has-normal-font-size\" style=\"background-color:#faaaeb\"><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>Evaluate the expression for&nbsp;<em>b<\/em>&nbsp;= 13&nbsp;and&nbsp;<em>c<\/em>&nbsp;= 12. Simplify your answer.<\/p>\n\n\n\n<p><strong> <\/strong>  b\/b-c =<\/p>\n<\/div><\/div>\n\n\n\n<p>Evaluate.<\/p>\n\n\n\n<p class=\"has-normal-font-size\"><strong>   b\/b-c<\/strong><\/p>\n\n\n\n<p>=<strong>13<\/strong>\/<strong>13<\/strong>&nbsp;\u2212&nbsp;<strong>12<\/strong><em>       <\/em><em>Plug-in&nbsp;b&nbsp;= 13&nbsp;and&nbsp;c&nbsp;= 12<\/em><br>=13\/1                 <em>Simplify the denominator<\/em><br>=13                  <em>Divide<\/em><\/p>\n<\/div><\/div>\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:#bdf3f3\"><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\" style=\"color:#b00012\"><strong>\ud83c\udfaf Evaluate the expression for&nbsp;<em>x<\/em>&nbsp;= 0.1&nbsp;and&nbsp;<em>y<\/em>&nbsp;= 8.8.<\/strong><\/p>\n\n\n\n<p><em>Write your answer as a decimal or whole number.<\/em><\/p>\n\n\n\n<p><em>xy<\/em>&nbsp;=&nbsp;<\/p>\n<\/div><\/div>\n\n\n\n<p>Plug in&nbsp;<em>x<\/em>&nbsp;= 0.1&nbsp;and&nbsp;<em>y<\/em>&nbsp;= 8.8, then simplify.<\/p>\n\n\n\n<p>xy<\/p>\n\n\n\n<p><strong>0.1<\/strong>(<strong>8.8<\/strong>)<\/p>\n\n\n\n<p>0.88<\/p>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-group has-background has-normal-font-size\" style=\"background-color:#f3c5d7\"><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\" style=\"color:#b00012\"><strong>\ud83c\udfaf Evaluate the expression for&nbsp;<em>y<\/em>&nbsp;=&nbsp;-12&nbsp;and&nbsp;<em>z<\/em>&nbsp;=&nbsp;<sup>\u2013<\/sup>4. <\/strong><\/p>\n\n\n\n<p>Simplify your answer.<\/p>\n\n\n\n<p>y\/z =<\/p>\n<\/div><\/div>\n\n\n\n<p>Evaluate.<\/p>\n\n\n\n<p>y\/z<\/p>\n\n\n\n<p>= -12\/-4           <em>Plug in&nbsp;y&nbsp;=&nbsp;-12&nbsp;and&nbsp;z&nbsp;=&nbsp;-4<\/em><\/p>\n\n\n\n<p>= 3                   <em>Divide<\/em><\/p>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-group has-background has-normal-font-size\" style=\"background-color:#dde3f9\"><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\" style=\"color:#b00012\"><strong>\ud83c\udfaf Evaluate the expression for&nbsp;<em>n<\/em>&nbsp;=&nbsp;-9. <\/strong><\/p>\n\n\n\n<p>Simplify your answer.<\/p>\n\n\n\n<p>n\/3 =<\/p>\n<\/div><\/div>\n\n\n\n<p>Evaluate.<\/p>\n\n\n\n<p>n\/3<\/p>\n\n\n\n<p>= -9\/3        Plug in&nbsp;n&nbsp;=&nbsp;-9<\/p>\n\n\n\n<p>= -3           <em>Divide<\/em><\/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\/76139\/956\/343\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-8.png\" alt=\"\" class=\"wp-image-7284\" srcset=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-8.png 500w, https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-8-300x300.png 300w, https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-8-150x150.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\/76165\/326\/483\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-8.png\" alt=\"\" class=\"wp-image-7285\" srcset=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-8.png 500w, https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-8-300x300.png 300w, https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-8-150x150.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 variable expressions involving rational numbers key notes : Understanding Variable Expressions Definition: Examples: Evaluating Variable Expressions Substitution: Order of Operations: Steps for Evaluation Substitute Values: Simplify Inside Parentheses: Apply Exponents: Perform Multiplication and Division: Perform Addition and Subtraction: Examples Simple Variable Expression: Expression with Multiple Variables: Expression with Parentheses: Complex Expression: Practice Problems Simple<a class=\"more-link\" href=\"https:\/\/9thclass.deltapublications.in\/index.php\/b-7-evaluate-variable-expressions-involving-rational-numbers\/\">Continue reading <span class=\"screen-reader-text\">&#8220;B.7 Evaluate variable 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-38","page","type-page","status-publish","hentry","entry"],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/9thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/38","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=38"}],"version-history":[{"count":33,"href":"https:\/\/9thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/38\/revisions"}],"predecessor-version":[{"id":18253,"href":"https:\/\/9thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/38\/revisions\/18253"}],"wp:attachment":[{"href":"https:\/\/9thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/media?parent=38"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}