{"id":39,"date":"2022-04-13T09:49:18","date_gmt":"2022-04-13T09:49:18","guid":{"rendered":"http:\/\/10thclass.deltapublications.in\/?page_id=39"},"modified":"2025-03-05T06:49:07","modified_gmt":"2025-03-05T06:49:07","slug":"b-7-evaluate-variable-expressions-involving-rational-numbers","status":"publish","type":"page","link":"https:\/\/10thclass.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-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\" style=\"color:#00056d\"><strong>Evaluate variable expressions involving rational numbers<\/strong><\/h2>\n\n\n\n<p><strong>Key notes:<\/strong><\/p>\n\n\n\n<h4 class=\"wp-block-heading\"><strong>Understanding Variable Expressions<\/strong><\/h4>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>Definition:<\/strong>\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<\/li>\n\n\n\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-46.png\" alt=\"\" class=\"wp-image-14672\" style=\"width:190px;height:auto\"\/><\/figure><\/div>\n\n\n<h4 class=\"wp-block-heading\"><strong>Evaluating Variable Expressions<\/strong><\/h4>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>Substitution:<\/strong>\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<\/li>\n\n\n\n<li><strong>Order of Operations:<\/strong>\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<\/li>\n<\/ol>\n\n\n\n<h4 class=\"wp-block-heading\"><strong>Steps for Evaluation<\/strong><\/h4>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>Substitute Values:<\/strong>\n<ul class=\"wp-block-list\">\n<li>Replace each variable in the expression with its given value.<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li><strong>Simplify Inside Parentheses:<\/strong>\n<ul class=\"wp-block-list\">\n<li>If the expression contains parentheses, simplify the expression inside them first.<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li><strong>Apply Exponents:<\/strong>\n<ul class=\"wp-block-list\">\n<li>If the expression contains exponents, apply them next.<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li><strong>Perform Multiplication and Division:<\/strong>\n<ul class=\"wp-block-list\">\n<li>Perform all multiplication and division from left to right.<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li><strong>Perform Addition and Subtraction:<\/strong>\n<ul class=\"wp-block-list\">\n<li>Perform all addition and subtraction from left to right.<\/li>\n<\/ul>\n<\/li>\n<\/ol>\n\n\n\n<h4 class=\"wp-block-heading\"><strong>Examples<\/strong><\/h4>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Simple Variable 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-47.png\" alt=\"\" class=\"wp-image-14674\" style=\"width:469px;height:auto\"\/><\/figure><\/div>\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Expression with Multiple Variables:<\/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-48.png\" alt=\"\" class=\"wp-image-14675\" style=\"width:468px;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-49.png\" alt=\"\" class=\"wp-image-14676\" style=\"width:508px;height:auto\"\/><\/figure><\/div>\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-50.png\" alt=\"\" class=\"wp-image-14677\" style=\"width:530px;height:auto\"\/><\/figure><\/div>\n\n\n<h4 class=\"wp-block-heading\"><strong>Practice Problems<\/strong><\/h4>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>Simple Expressions:<\/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-51.png\" alt=\"\" class=\"wp-image-14678\" style=\"width:451px;height:auto\"\/><\/figure><\/div>\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Expressions with Multiple Variables:<\/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-52.png\" alt=\"\" class=\"wp-image-14679\" style=\"width:536px;height:auto\"\/><\/figure><\/div>\n\n\n<ul class=\"wp-block-list\">\n<li class=\"has-large-font-size\"><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-53.png\" alt=\"\" class=\"wp-image-14680\" style=\"width:538px;height:auto\"\/><\/figure><\/div>\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Complex Expressions:<\/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-54.png\" alt=\"\" class=\"wp-image-14681\" style=\"width:574px;height:auto\"\/><\/figure><\/div>\n\n\n<h3 class=\"wp-block-heading\"><strong>Tips for Success<\/strong><\/h3>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>Careful Substitution:<\/strong>\n<ul class=\"wp-block-list\">\n<li>Ensure that each variable is correctly substituted with its given value.<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li><strong>Follow Order of Operations:<\/strong>\n<ul class=\"wp-block-list\">\n<li>Adhere strictly to the order of operations to avoid mistakes.<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li><strong>Simplify Step-by-Step:<\/strong>\n<ul class=\"wp-block-list\">\n<li>Simplify the expression step-by-step to prevent errors.<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li><strong>Check Your Work:<\/strong>\n<ul class=\"wp-block-list\">\n<li>After evaluating the expression, double-check each step to ensure accuracy.<\/li>\n<\/ul>\n<\/li>\n<\/ol>\n\n\n\n<p><strong> <\/strong><\/p>\n\n\n\n<p class=\"has-text-align-center has-text-color has-link-color has-large-font-size wp-elements-3fefd20f8ce119a518e5f53333ab5486\" 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:#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>\ud83d\udd2e Evaluate the expression for&nbsp;<em>t<\/em>&nbsp;=&nbsp;-0.7.<\/p>\n\n\n\n<p class=\"has-text-color has-link-color wp-elements-56ea5e06d339abaa5bfb643980d562e0\" style=\"color:#b00012\">Write your answer as a decimal or whole number.<\/p>\n\n\n\n<p class=\"has-text-align-center has-huge-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>-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-large-font-size\" style=\"background-color:#96e4f6\"><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>\ud83d\udd2e Evaluate the expression for&nbsp;<em>b<\/em>&nbsp;= 13&nbsp;and&nbsp;<em>c<\/em>&nbsp;= 12. <\/p>\n\n\n\n<p class=\"has-text-color has-link-color wp-elements-84aaae0472f63c80d22d71cc504e9a62\" style=\"color:#b00012\">Simplify your answer.<\/p>\n\n\n\n<p class=\"has-text-align-center has-text-color has-link-color has-huge-font-size wp-elements-f2b4a1d0387b7d65815d8241d95712e9\" style=\"color:#b00012\">b\/b-c =?<\/p>\n<\/div><\/div>\n\n\n\n<p>Evaluate.<\/p>\n\n\n\n<p class=\"has-large-font-size\"><strong> <\/strong>  <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>Plug-in&nbsp;b&nbsp;= 13&nbsp;and&nbsp;c&nbsp;= 12<br>=13\/1                 Simplify the denominator<br>=13                  Divide<\/p>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-group has-background has-large-font-size\" style=\"background-color:#b8c0f3\"><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>\ud83d\udd2e Evaluate the expression for&nbsp;<em>g<\/em>&nbsp;= 2&nbsp;and&nbsp;<em>h<\/em>&nbsp;= 0.5.<\/p>\n\n\n\n<p class=\"has-text-color has-link-color wp-elements-56ea5e06d339abaa5bfb643980d562e0\" style=\"color:#b00012\">Write your answer as a decimal or whole number.<\/p>\n\n\n\n<p><em>gh<\/em>&nbsp;\u2212 0.7 =&nbsp;<\/p>\n<\/div><\/div>\n\n\n\n<p>Plug in&nbsp;<em>g<\/em>&nbsp;= 2&nbsp;and&nbsp;<em>h<\/em>&nbsp;= 0.5, then simplify.<\/p>\n\n\n\n<p><strong><em>g<\/em><\/strong><strong><em>h<\/em><\/strong>&nbsp;\u2212 0.7<\/p>\n\n\n\n<p><strong>2<\/strong>(<strong>0.5<\/strong>)&nbsp;\u2212 0.7<\/p>\n\n\n\n<p>1&nbsp;\u2212&nbsp;0.7<\/p>\n\n\n\n<p>0.3<\/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\/76139\/956\/398\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-11.png\" alt=\"\" class=\"wp-image-6508\" srcset=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-11.png 500w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-11-300x300.png 300w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-11-150x150.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\/76189\/496\/464\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-11.png\" alt=\"\" class=\"wp-image-6509\" srcset=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-11.png 500w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-11-300x300.png 300w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-11-150x150.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 Evaluating Variable Expressions Steps for Evaluation Examples Practice Problems Tips for Success Learn with an example \ud83d\udd2e Evaluate the expression for&nbsp;t&nbsp;=&nbsp;-0.7. Write your answer as a decimal or whole number. -15t&nbsp;=_______ Plug in&nbsp;t&nbsp;=&nbsp;-0.7 and simplify. -15t -15(-0.7) Plug in&nbsp;t&nbsp;=&nbsp;-0.7 10.5 Multiply \ud83d\udd2e Evaluate the<a class=\"more-link\" href=\"https:\/\/10thclass.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-39","page","type-page","status-publish","hentry","entry"],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/10thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/39","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=39"}],"version-history":[{"count":22,"href":"https:\/\/10thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/39\/revisions"}],"predecessor-version":[{"id":17575,"href":"https:\/\/10thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/39\/revisions\/17575"}],"wp:attachment":[{"href":"https:\/\/10thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/media?parent=39"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}