{"id":6314,"date":"2020-05-06T23:09:16","date_gmt":"2020-05-06T17:39:16","guid":{"rendered":"https:\/\/physicscatalyst.com\/article\/?p=6314"},"modified":"2022-11-04T12:06:28","modified_gmt":"2022-11-04T06:36:28","slug":"bodmas-rule","status":"publish","type":"post","link":"https:\/\/physicscatalyst.com\/article\/bodmas-rule\/","title":{"rendered":"BODMAS Rule : Order Of Operation"},"content":{"rendered":"\n<h2 class=\"wp-block-heading\">Introduction<\/h2>\n\n\n\n<p>A numerical expression can have multiple operations like addition, subtractions, power, Division, multiplication, Brackets.<br>Example<br>15 of  6-[18-  { 14-(3+2) }]<\/p>\n\n\n\n<p>Now, this is easy to solve like multiple operations on two numbers. We can solve or simplify these types of Numerical expressions using the BODMAS rule.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">What is BODMAS Rule<\/h2>\n\n\n\n<p><strong>BODMAS<\/strong> is an acronym and it stands for Bracket, Order, Division, Multiplication, Addition, and Subtraction. In Canada, it is called BEDMAS(Bracket, Exponents, Division, Multiplication, Addition and Subtraction In the United States, it is called PEMDAS (Parentheses, Exponents, Multiplication, Division, Addition, and Subtraction) These all are synonyms of BODMAS.<\/p>\n\n\n\n<p>-B stands for brackets<br>-O stands for of, orders, square, roots<br>-D stands for divisions (\u00f7)<br>-M stands for multiplication (*)<br>-A stands for addition (+)<br>-S stands for subtraction (-)<\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"649\" height=\"107\" src=\"https:\/\/physicscatalyst.com\/article\/wp-content\/uploads\/2020\/05\/bodmas.png\" alt=\"BODMAS Rule\" class=\"wp-image-6315\" srcset=\"https:\/\/physicscatalyst.com\/article\/wp-content\/uploads\/2020\/05\/bodmas.png 649w, https:\/\/physicscatalyst.com\/article\/wp-content\/uploads\/2020\/05\/bodmas-300x49.png 300w\" sizes=\"auto, (max-width: 649px) 100vw, 649px\" \/><\/figure>\n\n\n\n<p>Now let us how to apply the BODMAS rule to solve the numerical expressions<\/p>\n\n\n\n<p>In order to simplify a numerical expression, we follow the conventions given ahead:<br>(i) we proceed from left to right.<br>(ii) The order of working is<br>brackets -&gt; orders(Exponents or powers) -&gt; division &amp; multiplication -&gt; addition &amp; subtraction.<br>(iii) The order of brackets is:<\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"370\" height=\"140\" src=\"https:\/\/physicscatalyst.com\/article\/wp-content\/uploads\/2020\/05\/order-of-bracket.png\" alt=\"Bracket precedence in BODMAS Rule \" class=\"wp-image-6316\" srcset=\"https:\/\/physicscatalyst.com\/article\/wp-content\/uploads\/2020\/05\/order-of-bracket.png 370w, https:\/\/physicscatalyst.com\/article\/wp-content\/uploads\/2020\/05\/order-of-bracket-300x114.png 300w\" sizes=\"auto, (max-width: 370px) 100vw, 370px\" \/><\/figure>\n\n\n\n<p>Expressions inside the brackets are simplified in order to the letters of the word BODMAS.<\/p>\n\n\n\n<p>(iv) Division and multiplication have the same precedence, so after brackets and orders are over, we just need to move from left to right doing whichever operations come first i.e if multiplication comes first, then do multiplication<br>(v)Similarly Addition and subtraction have the same precedence, so after brackets,orders, division and Multiplication are over we just need to move from left to right doing whichever operation comes<\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"666\" height=\"182\" src=\"https:\/\/physicscatalyst.com\/article\/wp-content\/uploads\/2020\/05\/bodmas-left-to-right.png\" alt=\"order of operations\" class=\"wp-image-6317\" srcset=\"https:\/\/physicscatalyst.com\/article\/wp-content\/uploads\/2020\/05\/bodmas-left-to-right.png 666w, https:\/\/physicscatalyst.com\/article\/wp-content\/uploads\/2020\/05\/bodmas-left-to-right-300x82.png 300w\" sizes=\"auto, (max-width: 666px) 100vw, 666px\" \/><\/figure>\n\n\n\n<h2 class=\"wp-block-heading\">BODMAS Rule Examples<\/h2>\n\n\n\n<p>Lets us see now few Examples<\/p>\n\n\n\n<p>(1) 15 of  6-[18-  { 14-(3+2) }]<br>Applying First the bracket rule<br>=15 of  6-[18-  { 14-5 }]<br>Applying Again the bracket rule<br>=15 of 6-[18- 9]<br>Applying Again the bracket rule<br>=15 of 6-9<br>Now Multiplication  comes before Subtraction<br>=90 -9 = 81<\/p>\n\n\n\n<p>(2) $2 \\times 5 + 50 \\div 2$<br>Here Multiplication and division have same ran, so we just need to move from left to right doing whichever operations comes first<br>$=10 + 25$<br>$=35$<\/p>\n\n\n\n<p>(3) $50 \\times 5 \\div 10$<br>Here Multiplication and division have the same ran, so we just need to move from left to right doing whichever operations come first<br>$=250 \\div 10$<br>=25<\/p>\n\n\n\n<p>(4) $25 \\div 5 \\times 5$<br>Here Multiplication and division have the same ran, so we just need to move from left to right doing whichever operations come first<br>$=5 \\times 5$<br>$=25$<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">BODMAS Exercise<\/h2>\n\n\n\n<p>(5) 105+[19-{2 of 6+(3-2)}]<\/p>\n\n\n\n<div class=\"wp-block-atomic-blocks-ab-accordion ab-block-accordion\"><details><summary class=\"ab-accordion-title\">Answer<\/summary><div class=\"ab-accordion-text\">\n\n<p>= 105 + [19 -{2 of 6 + 1}]<br>=105 + [19 &#8211; {12 + 1}]<br>=105 + [19 -13]<br>=105 + 6=111<\/p>\n\n<\/div><\/details><\/div>\n\n\n\n<p>(6) $\\frac{5}{9} \\div (1\\frac{1}{3}+\\frac{4}{9})+\\frac{3}{8}$<\/p>\n\n\n\n<div class=\"wp-block-atomic-blocks-ab-accordion ab-block-accordion\"><details><summary class=\"ab-accordion-title\">Answer<\/summary><div class=\"ab-accordion-text\">\n\n<p>$=\\frac{5}{9} \\div (\\frac{4}{3}+\\frac{4}{9})+\\frac{3}{8}$<br>Applying the bracket rule<br>$=\\frac{5}{9} \\div \\frac {16}{9} + \\frac{3}{8}$<br>$=\\frac {5}{9} \\times \\frac {9}{16} + \\frac{3}{8}$<br>$=\\frac {5}{16} + \\frac{3}{8}$<br>$=\\frac {11}{16}$<\/p>\n\n<\/div><\/details><\/div>\n\n\n\n<p>(7)  $\\frac{2}{7} &#8211; \\frac {1}{6} \\ of \\ \\frac {6}{7} \\div \\frac {4}{7} &#8211; 1\\frac {1}{3} + 5$<\/p>\n\n\n\n<div class=\"wp-block-atomic-blocks-ab-accordion ab-block-accordion\"><details><summary class=\"ab-accordion-title\">Answer<\/summary><div class=\"ab-accordion-text\">\n\n<p>$=\\frac{2}{7} &#8211; \\frac {1}{7} \\div \\frac {4}{7} &#8211; 1\\frac {1}{3} + 5$<br>$=\\frac{2}{7} &#8211; \\frac {1}{4} &#8211; \\frac {4}{3} + 5$<br>$=\\frac {24 &#8211; 21 &#8211; 112 + 420}{84}= \\frac {311}{84}$<\/p>\n\n<\/div><\/details><\/div>\n\n\n\n<p>(8) $(105 + 206) &#8211; 550 \\div 5^2 + 1$<\/p>\n\n\n\n<div class=\"wp-block-atomic-blocks-ab-accordion ab-block-accordion\"><details><summary class=\"ab-accordion-title\">Answer<\/summary><div class=\"ab-accordion-text\">\n\n<p>$= 311 &#8211; 550 \\div 5^2 + 1$<br>$= 311 &#8211; 550 \\div 25 + 1$<br>$=311 &#8211; 22 + 1$<br>=290<\/p>\n\n<\/div><\/details><\/div>\n\n\n\n<p>(9)  1.5{3.9-(4.5-3.2 \u00d7 0.5)}<\/p>\n\n\n\n<div class=\"wp-block-atomic-blocks-ab-accordion ab-block-accordion\"><details><summary class=\"ab-accordion-title\">Answer<\/summary><div class=\"ab-accordion-text\">\n\n<p>= 1.5 { 3.9 &#8211; (4.5 &#8211; 1.6)}<br>=1.5 {3.9 &#8211; 2.9}<br>=1.5<\/p>\n\n<\/div><\/details><\/div>\n\n\n\n<p>(10) 39-[23-{29- (17-9-3)}]<\/p>\n\n\n\n<div class=\"wp-block-atomic-blocks-ab-accordion ab-block-accordion\"><details><summary class=\"ab-accordion-title\">Answer<\/summary><div class=\"ab-accordion-text\">\n\n<p>=39 &#8211; [23 -{29 -5}]<br>=39 &#8211; [23 &#8211; 24]=39 + 1= 40<\/p>\n\n<\/div><\/details><\/div>\n\n\n\n<p>(11) $\\frac{2}{3} of (\\frac{1}{4}+ \\frac {1}{2} + \\frac {3}{8}) \\div \\frac {3}{2}$<\/p>\n\n\n\n<div class=\"wp-block-atomic-blocks-ab-accordion ab-block-accordion\"><details><summary class=\"ab-accordion-title\">Answer<\/summary><div class=\"ab-accordion-text\">\n\n<p>$=\\frac{2}{3} of (\\frac {2+ 4 +3}{8}) \\div \\frac {3}{2}$<br>$=\\frac{2}{3} of (\\frac {9}{8}) \\div \\frac {3}{2}$<br>$=\\frac{2}{3} of \\frac {9}{8} \\div \\frac {3}{2}$<br>$= \\frac {3}{4} \\div \\frac {3}{2}$<br>$= \\frac {1}{2}$<\/p>\n\n<\/div><\/details><\/div>\n\n\n\n<p>(12)  $\\frac {2}{3} &#8211; \\frac {1}{2} &#8211; \\frac {1}{3} \\ of \\frac {1}{2}$<\/p>\n\n\n\n<div class=\"wp-block-atomic-blocks-ab-accordion ab-block-accordion\"><details><summary class=\"ab-accordion-title\">Answer<\/summary><div class=\"ab-accordion-text\">\n\n<p>$=\\frac {2}{3} &#8211; \\frac {1}{2} -\\frac {1}{6}$<br>=0<\/p>\n\n<\/div><\/details><\/div>\n\n\n\n<p>(13) $5+ 5 \\ of \\ 5 \\div 5 \\ of \\ 5 \\times 5$<\/p>\n\n\n\n<div class=\"wp-block-atomic-blocks-ab-accordion ab-block-accordion\"><details><summary class=\"ab-accordion-title\">Answer<\/summary><div class=\"ab-accordion-text\">\n\n<p>$=5+(5 \\ of\\ 5) \\div 5 \\ of \\ 5 \\times 5$<br>$=5 + 25 \\div 5 \\ of \\ 5 \\times 5$<br>$=5+ 5 \\ of\\ 5 \\times 5$<br>$=5+ (5 \\ of \\ 5) \\times 5$<br>$=5+ 25 \\times 5$<br>$=5+125$<br>$=130$<\/p>\n\n<\/div><\/details><\/div>\n\n\n\n<p>(14)  $\\frac {5}{6} &#8211; \\frac {2}{3} \\ of \\ \\frac {1}{3} + \\frac {1}{9}$<\/p>\n\n\n\n<div class=\"wp-block-atomic-blocks-ab-accordion ab-block-accordion\"><details><summary class=\"ab-accordion-title\">Answer<\/summary><div class=\"ab-accordion-text\">\n\n<p>$=\\frac {5}{6} &#8211; \\frac {2}{9} + \\frac {1}{9}$<br>$=\\frac {13}{18}$<\/p>\n\n<\/div><\/details><\/div>\n\n\n\n<p><strong>Further Reference<\/strong><br><a href=\"https:\/\/en.wikipedia.org\/wiki\/Order_of_operations\">https:\/\/en.wikipedia.org\/wiki\/Order_of_operations<\/a><br><a href=\"https:\/\/physicscatalyst.com\/article\/algebraic-identities\/\">Algebraic Identities<\/a><br><a href=\"https:\/\/physicscatalyst.com\/article\/algebra-formulas-for-class-8\/\">Algebra Formula for Class 8<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Introduction A numerical expression can have multiple operations like addition, subtractions, power, Division, multiplication, Brackets.Example15 of 6-[18- { 14-(3+2) }] Now, this is easy to solve like multiple operations on two numbers. We can solve or simplify these types of Numerical expressions using the BODMAS rule. What is BODMAS Rule BODMAS is an acronym and [&hellip;]<\/p>\n","protected":false},"author":8,"featured_media":0,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_uag_custom_page_level_css":"","site-sidebar-layout":"default","site-content-layout":"default","ast-site-content-layout":"default","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","theme-transparent-header-meta":"default","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"default","ast-page-background-enabled":"default","ast-page-background-meta":{"desktop":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"ast-content-background-meta":{"desktop":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"footnotes":""},"categories":[498],"tags":[],"class_list":["post-6314","post","type-post","status-publish","format-standard","hentry","category-maths"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v27.3 - https:\/\/yoast.com\/product\/yoast-seo-wordpress\/ -->\n<title>BODMAS Rule : Order Of Operation , Exercise, Full Form<\/title>\n<meta name=\"description\" content=\"BODMAS Rule specifies of the order of operation in the Numerical expression. 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We can solve or simplify these types of Numerical expressions using the BODMAS rule. What is BODMAS Rule BODMAS is an acronym and&hellip;","_links":{"self":[{"href":"https:\/\/physicscatalyst.com\/article\/wp-json\/wp\/v2\/posts\/6314","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/physicscatalyst.com\/article\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/physicscatalyst.com\/article\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/physicscatalyst.com\/article\/wp-json\/wp\/v2\/users\/8"}],"replies":[{"embeddable":true,"href":"https:\/\/physicscatalyst.com\/article\/wp-json\/wp\/v2\/comments?post=6314"}],"version-history":[{"count":3,"href":"https:\/\/physicscatalyst.com\/article\/wp-json\/wp\/v2\/posts\/6314\/revisions"}],"predecessor-version":[{"id":6803,"href":"https:\/\/physicscatalyst.com\/article\/wp-json\/wp\/v2\/posts\/6314\/revisions\/6803"}],"wp:attachment":[{"href":"https:\/\/physicscatalyst.com\/article\/wp-json\/wp\/v2\/media?parent=6314"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/physicscatalyst.com\/article\/wp-json\/wp\/v2\/categories?post=6314"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/physicscatalyst.com\/article\/wp-json\/wp\/v2\/tags?post=6314"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}