{"id":8769,"date":"2020-12-15T09:55:30","date_gmt":"2020-12-15T04:25:30","guid":{"rendered":"https:\/\/cbselibrary.com\/?p=8769"},"modified":"2020-12-15T10:15:57","modified_gmt":"2020-12-15T04:45:57","slug":"order-operations-evaluating-expressions","status":"publish","type":"post","link":"https:\/\/cbselibrary.com\/order-operations-evaluating-expressions\/","title":{"rendered":"Order of Operations and Evaluating Expressions"},"content":{"rendered":"<h2><span style=\"color: #00ccff;\"><strong>Order of Operations and Evaluating Expressions<\/strong><\/span><\/h2>\n<p><strong>Order of Operations<\/strong><br \/>\nWhen a numerical expression involves two or more operations, there is a specific order in which these operations must be performed.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-132750\" src=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2020\/12\/Order-of-Operations-and-Evaluating-Expressions-4.png\" alt=\"Order of Operations and Evaluating Expressions 4\" width=\"535\" height=\"74\" srcset=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2020\/12\/Order-of-Operations-and-Evaluating-Expressions-4.png 535w, https:\/\/cbselibrary.com\/wp-content\/uploads\/2020\/12\/Order-of-Operations-and-Evaluating-Expressions-4-300x41.png 300w\" sizes=\"(max-width: 535px) 100vw, 535px\" \/><\/p>\n<p><strong>When evaluating an expression, proceed in this order:<\/strong><\/p>\n<ol>\n<li>parentheses are done first.<\/li>\n<li>exponents are done next.<\/li>\n<li>multiplication and division are done as they are encountered from left to right.<\/li>\n<li>addition and subtraction are done as they are encountered from left to right.<\/li>\n<\/ol>\n<p>The proper application of &#8220;order of operations&#8221; is needed when working with such mathematical topics as evaluating formulas, solving equations, evaluating algebraic expressions, and simplifying monomials and polynomials.<\/p>\n<p>There is a phrase that may help you to remember this order: <strong>PEMDAS<\/strong><br \/>\n<strong>Parenthesis, Exponents, (Multiplication\/Division), (Add\/Subtract)<\/strong><\/p>\n<p>While PEMDAS lists M before D, remember that multiplication and division are done as they are read from left to right. It may not always be the case that multiplication is done &#8220;before&#8221; division.<br \/>\nThe expression 16 \u00f7 4 x 2 = 8 (not 2).<br \/>\nThe same is true of addition and subtraction: 8 &#8211; 4 + 2 = 6 (not 2).<\/p>\n<p><img loading=\"lazy\" class=\"size-full wp-image-12106 aligncenter\" src=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2016\/12\/order-operations-evaluating-expressions-1.png\" alt=\"\" width=\"1400\" height=\"509\" srcset=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2016\/12\/order-operations-evaluating-expressions-1.png 1400w, https:\/\/cbselibrary.com\/wp-content\/uploads\/2016\/12\/order-operations-evaluating-expressions-1-300x109.png 300w, https:\/\/cbselibrary.com\/wp-content\/uploads\/2016\/12\/order-operations-evaluating-expressions-1-768x279.png 768w, https:\/\/cbselibrary.com\/wp-content\/uploads\/2016\/12\/order-operations-evaluating-expressions-1-1024x372.png 1024w\" sizes=\"(max-width: 1400px) 100vw, 1400px\" \/><\/p>\n<p>The reason (multiplication &amp; division &#8211; MD) and (add &amp; subtract &#8211; AS) are &#8220;grouped&#8221; in sets of parentheses is that when those operations are next to each other you do the math from<strong> left to right.<\/strong> You do not always do multiplication or addition first. It may be the case where division will be done BEFORE multiplication or subtraction will be done BEFORE addition.<\/p>\n<p><img loading=\"lazy\" class=\"size-full wp-image-12107 aligncenter\" src=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2016\/12\/order-operations-evaluating-expressions-2.gif\" alt=\"\" width=\"560\" height=\"334\" \/><\/p>\n<p>&nbsp;<\/p>\n<p><strong>Read More:<\/strong><\/p>\n<ul>\n<li><a href=\"https:\/\/cbselibrary.com\/integer-examples\/\">Integers and Examples<\/a><\/li>\n<li><a href=\"https:\/\/cbselibrary.com\/fundamental-operations-integers\/\">Fundamental Operations on Integers<\/a><\/li>\n<li><a href=\"https:\/\/cbselibrary.com\/whole-numbers-properties\/\">Whole Numbers And Its Properties<\/a><\/li>\n<li><a href=\"https:\/\/cbselibrary.com\/hints-remembering-properties-real-numbers\/\">Hints for Remembering the Properties of Real Numbers<\/a><\/li>\n<li><a href=\"https:\/\/cbselibrary.com\/four-basic-operations-in-mathematics\/\">What Are The Four Basic Operations In Mathematics<\/a><\/li>\n<li><a href=\"https:\/\/cbselibrary.com\/absolute-value\/\">Absolute Value<\/a><\/li>\n<\/ul>\n<p><iframe loading=\"lazy\" title=\"Order of operations\" width=\"1200\" height=\"900\" src=\"https:\/\/www.youtube.com\/embed\/SWRCjspjJko?feature=oembed\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture; web-share\" allowfullscreen><\/iframe><\/p>\n<p>It may be helpful to build a PEMDAS table. Check off the operation after it has been performed. For operations that are not part of the problem, place a hyphen.<\/p>\n<ol>\n<li>Simplify any parenthesis first, starting with the inner most group, and check off the &#8220;P&#8221; box.<\/li>\n<li>Simplify any powers ( exponents) and check off the &#8220;E&#8221; box.<\/li>\n<li>Perform the multiplication and division in order from left to right and check off the &#8220;M&#8221; &amp; &#8220;D&#8221; boxes.<\/li>\n<li>Do the addition and subtraction last. Remember, if the operations are written next to each other work from left to right and check off the last two boxes.<\/li>\n<\/ol>\n<p>When there are two or more parenthesis, or grouping symbols, perform the inner most grouping symbol first.<\/p>\n<p><strong>Example 1:\u00a0Simplify 40 &#8211; 2(6 &#8211; 4)<sup>2<\/sup><\/strong><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-132743\" src=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2020\/12\/Order-of-Operations-and-Evaluating-Expressions-1.png\" alt=\"Order of Operations and Evaluating Expressions 1\" width=\"234\" height=\"98\" \/><\/p>\n<p><strong>Example 2:\u00a0Simplify 30 &#8211; (8 &#8211; 15 \u00f7 3) \u00d7 2<\/strong><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-132746\" src=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2020\/12\/Order-of-Operations-and-Evaluating-Expressions-2.png\" alt=\"Order of Operations and Evaluating Expressions 2\" width=\"321\" height=\"96\" srcset=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2020\/12\/Order-of-Operations-and-Evaluating-Expressions-2.png 321w, https:\/\/cbselibrary.com\/wp-content\/uploads\/2020\/12\/Order-of-Operations-and-Evaluating-Expressions-2-300x90.png 300w\" sizes=\"(max-width: 321px) 100vw, 321px\" \/><\/p>\n<p><strong>Example 3:<\/strong> <strong>Simplify: 2(20 &#8211; 3<sup>2<\/sup> + 1) &#8211; (42 \u00f7 2 \u00d7 3)<\/strong><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-132749\" src=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2020\/12\/Order-of-Operations-and-Evaluating-Expressions-3.png\" alt=\"Order of Operations and Evaluating Expressions 3\" width=\"449\" height=\"136\" srcset=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2020\/12\/Order-of-Operations-and-Evaluating-Expressions-3.png 449w, https:\/\/cbselibrary.com\/wp-content\/uploads\/2020\/12\/Order-of-Operations-and-Evaluating-Expressions-3-300x91.png 300w\" sizes=\"(max-width: 449px) 100vw, 449px\" \/><\/p>\n<p><strong>It is very important to understand that it DOES make a difference if the order is not performed correctly!!!<\/strong><\/p>\n<p>&nbsp;<\/p>\n<p><a class=\"button-red\" title=\"Maths\" href=\"https:\/\/cbselibrary.com\/maths\/\">Maths<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Order of Operations and Evaluating Expressions Order of Operations When a numerical expression involves two or more operations, there is a specific order in which these operations must be performed. When evaluating an expression, proceed in this order: parentheses are done first. exponents are done next. multiplication and division are done as they are encountered &#8230; <a title=\"Order of Operations and Evaluating Expressions\" class=\"read-more\" href=\"https:\/\/cbselibrary.com\/order-operations-evaluating-expressions\/\" aria-label=\"More on Order of Operations and Evaluating Expressions\">Read more<\/a><\/p>\n","protected":false},"author":3,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"spay_email":""},"categories":[5],"tags":[3207,55912,3206,3205,55948],"yoast_head":"<!-- This site is optimized with the Yoast SEO Premium plugin v17.8 (Yoast SEO v18.4.1) - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Order of Operations and Evaluating Expressions - CBSE Library<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/cbselibrary.com\/order-operations-evaluating-expressions\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Order of Operations and Evaluating Expressions\" \/>\n<meta property=\"og:description\" content=\"Order of Operations and Evaluating Expressions Order of Operations When a numerical expression involves two or more operations, there is a specific order in which these operations must be performed. 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