{"id":6339,"date":"2013-09-25T15:09:58","date_gmt":"2013-09-25T15:09:58","guid":{"rendered":"https:\/\/schooltutoring.com\/scholarship\/?p=6339"},"modified":"2014-12-02T08:26:58","modified_gmt":"2014-12-02T08:26:58","slug":"review-of-order-of-operations-and-parentheses-in-mathematics","status":"publish","type":"post","link":"https:\/\/schooltutoring.com\/scholarship\/2013\/09\/25\/review-of-order-of-operations-and-parentheses-in-mathematics\/","title":{"rendered":"Review of Order of Operations and Parentheses in Mathematics"},"content":{"rendered":"

Overview<\/strong><\/p>\n

The order of operations is a set of rules in algebra to define what operations must be done first in order to obtain the correct answer to a problem.\u00a0 Without sequencing rules, it would be possible to work problems and get different answers depending on the way the numbers and variables are combined.\u00a0 Instead, conventions ensure that a particular answer to a problem is the correct one.<\/p>\n

Why Is Order of Operations Important?<\/strong><\/p>\n

Suppose the problem is as simple as 85 +9 X 2.\u00a0 Without an order of operations, one person might calculate the problem as (85 +9) X 2\u00a0 or 94 X 2 = 188, while another might calculate it as 85 + (9 X 2) or 85 + 18 =103.\u00a0 Similarly, does 2 X 34<\/sup> mean 64<\/sup>, or 1296, or does it mean to work the 34<\/sup>and then multiply by 2, or 81 X 2 = 162?<\/p>\n

What Is the Order of Operations?<\/strong><\/p>\n

By convention, exponents are solved first, then multiplications or divisions, from left to right, then additions or subtractions, from left to right.\u00a0 Therefore, the correct answer to\u00a0 85 + 9 X 2 is not 188, but 103.\u00a0 There are no exponents in the problem, but there is a multiplication, 9 X 2, equaling 18.\u00a0 Working from left to right, the last step is adding 85 + 18, to equal 103.\u00a0 Similarly, in 2 X 34<\/sup>, the exponent is worked first, then the multiplication.<\/p>\n

What Do Parentheses Do?<\/strong><\/p>\n

Parentheses in mathematical sentences take priority over all other operations, so they are solved first, from left to right.\u00a0 Suppose the problem really were (85 +9) X 2.\u00a0 In that case, the correct answer would be to solve within the parentheses first, then the multiplication.\u00a0 Similarly, (4x)3<\/sup> does not mean the same as 4x3<\/sup>.\u00a0 Within the order of operations, if x equals 2, (4x)3<\/sup>would equal 83<\/sup> or 512. \u00a0If x equals 2, 4x3<\/sup> would equal 4 X 23<\/sup> or 32.<\/p>\n

Does Your Calculator Follow Order of Operations?<\/strong><\/p>\n

When they are buying school supplies, students may wonder why their teachers specify certain types of calculators.\u00a0 That is because scientific calculators follow the algebraic order of operations, while other calculators do not.\u00a0 A scientific calculator will calculate the problem 85 +9 X 2 by doing the multiplication first, coming up with the answer 103, while a regular calculator will do the operations from left to right only, answering 188.<\/p>\n

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Overview The order of operations is a set of rules in algebra to define what operations must be done first in order to obtain the correct answer to a problem.\u00a0 Without sequencing rules, it would be possible to work problems and get different answers depending on the way the numbers and variables are combined.\u00a0 Instead, […]<\/p>\n","protected":false},"author":22,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"inline_featured_image":false,"footnotes":""},"categories":[13],"tags":[1257,1285,1870],"class_list":["post-6339","post","type-post","status-publish","format-standard","hentry","category-pre-algebra","tag-order-of-operations","tag-parentheses","tag-types-of-calculators"],"acf":[],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/posts\/6339","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/users\/22"}],"replies":[{"embeddable":true,"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/comments?post=6339"}],"version-history":[{"count":0,"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/posts\/6339\/revisions"}],"wp:attachment":[{"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/media?parent=6339"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/categories?post=6339"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/tags?post=6339"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}