{"id":5555,"date":"2013-03-04T17:40:22","date_gmt":"2013-03-04T17:40:22","guid":{"rendered":"http:\/\/schooltutoring.com\/scholarship\/?p=5555"},"modified":"2014-12-02T08:27:04","modified_gmt":"2014-12-02T08:27:04","slug":"basica-of-algebra-order-of-operations","status":"publish","type":"post","link":"https:\/\/schooltutoring.com\/scholarship\/2013\/03\/04\/basica-of-algebra-order-of-operations\/","title":{"rendered":"Basica of Algebra: Order of Operations"},"content":{"rendered":"

Overview:\u00a0 A Set of Rules<\/strong>
\nThe order of operations refers to a set of rules that are commonly agreed upon in mathematics, so that the answer to a problem is always the same when the correct order is followed.\u00a0 If numbers are combined in a different order, then different answers will result.\u00a0 When numbers are replaced by variables, as in algebra, the problem becomes compounded.<\/p>\n

Parentheses and Fractions are First<\/strong>
\nExpressions that are grouped within parentheses are solved first.\u00a0 Usually, they are grouped within parentheses or brackets because grouping the numbers differently would change the meaning.\u00a0 For example, suppose the number sentence is 3[15-(5+3)].\u00a0 To solve it, the innermost parenthesis (5+3) equals 8, 15-8 = 7 and 3 X 7 =21.\u00a0 If the number sentence read 3[(15-5)+3] the innermost parenthesis would be 10 , and the problem would read 3 (13) which would equal 39.\u00a0 Parentheses, brackets, and fraction bars are signals that numbers are to be grouped together.<\/p>\n

Multiplication and Division Are Next<\/strong>
\nMultiplication and its inverse, division, are next.\u00a0 They go in order from left to right.\u00a0 Exponents are a form of multiplication, and square roots are a form of division.\u00a0 For example if the problem is 2 X 18 + 4 X 35, it is solved as if it were read (2 X 18) + (4 X 35), or 36 + 140 = 176.\u00a0 Because of the rules of order of operations, the parentheses are not necessary.<\/p>\n

Finally, Addition and Subtraction<\/strong>
\nLast, addition and its inverse, subtraction, are done.\u00a0 If there are no signals such as parentheses that numbers are to be grouped together, those operations are performed last.\u00a0 That is another way to ensure that the problem has one unique answer.\u00a0\u00a0\u00a0 Students can always read the problem in order to evaluate what is in parentheses or grouped in fractions, what numbers need to be multiplied or divided, and then what needs to be added or subtracted to solve for a unique answer.<\/p>\n

Scientific Calculators Follow the Rules<\/strong>
\nScientific calculators have the rules programmed into them.\u00a0 In order to use a calculator as a shortcut to solve a mathematical problem, it is very important to remember to enter the parentheses to work the problem correctly.\u00a0 The parentheses are a clue that numbers are being combined in a \u00a0different order, and are an essential part of the number sentence.\u00a0 If there are no parentheses in the number sentence, the numbers and operations are entered in order from left to right.\u00a0 The scientific calculator will use the rules of the order of operations to solve for the correct answer.<\/p>\n

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Overview:\u00a0 A Set of Rules The order of operations refers to a set of rules that are commonly agreed upon in mathematics, so that the answer to a problem is always the same when the correct order is followed.\u00a0 If numbers are combined in a different order, then different answers will result.\u00a0 When numbers are […]<\/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":[2,11],"tags":[50,529,1159,1257,1285,1762],"class_list":["post-5555","post","type-post","status-publish","format-standard","hentry","category-algebra","category-math-fundamentals","tag-addition","tag-division","tag-multiplication","tag-order-of-operations","tag-parentheses","tag-subtraction"],"acf":[],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/posts\/5555","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=5555"}],"version-history":[{"count":0,"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/posts\/5555\/revisions"}],"wp:attachment":[{"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/media?parent=5555"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/categories?post=5555"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/tags?post=5555"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}