{"id":6922,"date":"2014-04-22T17:00:42","date_gmt":"2014-04-22T17:00:42","guid":{"rendered":"https:\/\/schooltutoring.com\/help\/?p=6922"},"modified":"2014-12-02T08:25:30","modified_gmt":"2014-12-02T08:25:30","slug":"math-review-of-using-parentheses-in-equations","status":"publish","type":"post","link":"https:\/\/schooltutoring.com\/help\/math-review-of-using-parentheses-in-equations\/","title":{"rendered":"Math Review of Using Parentheses in Equations"},"content":{"rendered":"<p><strong>Overview:<\/strong><\/p>\n<p>Parentheses in equations mean that numbers and variables should be combined first, regardless of the standard order of operations.\u00a0 For example, an expression such as (3 + 4)\u2219 5, which equals 35, has a different meaning than 3 + (4 \u2219 5), which equals 23.\u00a0 Similarly, an expression such as (2 + 3)\/7x has a different meaning than 2 + 3\/7x.<\/p>\n<p><strong>What Is the Order of Operations?<\/strong><\/p>\n<p>In the standard order of operations, multiplication and division are performed before addition and subtraction.\u00a0 A scientific calculator will evaluate an expression such as 3 + 4 \u2219 5 by performing the multiplication first, or as 3 + 20 or 23.\u00a0 Similarly, 12x + 8\/4 will be evaluated as 12x + 2, so that if the equation were 12x + 8\/4 = 14, it would be solved as 12x = 14 \u2013 2 , or 12x = 12, or x = 1.<\/p>\n<p><strong>Parentheses Have Priority<\/strong><\/p>\n<p>Parentheses mean that the expression within the parentheses must be solved first, even if those numbers wouldn\u2019t normally be combined first.\u00a0 Suppose the equation were (4 + 3)x -14 = 0.\u00a0 If 7x = 14, then x = 2.\u00a0 If the parentheses were not there, the equation would be 4 + 3x \u2013 14 = 0 or 3x \u2013 10 = 0, combining the 4 and the -14.\u00a0 Then 3x = 10, so x = 3.33, or 3 1\/3.<\/p>\n<p><strong>Parentheses Even Have Priority Over Exponents<\/strong><\/p>\n<p>Similarly, an expression such as 4x<sup>2<\/sup> is very different from (4x)<sup>2<\/sup>.\u00a0 The expression 4x<sup>2<\/sup>means 4x \u2219 x, while the expression (4x)<sup>2<\/sup>means 4x \u2219 4x.\u00a0 Suppose the equation is 4x<sup>2<\/sup> = 100.\u00a0 Then x<sup>2<\/sup> = 25, or x = 5.\u00a0 If the equation were (4y)<sup>2<\/sup> = 160, then 16y<sup>2<\/sup> = 160 or y<sup>2<\/sup> = 10 , so that y = \u221a10.<\/p>\n<p><strong>Is There an Order of Operations within Parentheses?<\/strong><\/p>\n<p>Suppose the expression were (13 \u2013 2 \u2219 3)(6\/3 &#8211; 1).\u00a0 The order of operations would be followed, so that (13 &#8211; 6) (2 &#8211; 1) or 7.\u00a0 If numbers were to be combined differently, there would be parentheses within parentheses or ((13 &#8211; 2)3)(6\/(3-1)) or 33(3) or 99.\u00a0 Similarly, suppose the equation were (13 \u2013 (2x)<sup>2<\/sup>)(3 \u2013 1) = 0.\u00a0 That would be solved by working the expressions within parentheses first, so that (13 \u2013 4x<sup>2<\/sup>)(2) = 0, or 26 &#8211; 8x<sup>2<\/sup> = 0, or 26 = 8x<sup>2<\/sup> , or 26\/8 = x<sup>2.<\/sup>.\u00a0 Since 26\/8 in simplest terms is 13\/4, then x = \u221a 13\/4.<\/p>\n<p>Interested in <a href=\"https:\/\/schooltutoring.com\/math-tutoring\/pre-algebra-tutoring\/\">pre-algebra tutoring services<\/a>? Learn more about how we are assisting thousands of students each academic year.<\/p>\n<p><span class=\"tutorOrange\">SchoolTutoring Academy<\/span> is the premier educational services company for K-12 and college students. We offer tutoring programs for students in K-12, AP classes, and college. To learn more about how we help parents and students in Metairie, LA: visit <a href=\"https:\/\/schooltutoring.com\/tutoring-in-metairie-louisiana\/\">Tutoring in Metairie, LA<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Overview: Parentheses in equations mean that numbers and variables should be combined first, regardless of the standard order of operations.\u00a0 For example, an expression such as (3 + 4)\u2219 5, which equals 35, has a different meaning than 3 + (4 \u2219 5), which equals 23.\u00a0 Similarly, an expression such as (2 + 3)\/7x has [&hellip;]<\/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],"class_list":["post-6922","post","type-post","status-publish","format-standard","hentry","category-pre-algebra","tag-order-of-operations","tag-parentheses"],"acf":[],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/posts\/6922","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/users\/22"}],"replies":[{"embeddable":true,"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/comments?post=6922"}],"version-history":[{"count":0,"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/posts\/6922\/revisions"}],"wp:attachment":[{"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/media?parent=6922"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/categories?post=6922"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/tags?post=6922"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}