{"id":7220,"date":"2014-07-04T17:46:31","date_gmt":"2014-07-04T17:46:31","guid":{"rendered":"https:\/\/schooltutoring.com\/help\/?p=7220"},"modified":"2014-12-02T08:25:28","modified_gmt":"2014-12-02T08:25:28","slug":"math-review-of-least-common-multiples-and-denominators-in-rational-expressions","status":"publish","type":"post","link":"https:\/\/schooltutoring.com\/help\/math-review-of-least-common-multiples-and-denominators-in-rational-expressions\/","title":{"rendered":"Math Review of Least Common Multiples and Denominators in Rational Expressions"},"content":{"rendered":"

Overview<\/h3>\n

Rational expressions are like fractions, and must have common denominators in order to be added or subtracted.\u00a0 In order to find the smallest denominator in common, the least common multiple should be found between the denominators.\u00a0 The least common multiple can also be calculated when the denominators are algebraic expressions.<\/p>\n

Least Common Multiple<\/h3>\n

The least common multiple for rational expressions is found in two steps.\u00a0 Factor the denominators in the rational expressions to be added or subtracted.\u00a0 The least common multiple will be the factors that both denominators have in common times the factors that are not in common.\u00a0 Suppose the rational expressions to be added are x\/36 and x\/48.\u00a0 The constant 36 can be factored as 2\u22192\u22193\u22193.\u00a0 The constant 48 can be factored as 2\u22192\u22192\u22192\u22193.\u00a0 The factors that 36 and 48 have in common are 2\u22192\u22193.\u00a0 The factors that they do not have in common are an additional 2.2.3.\u00a0 The least common multiple is 2\u22192\u22192\u22192\u22193\u22193, or 144.\u00a0 To check, 144\/36 is 4 and 144\/48 is 3.<\/p>\n

Figure 1:\u00a0 The least common multiple (LCM) contains the factors in common and the factors not in common.<\/p>\n

\"monohybridcross\"<\/a><\/p>\n

Finding the Numerator<\/h3>\n

Before the expressions can be added, both rational expressions must be changed to their equivalents with the common denominator as the least common multiple.\u00a0 Using the example, x\/36 is multiplied by 4\/4 as 4x\/144 and x\/48 is multiplied by 3\/3 as 3x\/144.\u00a0 Then they can be added as rational expressions with common denominators.<\/p>\n

Adding the Expressions<\/h3>\n

Still using the example, 4x\/144 + 3x\/144 equals 7x\/144.\u00a0 The expression is already in simplest terms, because neither 7 nor x are factors of 144.\u00a0 Suppose x equaled 2.\u00a0 Then, the first fraction would be 8\/144 and the second fraction would be 6\/144, or 14\/144.\u00a0 The fraction 14\/144 can be simplified to 7\/72.\u00a0 Suppose x equaled 5.\u00a0 Then the first fraction would be 20\/144 and the second fraction would be 15\/144.\u00a0 Adding them together would be 35\/144, which would be in simplest terms.<\/p>\n

Figure 2:\u00a0 To add rational expressions, each expression must have the same denominator.<\/p>\n

\"monohybridcross\"<\/a><\/p>\n

LCM of Algebraic Expressions<\/h3>\n

Finding the least common multiple when algebraic expressions are in the denominators of rational expressions is a similar process to finding the least common multiple for fractions with a constant in the denominator.\u00a0 Suppose that the denominator of one expression is (x2<\/sup> \u2013 49) and the denominator of another expression is (x2<\/sup> + 14x + 49).\u00a0 The expression (x2<\/sup> – 49) can be factored as (x + 7)(x – 7).\u00a0 The expression (x2<\/sup> + 14x + 49) can be factored as (x + 7)(x + 7).\u00a0 The factor each expression has in common is (x + 7).\u00a0 The factors they do not have in common are (x + 7)(x – 7).\u00a0 The least common denominator would be (x + 7)(x + 7)(x – 7).<\/p>\n

Figure 3:\u00a0 To calculate the LCM, factor algebraic expressions for the common factors and the factors not in common.<\/p>\n

\"monohybridcross\"<\/a><\/p>\n

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Overview Rational expressions are like fractions, and must have common denominators in order to be added or subtracted.\u00a0 In order to find the smallest denominator in common, the least common multiple should be found between the denominators.\u00a0 The least common multiple can also be calculated when the denominators are algebraic expressions. Least Common Multiple The […]<\/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":[2,9],"tags":[78,1022,2734],"class_list":["post-7220","post","type-post","status-publish","format-standard","hentry","category-algebra","category-fractions-2","tag-algebraic-expressions","tag-least-common-multiple","tag-rational-expressions"],"acf":[],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/posts\/7220","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=7220"}],"version-history":[{"count":0,"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/posts\/7220\/revisions"}],"wp:attachment":[{"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/media?parent=7220"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/categories?post=7220"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/tags?post=7220"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}