{"id":66913,"date":"2017-08-12T19:27:47","date_gmt":"2017-08-12T19:27:47","guid":{"rendered":"https:\/\/schooltutoring.com\/scholarship\/?p=66913"},"modified":"2017-08-12T19:27:47","modified_gmt":"2017-08-12T19:27:47","slug":"math-review-of-multiplying-and-dividing-rational-expressions","status":"publish","type":"post","link":"https:\/\/schooltutoring.com\/scholarship\/2017\/08\/12\/math-review-of-multiplying-and-dividing-rational-expressions\/","title":{"rendered":"Math Review of Multiplying and Dividing Rational Expressions"},"content":{"rendered":"

Overview<\/strong><\/h3>\n

The process of multiplying and dividing rational expressions is similar to multiplying and dividing rational numbers.\u00a0 In order to multiply, first multiply the numerators, then the denominators, and then simplify the expression.\u00a0 Division is the inverse of multiplication, so multiply by the reciprocal (or inverse) of the divisor, and then simplify the expression.<\/p>\n

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Multiplying Rational Numbers<\/strong><\/h3>\n

Rational numbers are also known as fractions.\u00a0 The fraction \u00be is a rational number, as is the fraction 3\/5.\u00a0 The numerator 3 is in a ratio to the denominator 4.\u00a0 To multiply \u00be by 3\/5, multiply the numerators 3\u00b73, and then multiply the denominators 4\u00b75, to result in the new fraction or ratio of 9\/20.\u00a0 The fraction 9\/20 is in the simplest form, because there are no factors common to both 9 and 20 except for 1.\u00a0 Suppose one ratio were a\/9 and another were 7\/10. The process of multiplication would be similar, so that a\/9 times 7\/10 would equal 7a\/90.<\/p>\n

<\/h3>\n

Multiplying Rational Expressions<\/strong><\/h3>\n

Suppose the problem were (5a3<\/sup>)\/4 times 2\/ (5a).\u00a0 The numerator is 5a3<\/sup>\u00b72 or 10a3<\/sup>, and the denominator is 4 \u00b75a or 20a.\u00a0 The new expression, (10a3<\/sup>)\/20a can be simplified to \u00bd \u00b7a2<\/sup> or a2<\/sup>\/2.\u00a0 If the problem were 4\/ (5x2<\/sup>) \u00b7(x-2)\/ (2x3<\/sup>), the new numerator would be 4(x-2) and the new denominator would be (5x2<\/sup>) \u00b7 (2x3<\/sup>) or 10x5<\/sup>.\u00a0 The new expression is then [4(x-2)]\/ (10x5<\/sup>), which is not in simplest form.\u00a0 The fraction 4\/10 can be simplified to 2\/5, so the expression in simplest form is [2(x-2)]\/ (5x5<\/sup>)].<\/p>\n

Dividing Rational Numbers<\/strong><\/h3>\n

Remember that dividing rational numbers is the same as multiplying by the reciprocal of the divisor, so that 4\/5 \u00f72\/3 is the same as 4\/5 \u00b73\/2, so that 4\u00b73 equals 12 and 5\u00b72 equals 10.\u00a0 Since 2 is a common factor in both the numerator and denominator, the fraction in simplest terms is 6\/5.\u00a0 There are no common factors to both 6 and 5 except for 1 so the fraction is in simplest terms.<\/p>\n

Dividing Rational Expressions<\/strong><\/h3>\n

Similar to dividing rational numbers, when dividing rational expressions, also multiply by the reciprocal of the divisor.\u00a0 Therefore (8n5<\/sup>)\/3 \u00f7 (2n2<\/sup>)\/9 becomes (8n5<\/sup>)\/3 \u00b79\/ (2n2<\/sup>).\u00a0 Multiply [(8n5<\/sup>) \u00b7 9], the numerator and [3\u00b7 (2n2<\/sup>)].\u00a0 However, the resulting expression (72n5<\/sup>)\/ (6n2<\/sup>) is not in simplest terms.\u00a0 First, factor out the common coefficients, so that 12 is left.\u00a0 (The number 72 divided by 6 equals 12.)\u00a0 Next factor out the common variables, so that n5<\/sup>\/n2<\/sup> equals n3<\/sup>.\u00a0 The quotient in simplest form is 12n3<\/sup>. Likewise, suppose the problem were [(4m-8)\/5] \u00f7 [(m-2)\/10].\u00a0 The new expression would then be [(4m-8)\/5] \u00b7 [10\/ (m-2)].\u00a0 The new numerator can be factored as [4(m-2)]10, and the new denominator can be factored as 5(m-2).\u00a0 Since (m-2) is a common factor for both the numerator and the denominator, (m-2)\/(m-2) equals 1 and cancels out, leaving 4(10)\/5, or 8.<\/p>\n

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Overview The process of multiplying and dividing rational expressions is similar to multiplying and dividing rational numbers.\u00a0 In order to multiply, first multiply the numerators, then the denominators, and then simplify the expression.\u00a0 Division is the inverse of multiplication, so multiply by the reciprocal (or inverse) of the divisor, and then simplify the expression. Multiplying […]<\/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],"tags":[4064,4065,2755],"class_list":["post-66913","post","type-post","status-publish","format-standard","hentry","category-algebra","tag-dividing-rational-expressions","tag-factoring-and-simplifying","tag-multiplying-rational-expressions"],"acf":[],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/posts\/66913","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=66913"}],"version-history":[{"count":0,"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/posts\/66913\/revisions"}],"wp:attachment":[{"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/media?parent=66913"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/categories?post=66913"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/tags?post=66913"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}