66 Chapter 1 The Set of Real Numbers Division of Real Numbers Let a and b be real numbers such that .Then, . a b a 1b b 0 Consider the quotient . The reciprocal of 5 is so we have multiply reciprocal 10 5 2 or equivalently, 10 Because division of real numbers can be expressed in terms of multiplication, then the sign rules that apply to multiplication also apply to division. Dividing Real Numbers • The quotient of two real numbers with the same sign is positive. Examples: 24 4 6 36 9 4 • The quotient of two real numbers with different signs is negative. Examples: 100 152 20 Dividing Real Numbers Example 3 Divide the real numbers. a. b. c. d. Solution: a. Different signs. Quotient is negative. 200 1102 20 48 16 b. 3 Different signs. Quotient is negative. 6.25 1.25 c. Same signs. Quotient is positive. 9 5 5 9 5 d. Same signs. Quotient is positive. Because 5 does not divide into 9 evenly the answer can be left as a fraction. Skill Practice Divide. 11. 12. 13. 14. 7 3 7.6 1.9 18 3 14 7 9 5 6.25 1.25 48 16 200 1102 12 4 3 1 5 2 15 10 5 , TIP: If the numerator and denominator of a fraction are both negative, then the quotient is positive. Therefore, can be simplified to . 95 Answers 11. 12. 13. 4 14. 7 3 2 6 9 5
miller_beginning_intermediate_algebra_4e_ch1_3
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