Page 46

miller_introductory_algebra_3e_ch1_3

88 Chapter 1 The Set of Real Numbers (0.4)3 (0.4)(0.4)(0.4) 0.064 c. Multiply three factors of 0.4. d. Multiply 1 by three factors of 0.4. 0.43 110.4210.4210.42 0.064 1 2 a e. Multiply three factors of . 3. Division of Real Numbers Two numbers are reciprocals if their product is 1. For example, are reciprocals because . Symbolically, if a is a nonzero real number, then the reciprocal of a is because . This definition also implies that a number 1 1a and its reciprocal have the same sign. The Reciprocal of a Real Number Let a be a nonzero real number. Then, the reciprocal of a is . Recall that to subtract two real numbers, we add the opposite of the second number to the first number. In a similar way, division of real numbers is defined in terms of multiplication. To divide two real numbers, we multiply the first number by the reciprocal of the second number. Division of Real Numbers Let a and b be real numbers such that . Then, . 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 12 4 3 1 5 2 15 10 5 , a b a 1b b 0 1a a 1a 27 172 2 1 27 and 72 1 2b3 a 1 2b a 1 2b a 1 2b 1 8


miller_introductory_algebra_3e_ch1_3
To see the actual publication please follow the link above