86 Chapter 1 The Set of Real Numbers The pattern increases by 4 with each row. Thus, the product of two negative numbers must be positive for the pattern to continue. Skill Practice Multiply. 1. 2. 3. 4. 9132 1.511.52 1 3 6142 1152 9 5014.12 b 5. 6. 5 9 a Answers 1. 27 2. 2.25 3. 24 4. 5 5. 0 6. 1 Now suppose we have a product of two negative numbers. To determine the sign, consider the following pattern of products. 4 3 12 4 2 8 4 1 4 4 0 0 4 (1) 4 4 (2) 8 4 (3) 12 From the first four rows, we see that the product increases by 4 for each row. For the pattern to continue, it follows that the product of two negative numbers must be positive. We now summarize the rules for multiplying real numbers. Multiplying Real Numbers • The product of two real numbers with the same sign is positive. Examples: 152162 30 1421102 40 • The product of two real numbers with different signs is negative. Examples: 122152 10 142192 36 • The product of any real number and zero is zero. Examples: 182102 0 Multiplying Real Numbers Multiply the real numbers. a. b. c. 8142 2.511.72 71102 7 2018.32 b 1 2 182 d. e. f. Solution: a. 8142 32 Same signs. Product is positive. b. 2.511.72 4.25 Same signs. Product is positive. c. Different signs. Product is negative. 71102 70 1 2 182 4 d. Different signs. Product is negative. 018.32 0 e. The product of any real number and zero is zero. 14 14 f. Same signs. Product is positive. 1 Simplify. 2 7 a 7 2b 2 7 a Example 1 102162 0 Classroom Examples: p. 93, Exercises 8 and 14
miller_introductory_algebra_3e_ch1_3
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