18 Chapter 1 Real Numbers and Algebraic Expressions Multiplying and Dividing Real Numbers Multiplication and division of real numbers also arise in everyday situations, though the occurrences may not be as obvious as adding and subtracting real numbers. Some examples are shown. Both signs are positive: Todd wins $50 for each of three hands of poker. So, he wins a total of $150. a number of hands played b a money won each hand b = a total winnings b 3($50) = $150 Both signs are negative: Nadine typically bets $10 for a hand of poker. For two hands, she gets lousy cards and decides not to make a bet. By not playing, she saves a total of $20. anumber of hands not played b a money that would be lost b = a money saved b (-2)(-$10) = $20 Signs are different: Anthony loses $25 for each of four hands of poker. So, he loses a total of $100. a number of hands played b a money lost each hand b = a total money lost b (4)(-$25) = -$100 Note: Recall multiplication represents repeated addition. So, we can think of this product as 4(-25) = (-25) + (-25)+ (-25) + (-25) = -100 These rules can be summarized as follows. Procedure: Multiplying Real Numbers Step 1: Determine the signs of the numbers being multiplied. Step 2: Multiply using the following rules. a. If the signs of the nonzero numbers are the same, their product is positive. b. If the signs of the nonzero numbers are different, their product is negative. The rules stated previously apply to nonzero numbers. When one of the numbers being multiplied is zero, the result is zero. We state the property as follows. Property: Product Property of Zero The product of any number a and zero is zero. a · 0 = 0 To define the rules for dividing real numbers, we rely on facts that we already know. 6 3 = 2 and 6 · 1 3 = 2 So, it follows that 6 3 = 6 ÷ 3 = 6 · 1 3 Objective 2 ▶ Multiply and divide real numbers.
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