Section 1.6 Multiplication and Division of Real Numbers 63 Multiplication and Division of Real Numbers Section 1.6 1. Multiplication of Real Numbers Multiplication of real numbers can be interpreted as repeated addition. For example: Add 3 groups of 4. Add 3 groups of 4. 3142 4 4 4 12 3142 4 142 142 12 These results suggest that the product of a positive number and a negative number is negative. Consider the following pattern of products. 4 3 12 4 2 8 4 1 4 4 0 0 4 112 4 4 122 8 The pattern decreases by 4 with each row. Thus, the product of a positive number and a negative number must be negative for the pattern to continue. 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 4 112 4 4 122 8 4 132 12 The pattern increases by 4 with each row. 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 102162 0 4 132 12 Concepts 1. Multiplication of Real Numbers 2. Exponential Expressions 3. Division of Real Numbers 4. Order of Operations Thus, the product of two negative numbers must be positive for the pattern to continue.
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