Section 1.2 Operations with Real Numbers and Algebraic Expressions 19 Dividing by a number is equivalent to multiplying by the reciprocal of the number. Two nonzero numbers b and 1 b are reciprocals. Property: Dividing Real Numbers For real numbers a and b (b 2 0), a b = a ÷ b = a · 1 b Because division is another form of multiplication, the sign rules for multiplication also apply to division. Procedure: Dividing Real Numbers Step 1: Determine the signs of the numbers being divided. Step 2: Divide using the following rules. a. If the signs of the nonzero numbers are the same, their quotient is positive. b. If the signs of the nonzero numbers are different, their quotient is negative. When zero is involved in a quotient, one of the two following cases apply. Property: Division Properties with Zero 1. Zero divided by a nonzero number is 0: 0 b = 0 for b 2 0. 2. A nonzero number divided by zero is undefined: a 0 is undefined for a ≠ 0. Note: When multiplying or dividing real numbers, 1. A product or quotient of two real numbers with the same sign is positive. 2. A product or quotient of two real numbers with different signs is negative. 3. A product of a number and zero is zero. 4. A quotient of zero and a nonzero number is zero. 5. A quotient of a nonzero number and zero is undefined. If three or more numbers are multiplied or divided, then we multiply or divide from left to right. Objective 2 Examples Perform the indicated operation. Problems Solutions 2a. (-4)(-8) (-4)(-8) = 32 2b. a- 5 2 ba2 5 b a- 5 2 ba2 5 b =- 10 10 =-1 2c. (-2.3)(-10) (-2.3)(-10) = 23
hendricks_intermediate_algebra_1e_ch1_3
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