Multiplying and Dividing Real Numbers Section 1.3 Multiplying and Dividing Real Numbers

Multiplication of Real Numbers To multiply two real numbers with the same sign, multiply the absolute values. The sign of the result is positive. To multiply two real numbers with different signs, multiply the absolute values. The sign of the result is negative.

Example Multiply. a. –75 × (–3) b. = 225 When multiplying two numbers with the same sign, the result is a positive number. 1 6

Example Multiply. a. –6(4) b. 12(–9) = –24 = –108 When multiplying two numbers with different signs, the result is a negative number. = –108

Example Multiply. a. b. When you multiply two or more nonzero numbers: 1. The result is always positive if there is an even number of negative signs. 2. The result is always negative if there is an odd number of negative signs.

Multiplication Properties for Real Numbers 1. Multiplication is commutative. If two numbers are multiplied, the order of the numbers does not affect the result. (3)(1) = (1)(3) = 3 2. Multiplication of any number by zero will result in zero. (4)(0) = (0)(4) = 0 3. Multiplication of any number by 1 will result in that number. (6)(1) = (1)(6) = 6 4. Multiplication is associative. If three numbers are multiplied, it does not matter which two numbers are grouped together and multiplied first. 2 × (3 × 1) = (2 × 3) × 1 2 × 3 = 6 × 1 6 = 6

Division of Real Numbers To divide two real numbers with the same sign, divide the absolute values. The sign of the result is positive. To divide two real numbers with different signs, divide the absolute values. The sign of the result is negative.

Example Divide. a. –75 ÷ (–3) b. = 25 When dividing two numbers with the same sign, the result is a positive number. 1 6

Example Divide. a. –6 ÷ 2 b. 120 ÷ (–10) = –3 = –12 When dividing two numbers with different signs, the result is a negative number. = –12

Example Divide. 6 1

Division Properties for Real Numbers 1. Division of 0 by any nonzero number gives 0 as a result. 0 ÷ (20) = 0, 0 ÷ 3 = 0 2. Division of any real number by 0 is undefined. 4 ÷ 0 undefined

Example Divide. –6 ÷ 0 Division by 0 is undefined.