Section 1.6 Properties of Real Numbers and Simplifying Expressions 99 Applying the Associative Property Example 4 Use the associative property of addition or multiplication to rewrite each expression. Then simplify the expression if possible. a. b. c. Solution: a. Apply the associative property of addition. Simplify. 1y 52 6 y 15 62 y 11 b. 4(5z) Apply the associative property of multiplication. Simplify. c. Apply the associative property of multiplication. Simplify. 14 52z 20z c 1w Note: In most cases, a detailed application of the associative property will not be shown. Instead, the process will be written in one step, such as 3. Identity and Inverse Properties of Real Numbers The number 0 has a special role under the operation of addition. Zero added to any real number does not change the number. Therefore, the number 0 is said to be the additive identity (also called the identity element of addition). For example: The number 1 has a special role under the operation of multiplication. Any real number multiplied by 1 does not change the number. Therefore, the number 1 is said to be the multiplicative identity (also called the identity element of multiplication). For example: 1821 8 112.852 2.85 1a1 5b 1 5 4 0 4 0 5.7 5.7 0 3 4 3 4 1y 52 6 y 11, 415z2 20z, and 3 2 a 2 3 wb w w 3 2 a 2 3bdw 3 2 a 2 3 wb 3 2 a 2 3 1y 52 6 415z2 wb Skill Practice Use the associative property of addition or multiplication to rewrite each expression. Simplify if possible. 7. 1x 42 3 8. 214x2 9. 5 4 a4 5 tb Classroom Examples: p. 107, Exercises 28 and 30 Answers 7. 8. 9. a5 x 14 32; x 7 12 42x ; 8x 4 4 5bt ; t Identity Properties of Real Numbers If a is a real number, then 1. a 0 0 a a identity property of addition 2. a 1 1 a a identity property of multiplication
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