100 Chapter 1 The Set of Real Numbers The sum of a number and its opposite equals 0. For example, 12 12 0. For any real number, a, the opposite of a (also called the additive inverse of a) is a a 1a2 a a 0. and The inverse property of addition states that the sum of any number and its additive inverse is the identity element of addition, 0. For example: Number Additive Inverse (Opposite) Sum 9 21.6 21.6 21.6 0 21.6 2 2 a2 b 0 7 7 72 7 9 9 192 0 If b is a nonzero real number, then the reciprocal of b (also called the multiplicative inverse of b) is The inverse property of multiplication states that the product of b and its multiplicative inverse is the identity element of multiplication, 1. Symbolically, we have For example: b 1b Number Multiplicative Inverse (Reciprocal) Product 7 3.14 5 3 5 5 a b 1 3 3 3 5 3.14a 1 3.14b 1 1 3.14 7 1 7 1 1 7 1b b 1. 1b . Inverse Properties of Real Numbers If a is a real number and b is a nonzero real number, then 1. inverse property of addition a 1a2 a a 0 2. b inverse property of multiplication 4. Distributive Property of Multiplication over Addition The operations of addition and multiplication are related by an important property called the distributive property of multiplication over addition. Consider the expression The order of operations indicates that the sum 2 3 is evaluated first, and then the result is multiplied by 6: 612 32 6152 30 612 32. 1 b 1 b b 1 Concept Connections Fill in the blanks. State whether the property used is an inverse property or an identity property. 10. 11. 12. 13. 5 0 8 8 1 2 a b 1 a b Answers 10. 5; inverse 11. 1; identity 12. 2; inverse 13. 0; identity
miller_introductory_algebra_3e_ch1_3
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