By Lial M.L., Hornsby J.

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1 D. MyMathLab 1 . a 3. The additive inverse of a is InterAct Math Tutorial Software A. Ϫa B. 0 C. 1 D. 1 . a AW Math Tutor Center MathXL Digital Video Tutor CD 1/Videotape 1 2. The identity element for multiplication is A. Ϫa B. 0 C. 1 D. 4. The multiplicative inverse of a, where a 0, is A. Ϫa B. 0 C. 1 D. Complete each statement. 5. The multiplication property of 0 says that the is . 1 . a of 0 and any real number An Addison-Wesley product. Copyright © 2004 Pearson Education, Inc. 1 . a 38 CHAPTER 1 Review of the Real Number System 6.

12 ϩ 3 и 4 9и4Ϫ8Ϭ2 Ϫ3͑5͒2 Ϫ ͑Ϫ2͒͑Ϫ8͒ Ϫ4 Ϫ 3 и 5 ϩ 62 6͉4 Ϫ 5͉ Ϫ 24 Ϭ 3 68. ͑Ϫ6 Ϫ 3͉͒Ϫ2 Ϫ 3͉ Ϭ 9 ͩ ͪ 71. Ϫ14 Ϫ 73. 75. Ϭ ͑2 и 6 Ϫ 10͒ ͑ Ϫ5 ϩ ͙4 ͒͑Ϫ22͒ Ϫ5 Ϫ 1 2͑Ϫ5͒ ϩ ͑Ϫ3͒͑Ϫ2͒ Ϫ8 ϩ 32 Ϫ 1 ͩ ͪ Ϫ5 Ϫ 9 Ϫ6 Ϫ7 Ϫ9 Ϫ 11 ϩ 3 и 7 5Ϫ3 77. 2 7 15 ϩ 5 и 2 10 ϩ 30 Ϭ 2 и 3 Ϫ9͑2͒2 Ϫ ͑Ϫ3͒͑Ϫ2͒ Ϫ7͑ ͙36 ͒ Ϫ ͑Ϫ2͒͑Ϫ3͒ Ϫ4͉2 Ϫ 4͉ ϩ 8 и 2 2 5 69. 6 ϩ ͑Ϫ9͒ Ϫ и 16 3 8 6 и 3 Ϫ 12 Ϭ 4 12 ϩ 24 Ϭ 3 и 2 5 Ϫ 7 и 3 Ϫ ͑Ϫ2͒3 Ϫ8͑ ͙64 ͒ Ϫ ͑Ϫ3͒͑Ϫ7͒ ͉Ϫ6 Ϫ 5͉͑Ϫ8͒ ϩ 32 5 3 70. 7 Ϫ ͑Ϫ8͒ ϩ 12 и 4 6 54. 57. 60. 63. 66. 55. 58. 61. 64. 67. ͩ ͪ 72.

As mentioned there, another name for reciprocal is multiplicative inverse. This is similar to the idea of an additive inverse. Thus, 4 and 41 are multiplicative inverses, as are Ϫ 23 and Ϫ 32 . ) We can extend these properties of arithmetic, the inverse properties of addition and multiplication, to the real numbers of algebra. Inverse Properties For any real number a, there is a single real number Ϫa, such that and a ؉ (؊a) ؍0 ؊a ؉ a ؍0. The inverse “undoes” addition with the result 0. 1 For any nonzero real number a, there is a single real number a such that 1 1 aؒ ؍1 and ؒ a ؍1.