Section 1.6 Properties of Real Numbers and Simplifying Expressions 107 Concept 1: Commutative Properties of Real Numbers For Exercises 15–22, rewrite each expression using the commutative property of addition or the commutative property of multiplication. (See Examples 1 and 3.) 15. 5 182 8 5 16. 7 122 2 7 17. 8 x x 8 18. p 11 11 p 19. 5(4) 20. 10(8) 21. 22. 4(5) 8(10) x1122 12x y1232 23y For Exercises 23–26, rewrite each expression using addition. Then apply the commutative property of addition. (See Example 2.) 23. x 3 24. y 7 25. 4p 9 26. 3m 12 x 132; 3 x y 172; 7 y 4p 192; 9 4p 3m 1122; 12 3m Concept 2: Associative Properties of Real Numbers For Exercises 27–34, use the associative property of addition or multiplication to rewrite each expression. Then simplify the expression if possible. (See Example 4.) 27. 28. 29. 30. 1x 42 9 3 15 z2 513x2 1214z2 x 14 92; x 13 13 52 z; 2 z 15 32x; 15x 112 42z; 48z 1 4 tb 3 5 a5 3 xb 6 11 a11 6 xb 54 a wb 31. 32. 33. 34. 5 a 1 a4 a1 5 b w; w 55 3a b x; x 6 11 1 4a b t; t 3 5 Concept 3: Identity and Inverse Properties of Real Numbers 35. What is another name for multiplicative inverse? 36. What is another name for additive inverse? 37. What is the additive identity? 38. What is the multiplicative identity? Concept 4: Distributive Property of Multiplication over Addition For Exercises 39–58, use the distributive property to clear parentheses. (See Examples 5 and 6.) 39. 40. 41. 42. 615x 12 21x 72 21a 82 312z 92 315c d2 41w 13z2 71y 22 214x 12 43. 44. 45. 46. 1 4 12b 82 2 31x 62 47. 48. 49. 50. 12p 102 17q 12 213w 5z 82 417a b 32 51. 52. 53. 54. 41x 2y z2 612a b c2 16w x 3y2 1p 5q 10r2 55. 56. 57. 58. Mixed Exercises For Exercises 59 –70, use the associative property or distributive property to clear parentheses. 59. 60. 61. 62. 9 116 y2 7 y 1b 802 21 b 101 213 x2 6 2x 514 y2 20 5y 24z 16p 20 130 r2 50 r 7 111 a2 18 a 63. 4(6z) 64. 8(2p) 65. 66. 67. 20130 r2 600 20r 68. 7111 a2 77 7a 69. 20130r2 600r 70. 7111a2 77a 2 5 n 2 1 2 1n 52 3 m 1 5 1 1 3 1m 32 2 b 2 2 3 x 4 0 1 11 6 b x; x Reciprocal Opposite 30x 6 2x 14 2a 16 6z 27 15c 3d 4w 52z 7y 14 8x 2 2p 10 7q 1 6w 10z 16 28a 4b 12 4x 8y 4z 12a 6b 6c 6w x 3y p 5q 10r Writing Translating Expression Geometry Scientific Calculator Video
miller_introductory_algebra_3e_ch1_3
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