Chapter 2
Recognizing Algebraic Properties and Notation
The properties used in mathematics were established hundreds of years ago. Mathematicians around the world wanted to be able to communicate with one another; more specifically, they wanted to get the same answers when working on the same questions. To help with that, they developed and adopted rules such as the commutative property of addition and multiplication, the associative property of addition and multiplication, and the distributive property.
The Problems You'll Work On
To strengthen your skills with algebraic properties and notation, you'll practice doing the following in this chapter:
What to Watch Out For
Here are a few things to keep in mind while you work in this chapter:
Applying Traditional Grouping Symbols
51–58 Simplify the expressions.
51. 6 − (5 − 3) =
52. (4 − 3) − 5 =
53. 5[6 + (3 − 5)] =
54. 8{3−[4 + (5 − 6)]} =
55. 
56. 
57. 
58. 
Introducing Some Non-Traditional Grouping Symbols
59–64 Simplify the expressions involving radicals and absolute value.
59. 
60. 
61. 
62. |5 − 6|−7 =
63. 5−|4 − 7| =
64. 
Distributing Multiplication over Addition and Subtraction
65–72 Perform the distributions over addition and subtraction.
65. 2(7 − y) =
66. −62(x + 4) =
67. 
68. 
69. x(y − 6) =
70. −4x(x − 2y + 3) =
71. 
72. 
Associating Terms Differently with the Associative Property
73–78 Use the associative property to simplify the expressions.
73. 47 + (−47 + 90) =
74. (−6 + 23) − 23 =
75. 
76. 
77. (16 + 19) + (−19 + 4) =
78. (77 − 53.2) + 53.2 =
Rearranging with the Commutative Property
79–84 Use the commutative property to simplify the expressions.
79. −16 + 47 + 16 =
80. 
81. 432 + 673 − 432 =
82. 
83. 
84. −3 + 4 + 23 + 3 − 23 =
Applying More Than One Property to an Expression
85–90 Simplify each expression using the commutative, associative, and distributive properties.
85. −32 + 4(8 − x) =
86. −5(x − 2) − 10 =
87. 
88. 
89. −2(3 + y) + 3(y + 2) =
90. 