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.
To strengthen your skills with algebraic properties and notation, you'll practice doing the following in this chapter:
Here are a few things to keep in mind while you work in this chapter:
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.
59–64 Simplify the expressions involving radicals and absolute value.
59.
60.
61.
62. |5 − 6|−7 =
63. 5−|4 − 7| =
64.
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.
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 =
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 =
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.