38 CHAPTER 1 Review of the Real Number System
47.
(identity property)48.
(identity property)1 # 7 = - 12 x+ 0 =
49.
(inverse property)-
1
4
ty+1
4
ty=51.
(distributive property)52.
(distributive property)81 - 4 +x 2 = 31 x-y+z 2 =53.
(multiplication
property of 0)54.
(multiplication
property of 0)01 0.875x+ 9 y- 88 z 2 = 0135 t^2 - 8 t+ 122 =55.Concept Check Give an “everyday” example of a commutative operation and of an
operation that is not commutative.
56.Concept Check Give an “everyday” example of inverse operations.The distributive property can be used to mentally perform calculations. For example, calcu-
late as follows.
Distributive property
Add inside the parentheses.
Multiply.
Use the distributive property to calculate each value mentally.60. 61. 62.
8
5
1172 +
8
5
8.75 1152 - 8.75 152 4.31 1692 +4.31 1312 1132
58 #
3
2
- 8 #
3
2
96 # 19 + 4 # 19 27 # 60 + 27 # 40
= 760
= 381202
38 # 17 + 38 # 3 = 38117 + 32
38 # 17 + 38 # 3
EXERCISES 63–68FOR INDIVIDUAL OR GROUP WORK
When simplifying the expression to ,some steps are usually
done mentally. Work Exercises 63–68 in order,providing the property that justifies
each statement in the given simplification. ( These steps could be done in other orders.)63.
64.
65.
66.
67.
- = 5 x+ 11
= 13 + 22 x+ 14 + 72= 13 x+ 2 x 2 + 14 + 72= 3 x+ 12 x+ 42 + 7= 3 x+ 14 + 2 x 2 + 7= 13 x+ 42 + 12 x+ 723 x+ 4 + 2 x+ 73 x+ 4 + 2 x+ 7 5 x+ 11RELATING CONCEPTS
69.By the distributive property,. This property is more completely
named the distributive property of multiplication with respect to addition. Is there a dis-
tributive property of addition with respect to multiplication? In other words, istrue for all real numbers, a, b, and c? To find out, try some sample values of a, b, and c.
70.Explain how the distributive property is used to combine like terms. Give an example.a+ 1 b#c 2 = 1 a+b 21 a+c 2
a 1 b+c 2 =ab+ac50.
(inverse property)-
9
8
a-8
9
b =