Beginning Algebra, 11th Edition

60 CHAPTER 1 The Real Number System

10. 11. 12.

13. 14. 15.

16. 17. 18.

19. 20. 21.

22. 23. 24.

25. 26. 27.

28. 29. 30.

31. 32. 33.

Evaluate each expression for and

37. 38. 39.

1. a

a x

b

2 a

x y

b

3

x^2 + 3 y

x^2 - y^2 x^2 +y^2

2 x+ 3 y a-xy

a

1

2

x+

2

3

yba-

1

4

ab

x+y- 3 a 1 x+ 623 - y^31 x-y 2 - 1 a- 2 y 2

x=-2,y=3, a=4.

- 32 - 22 |- 2132 + 4 |-|- 2 | 40 + 21 - 5 - 32

a -0.9 1 - 3.7 2 - 5.1 1 - 0.2 2

1

2

-

1

3

b -

5

6

c

5

8

a-

1

16

bd+

3

8

82 - 12

1 - 522 + 2162

1

2

,a-

1

2

b

-

3

4

,a-

5

8

b

1 - 1022 + 102

- 10152

32 - 52

1 - 922 - 92

61 - 10 + 32

151 - 22 - 31 - 92

|- 4192 |-|- 11 |

- 91 - 62 + 1 - 22 1272

318 - 92

43 - 33

- 51 - 4 + 22

12 + 422

15 - 322

22 + 42

52 - 32

91 - 62 - 3182

41 - 72 + 1 - 221 - 112

161 - 8 + 52

151 - 32 + 1 - 7 - 421 - 32

62 - 8

- 2122 + 41 - 12

51 - 8 + 32

131 - 22 + 1 - 721 - 32

- 3 - 1 - 9 + 12

- 7 - 1 - 62

51 - 42

- 7 - 1 - 22

OBJECTIVES In the basic properties covered in this section, a, b, and crepresent real numbers.

OBJECTIVE 1 Use the commutative properties. The word commutemeans to

go back and forth. Many people commute to work or to school. If you travel from

home to work and follow the same route from work to home, you travel the same dis-

tance each time.

The commutative propertiessay that if two numbers are added or multiplied in

any order, the result is the same.

Properties of Real Numbers

1.7

1 Use the commutative properties. 2 Use the associative properties. 3 Use the identity properties. 4 Use the inverse properties. 5 Use the distributive property.

Commutative Properties

Addition

abba Multiplication

abba

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