Beginning Algebra, 11th Edition

SECTION 1.7 Properties of Real Numbers^67

Concept Check Tell whether or not the following everyday activities are commutative.

Complete solution available
on the Video Resources on DVD

1.7 EXERCISES

1.Concept Check Match each item in Column I with the correct choice(s) from Column II.

Choices may be used once, more than once, or not at all.

III

A.

B. 0

C.

D.

E.

F. 1

G.

H.

I.

1

a

514 + 32 = 5 # 4 + 5 # 3

15 # 42 # 3 = 3 # 15 # 42

5 # 4 # 3 = 60

- 1

• a

15 # 42 # 3 = 5 # 14 # 32

2.Concept Check Fill in the blanks: The commutative property allows us to change the

of the terms in a sum or the factors in a product. The associative property allows

us to change the of the terms in a sum or the factors in a product.

3.Washing your face and brushing your

teeth

4.Putting on your left sock and putting on

your right sock

5.Preparing a meal and eating a meal 6.Starting a car and driving away in a car

7.Putting on your socks and putting on

your shoes

8.Getting undressed and taking a shower

9.Concept Check Use parentheses to show how the associative property can be used to

give two different meanings to the phrase “foreign sales clerk.”

10.Concept Check Use parentheses to show how the associative property can be used to

give two different meanings to the phrase “defective merchandise counter.”

Use the commutative or the associative property to complete each statement. State which

property is used. See Examples 1 and 2.

11. 
    
    
    
    12. 
        
    
    
    
    


12. 
    
    
    
    14. 
        
    
    
    
    


13. 
    
    
    
    16. 
        
    
    
    
    


14. 
    
    
    
    18. 19.Concept Check Evaluate and evaluate Do you think
        subtraction is associative?
        20.Concept Check Evaluate and evaluate Do you
        think division is associative?
    
    
    
    

180 , 115 , 32 1180 , 152 ,3.

25 - 16 - 22 125 - 62 - 2.

7 # 12 # 52 = 1 # 22 # 5 8 # 16 # 42 = 18 # 2 # 4

13 + 62 + 7 = 3 + 1 + 72 1 - 2 + 32 + 6 =- 2 + 1 + 62

• 8 # 3 = # 1 - 82 - 12 # 4 = 4 #

- 15 + 9 = 9 + 6 + 1 - 22 =- 2 +

(a)Identity element for addition

(b)Identity element for multiplication

(c) Additive inverse of a

(d)Multiplicative inverse, or reciprocal, of the

nonzero number a

(e) The number that is its own additive inverse

(f ) The two numbers that are their own multi-

plicative inverses

(g)The only number that has no multiplicative

inverse

(h)An example of the associative property

(i) An example of the commutative property

(j)An example of the distributive property