SECTION 1.7 Properties of Real Numbers^63

Using the Inverse Properties

Use an inverse property to complete each statement.

(a)

The inverse property of addition is used in parts (a) – (c).

-

1

2

+

1

2

= 0

? +

1

2

= 0

EXAMPLE 7

NOW TRY
EXERCISE 6
Simplify.

(a) (b)

2

5

+

3

20

16

20

Using the Identity Property to Simplify Expressions

Simplify.

(a)

Factor.

Write as a product.

Divide.

= Identity property

7

5

=

7

5

1

=

7

5

#^7

7

=

7 # 7

5 # 7

49

35

EXAMPLE 6

(b)

Identity property

Multiply.

= Add.

23

24

=

18

24

+

5

24

=

3

4

#^6

6

+

5

24

=

3

4

1 +^5

24

3

4

+

5

24

Use to get

a common

denominator.

1 =^66

NOW TRY

OBJECTIVE 4 Use the inverse properties.Each day before you go to work or

school, you probably put on your shoes. Before you go to sleep at night, you proba-

bly take them off, and this leads to the same situation that existed before you put them

on. These operations from everyday life are examples of inverseoperations.

The inverse propertiesof addition and multiplication lead to the additive and

multiplicative identities, respectively. Recall that is the additive inverse,or

opposite,of aand is the multiplicative inverse,or reciprocal,of the nonzero num-

ber a. The sum of the numbers aand is 0, and the product of the nonzero num-

bers aand is 1.^1 a

- a

1

a

- a

Inverse Properties

and Addition

and 1 a 02 Multiplication

1

a

a#^1 #a 1

a

 1

a  1 a 2  0 aa 0

NOW TRY ANSWERS

6. (a)^45 (b)^1120

NOW TRY
EXERCISE 7
Use an inverse property to
complete each statement.

(a)

(b) - 9 # = 1

10 + = 0 (b)

4 + 1 - 42 = 0

4 +? = 0 (c)

- 0.75+

3

4

= 0

- 0.75+

3

4

=?

(d)

The inverse property of multiplication is used in parts (d) – (f ).

2

5

#^5

2

= 1

? #

5

2

= 1 (e)

- 5 a-

1

5

b = 1

- 51? 2 = 1 (f )

41 0.25 2 = 1

41 0.25 2 =?

7. (a) (b)- NOW TRY
   1

• (^109)