Intermediate Algebra (11th edition)

Multiplying Real Numbers

Find each product.

(a) Same sign; product is positive.

(b)

(c)

Factor to write in lowest terms.

= Divide out the common factor, 3.

5

8

=

5 # 3

8 # 3

-

3

4

a-

5

6

b =

15

24

- 0.5 1 - 0.4 2 =0.2

- 31 - 92 = 27

EXAMPLE 6

18 CHAPTER 1 Review of the Real Number System

NOW TRY
EXERCISE 6
Find each product.

(a)

(b)

(c)-

8

11

1332

0.7 1 - 1.2 2

- 31 - 102

(d) Different signs; product is negative.

(e) (f ) ( g)

NOW TRY

OBJECTIVE 5 Find reciprocals and divide real numbers.The definition of

division depends on the idea of a multiplicative inverse,or reciprocal.Two numbers

are reciprocalsif they have a product of 1.

2

3

- 1 - 62 =- 4

5

8

a

12

13

b =-

15

26

- 0.05 1 0.3 2 =-0.015

61 - 92 = - 54 -^6 =-

6

1

0.05 1202 = 1

7

11 A

11

7 B=^1

• 6 A-^16 B= 1
  -^25 A-^52 B= 1
  Reciprocals have
  a product of 1.

Number Reciprocal

0.05 20

0 None

11

7

7

11

• 6, or -^61 -^16
  -^25 -^52

CAUTION A number and its additive inverse have opposite signs. However, a

number and its reciprocal always have the same sign.

The table gives several numbers and their reciprocals.

There is no reciprocal for 0 because there is no number that can be multiplied by 0 to

give a product of 1.

The result of dividing one number by another is called the quotient.For example,

we can write the quotient of 45 and 3 as which equals 15. The same answer

will be obtained if 45 and are multiplied, as follows.

45 , 3 =

45

3

= 45 #

1

3

= 15

1

3

45

3 ,

Reciprocal

The reciprocalof a nonzero number ais

1

a.

NOW TRY ANSWERS

6. (a) 30 (b)
   (c) - 24
   
   
   • 0.84
   
   
   
   

Multiply numerators.

Multiply denominators.