SECTION 1.1 Fractions^5

NOW TRY
EXERCISE 3
Find each product, and write
it in lowest terms.

(a) (b) 3

2

5

# 6 2

3

4

7

#^5

8

(b)

Write each mixed number

as an improper fraction.

Multiply numerators.

Multiply denominators.

Factor the numerator.

or

Write in lowest terms

(^12) and as a mixed number.

1

4

=

49

4

,

=

7 # 3 # 7

3 # 4

=

7 # 21

3 # 4

2

1

3

5 1

4

=

7

3

#^21

4

Think: , and

20 + 1 = 21 , so 5 41 =^214.

4 # 5 = 20

Think: means

12

4

gives

9

1

8

4 12 14.

 49

(^49449) ,4.
NOW TRY

NOTE Some students prefer to factor and divide out any common factors before

multiplying.

Example 3(a)

Divide out common factors. Multiply.

= The same answer results.

1

6

=

1

2 # 3

3

8

#^4

9

=

3

2 # 4

#^4

3 # 3

Two fractions are reciprocalsof each other if their product is 1. See the table in

the margin. Because division is the opposite (or inverse) of multiplication, we use re-

ciprocals to divide fractions.

A number and its

reciprocal have a product

of 1.For example,

3

4

4

3 =

12

12 =1.

Number Reciprocal

5, or

9, or^9119

5

1

1

5

7

11

11

7

4

3

3

4

Dividing Fractions

If and are fractions, then

That is, to divide by a fraction, multiply by its reciprocal.

a

b



c

d



a

b

#d

c

.

c

d

a

b

As an example of why this method works, we know that and also that

The answer to a division problem is called a quotient.For example, the

quotient of 20 and 10 is 2.

20 # 101 =2.

20 , 10 = 2

Dividing Fractions

Find each quotient, and write it in lowest terms.

(a)

Multiply by the reciprocal of the second fraction.

3

4

,

8

5

=

3

4

#^5

8

=

3 # 5

4 # 8

=

15

32

EXAMPLE 4

Make sure the answer

is in lowest terms.

(b) or 1

1

5

3

4

,

5

8

=

3

4

#^8

5

=

3 # 8

4 # 5

=

3 # 4 # 2

4 # 5

=

6

5

,

Think:

and

so 2 13 =^73.

6 + 1 =7,

3 # 2 =6,

NOW TRY ANSWERS

3. (a) 145 (b)^683 ,or 22 (^23)