Basic Mathematics for College Students

Simplify answers when multiplying fractions.

After multiplying two fractions, we need to simplify the result, if possible. To do that,
we can use the procedure discussed in Section 3.1 by removing pairs of common
factors of the numerator and denominator.

2

3.2 Multiplying Fractions 223

Self Check 2

Multiply:

Now TryProblem 25

5

6

a

1

3

b

EXAMPLE 2

Multiply:

StrategyWe will use the rule for multiplying two fractions that have different
(unlike) signs.

WHYOne fraction is positive and one is negative.

Solution

Since 3 and 32 have no common factors other than 1,

  (^) the result is in simplest form.

3

32

Multiply the numerators.

Multiply the denominators.

Since the fractions have unlike signs, make the answer negative.



3

4

a

1

8

b

3  1

4  8



3

4

a

1

8

b

c

ƒ

EXAMPLE 3

Multiply:

StrategyWe will begin by writing the integer 3 as a fraction.

WHYThen we can use the rule for multiplying two fractions to find the product.

Solution

Write 3 as a fraction:

Since 3 and 2 have no common factors other than 1,

 the result is in simplest form.

3

2

Multiply the numerators.

 Multiply the denominators.

1  3

2  1

3 ^31.

1

2

 3 

1

2



3

1

1

2

 3

Self Check 3

Multiply:

Now TryProblem 29

1

3

 7

EXAMPLE 4

Multiply and simplify:

StrategyWe will multiply the numerators and denominators, and make sure that
the result is in simplest form.

WHYThis is the rule for multiplying two fractions.

Solution

To prepare to simplify, write 4 and 8 in

prime-factored form.

Multiply the remaining factors in the numerator: 1 1  1  1.

 (^) Multiple the remaining factors in the denominator: 1 1  2  1  2.

1

2

To simplify, remove the common factors of 2

 (^) and 5 from the numerator and denominator.

5

1

 2

1

 2

1

2

1

 2

1

 2  5

1



5  2  2

2  2  2  5

Multiply the numerators.

(^) Multiply the denominators.

5

8



4

5



5  4

8  5

5

8



4

5

Self Check 4

Multiply and simplify:

Now TryProblem 33

11

25

#^10

11

4

~^2 ~^2

8

~^24

~^2 ~^2