Basic Mathematics for College Students

Two observations can be made from this result.

• The numerator of the answer is the product of the numerators of the original
  fractions.
  1  3  3

Answer

2  5  10

• The denominator of the answer is the product of the denominators of the
  original fractions.
  These observations illustrate the following rule for multiplying two fractions.

Multiplying Fractions

To multiply two fractions, multiply the numerators and multiply the

denominators. Simplify the result, if possible.

Success Tip In the newspaper example, we found a part of a partof a page.

Multiplying proper fractions can be thought of in this way. When taking a part

of a partof something, the result is always smaller than the original part that

you began with.

cc c

1

2



3

5



3

10

T T T

222 Chapter 3 Fractions and Mixed Numbers

Self Check 1

Multiply:

a.

b.

Now TryProblems 17 and 21

5

9

#^2

3

1

2

#^1

8

EXAMPLE 1

Multiply: a. b.

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.

a.

Since 1 and 24 have no common factors

other than 1, the result is in simplest form.

Solution

b.

Since 21 and 40 have no common factors

 (^) other than 1, the result is in simplest form.

21

40

Multiply the numerators.

Multiply the denominators.

7

8



3

5



7  3

8  5



1

24

Multiply the numerators.

Multiply the denominators.

1

6



1

4



1  1

6  4

7

8



3

5

1

6



1

4

The sign rules for multiplying integers also hold for multiplying fractions. When

we multiply two fractions with likesigns, the product is positive. When we multiply two

fractions with unlikesigns, the product is negative.