To multiply fractions, multiply the numerators to get the numerator of the product, and multiply the denominators to get the denominator of the product.

Example
A jug contains 20 ounces of orange juice. If Janet consumes two-fifths of the juice in the jug, then how many ounces of orange juice did she drink? Solution.
A whole number may be written as a fraction with 1 as its denominator, e.g., 20 = 20/1.

20

1

×

2

5

=

40

5

= 8.

Thus, Janet drank 8 ounces of orange juice.

When multiplying fractions, it is very convenient to cancel a common factor by dividing the numerator and denominator by the factor.
Remember do not multiply your problems. Dividing simplifies your problems.
For example to multiply 15/8 by 44/21, divide 15 and 21 by the common factor 3, and divide 8 and 44 by the common factor 4 as shown below.

15

8

×

44

21

=

15 × 44

8 × 21

=

5 × 11

2 × 7

=

55

14

.

Time and effort are saved in the above example by not multiplying 15 by 44, and 8 by 21.
Note that canceling can be done only between a numerator and a denominator of the same fraction or another fraction, but not between two numerators or between two denominators.

Division of fractions involves reciprocals. A fraction is the reciprocal of another fraction if their product is 1.
The reciprocal of a fraction is obtained by inverting the fraction, i.e., by interchanging the numerator and denominator.
So, the reciprocal of a fraction n/m is m/n, where both n and m are non-zero.
For example, the reciprocal of 2/5 is 5/2 and the reciprocal of 1/5 is 5.

To divide a fraction (dividend) by another fraction (divisor), multiply the dividend by the reciprocal of the divisor.
For example,

8

9

÷

3

5

=

8

9

×

5

3

=

40

27

.

Example
Debbie stitches a doll's dress in three-fourths of an hour. If Debbie works for 5¼ hours, then how many dresses will she stitch? Solution.
The first step is to convert the mixed number to a fraction. Now, 5¼ = 21/4, since 5 × 4 + 1 = 21.
In 3/4 hour, one dress is stitched.
So in 21/4 hours, 21/4 ÷ 3/4 dresses are stitched.