# Multiplying Fractions and Mixed Numbers

### Multiplying Fractions

*If your friend has one-quarter of a pie, and she gives you half, how much of the pie do you have?* Or, to put it another way, what's half of one-quarter? Or, to put it into mathematical notation:

^{1}/2 x^{1}/4 = ?

To get the answer, **multiply the numerators (the top parts) and denominators (the bottom parts) separately.**

In this case, first we multiply the numerators:

1 x 1 = 1

Next we multiply the denominators:

2 x 4 = 8

The answer has a numerator of 1 and a denominator of 8. In other words:

^{1}/2 x^{1}/4 =^{1 x 1}/2 x 4 =^{1}/8

*You have one-eighth of the pie.*

### Another Example

Let's try another.

^{2}/9 x^{3}/4 = ?

First we multiply the numerators:

2 x 3 = 6

Next we multiply the denominators:

9 x 4 = 36

The answer has a numerator of 6 and a denominator of 36. In other words:

^{2}/9 x^{3}/4 =^{2 x 3}/9 x 4 =^{6}/36

This can be further reduced:

^{6 6}/36 6 =^{1}/6

(See Reducing Fractions.)

### Multiplying Mixed Numbers

To multiply two mixed numbers, or a mixed number and a fraction, first convert each mixed number to a fraction. Then multiply the fractions.

What is 2^{1}/3 x^{1}/4 = ?

First we write 2^{1}/3 as a fraction:

2^{1}/3 =^{7}/3

Then we multiply the fractions.

^{7}/3 x^{1}/4 = ?

First we multiply the numerators:

7 x 1 = 7

Next we multiply the denominators:

3 x 4 = 12

The answer has a numerator of 7 and a denominator of 12. In other words:

2^{1}/3 x^{1}/4 =^{7 x 1}/3 x 4 =^{7}/12

**See also:**