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 2¹/3 x ¹/4 = ?

First we write 2¹/3 as a fraction:

2¹/3 = 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:

2¹/3 x ¹/4 = ^{7 x 1}/3 x 4 = ⁷/12