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

Mixed Numbers and Improper FractionsFactors and FractionsReciprocal Fractions

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