# Dividing Fractions

*If your friend has half a pie, how many quarter-pies are in that half?* Or, to put this into mathematical notation:

^{1}/2 ÷^{1}/4 = ?

To get the answer, **flip the divisor** (the second fraction) **over, and then multiply the fractions.** (Or, to put it another way, multiply the dividend [the first fraction] by the reciprocal of the divisor [the second fraction].)

In this case, that makes the problem:

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

We begin by multiplying the numerators:

1 x 4 = 4

And then we multiply the denominators:

2 x 1 = 2

The answer has a numerator of 4 and a denominator of 2. In other words:

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

This fraction can be reduced to lowest terms:

^{4 ÷ 2}/2 ÷ 2 =^{2}/1 = 2

*There are 2 quarter-pies in a half-pie.*

### Another Example

Let's try another:

^{4}/5 ÷^{6}/7 = ?

We flip the divisor over, and change the division sign to a multiplication sign:

^{4}/5 x^{7}/6 = ?

We multiply the numerators:

4 x 7 = 28

And we multiply the denominators:

5 x 6 = 30

The answer has a numerator of 28 and a denominator of 30. In other words:

^{4 x 7}/5 x 6 =^{28}/30

We can reduce this fraction by dividing the numerator and denominator by 2:

^{28 ÷ 2}/30 ÷ 2 =^{14}/15

### Mixed Numbers

Let's try one more, this time with a mixed number:

2^{1}/4 ÷^{2}/3 = ?

First we change the mixed number to an improper fraction:

^{9}/4 ÷^{2}/3 = ?

Next we flip the divisor over and change the division sign to a multiplication sign:

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

We multiply the numerators:

9 x 3 = 27

And we multiply the denominators:

4 x 2 = 8

The answer has a numerator of 27 and a denominator of 8. In other words:

^{9 x 3}/4 x 2 =^{27}/8

Finally, we turn the result—an improper fraction—into a mixed number.

^{27}/8 = 3^{3}/8 =