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:

2¹/4 ÷ 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 = 3³/8 =

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