# How to divide fractions

## Let's kick off with this simple example of dividing fractions

1/3     ÷     1/2

Change the division sign (÷) to a multiplication sign (x) and 'flip' the second fraction

1/3     x     2/1

It may help to imagine a pancake marked on one side with the fraction 1/2 - 'flip' the pancake to reveal the fraction 2/1 on the other side! Now follow the rules for multiplying fractions -

multiply the numerators

1  x  2   =   2

multiply the denominators

3  x  1   =   3

The resulting fraction is 2/3.

So

1/3  ÷  1/2   =   1/3  x  2/1   =   (1 x 2) / (3 x 1)   =   2/3

i.e.   one third divided by a half equals two thirds.

## Next consider

1/7     ÷     1/2     ÷     2/3

Change the division signs (÷) to multiplication signs (x) and 'flip' the second and third fractions

1/7     x     2/1     x     3/2

Now multiply the numerators

1  x  2  x  3   =   6

and multiply the denominators

7  x  1  x  2   =   14

Simplify the resulting fraction 6/14 to the equivalent fraction 3/7 by dividing numerator and denominator by factor 2 Bringing everything together

1/7     ÷     1/2     ÷     2/3

=

1/7     x     2/1     x     3/2

=

(1 x 2 x 3) / (7 x 1 x 2)

=

6/14

=

3/7

i.e.   one seventh divided by a half divided by two thirds equals three sevenths.

## Have a go at the following

3/4     ÷     3/4     ÷     1/2     ÷     1/2

5/3     ÷     2/2     ÷     1/2     ÷     2/3     ÷     1/2

Don't worry about how many fractions are involved or the improper fractions (5/3 and 2/2, numerator greater than or equal to denominator). Apply the same technique as shown in the previous examples of how to divide fractions.

To recap, change the division signs (÷) to multiplication signs (x) and 'flip' all the fractions except the first fraction. Then follow the rules for multiplying fractions - multiply the numerators and multiply the denominators.

The answers/workings out are as follows

3/4     ÷     3/4     ÷     1/2     ÷     1/2

=

3/4     x     4/3     x     2/1     x     2/1

=

(3 x 4 x 2 x 2) / (4 x 3 x 1 x 1)

=

48 / 12

(48 divided by 12)

=

4

i.e.   three quarters divided by three quarters divided by a half divided by a half equals 4.

5/3     ÷     2/2     ÷     1/2     ÷     2/3    ÷     1/2

=

5/3     x     2/2     x     2/1     x     3/2     x     2/1

=

(5 x 2 x 2 x 3 x 2) / (3 x 2 x 1 x 2 x 1)

=

120/12

(120 divided by 12)

=

10

i.e.   five thirds divided by two halves divided by a half divided by two thirds divided by a half equals 10.

## Feeling more confident about how to divide fractions?

Using the technique you've just learned, go ahead and divide fractions with confidence - regardless of the number of fractions or whether they're proper or improper!

What is a fraction?

Equivalent fractions

Simplifying fractions

How to subtract fractions

Multiplying fractions

Improper fractions

Mixed fractions (mixed numbers)

Comparing fractions

Ordering fractions

Fraction to decimal chart

Decimal to fraction

Fraction to percent

› How to divide fractions