*Before reading about how to divide fractions, please read the primer on 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.

**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.

**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.

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!

For more on fractions click here:

Mixed fractions (mixed numbers)