Dividing Fractions

Dividing two fractions is very similar to multiplying fractions. Make sure you know your multiplication table, and make sure that you know how to multiply fractions before you start on this section.

Dividing fractions takes two steps:

1. Invert the divisor (Don't understand what this step means? Don't worry - it's explained later!)
2. Multiply the resulting fractions.

Obviously, to do step 1 you have to know what a divisor is, and how to invert it. A divisor is the second half of a division. It is the number (or the fraction) that comes after the 'divided by' sign. The picture below shows you three different examples of divisors:

To invert a fraction means to 'flip it over'. (The numerator becomes the denominator and the denominator becomes the numerator.) For example, if you invert , you get the fraction .

Let's look at some examples of dividing fractions:

Example 1

Perform the following division:

Solution

In this example, 4/5 is the divisor. Step 1 says to invert this fraction. The inverse of this fraction is 5/4. Step 2 says to multiply the resulting fractions together. We end up with this question:

Now we just perform a multiplication of fractions. (If you need help with multiplying fractions, see the previous lesson.) You should end up with the following answer:

Example 2

Perform the following division:

Solution

This question looks more confusing than the last example, but it is the same type of question. If you read the above question out loud it says "2/3 divided by 4/7". If you wanted, you could re-write this question as follows (although this step is NOT required):

Now invert the divisor (4/7) and multiply:

You should end up with the following answer:

Again, don't worry about reducing this answer. If you would like information on reducing and enlarging fractions, go to that section. Now that you have seen some examples, you can try some division sample questions, or you can go back to the fractions main page.