Steps to Subtract Fractions

Frazer says "Here are 2 simple steps to subtract two fractions."

Step 1

Convert the fractions to the same denominator.

If the fractions already have the same denominator, you do not need to do anything!

Step 2

Subtract the second numerator from the first numerator, keeping the denominator the same, to get the answer.

You should now have the answer to your fraction subtraction!

Step 3 (optional)

You may want to convert this into simplest form by cancelling common factors.

See below for a step-by-step breakdown of how to add fractions.

Step 1: Convert the fractions to the same denominator.

If the fractions already have the same denominator, skip the rest of this part.

If the fractions have different denominators, keep reading!

We can only subtract two fractions together if they have the same denominator.

It is a bit like when you are subtracting two amounts, one given in inches and one in centimetres - you need to convert both measures to the same units - either centimetres or inches - before you do the subtraction!

There are two different possibilities for the this step:

Step 1a) If one of the denominators is a multiple of the other denominator.

If this is the case, you just need to multiply the numerator and denominator of the fraction with the lower denominator so that the two denominators are the same.

Step 1b) If one of the denominators is not a multiple of the other denominator.

The easiest and simplest way to convert the two fractions to equivalent fractions with the same denominators is to multiply the numerator and denominator of each fraction by the other fraction's denominator.

Step 2: Subtract the second numerator from the first

Once the two fractions have the same denominator, we can subtract the second numerator from the first one.

This will give us the answer we are looking for.

Have a look at the examples below to see how it all works!

Example 1)   4 5 -      8  15

Step 1)

You will notice that the second denominator (15) is a multiple of the first denominator (5) so we need to follow Step 1a)

So we need to multiply the numerator and denominator of the first fraction by 3.

This give us:

4 5 =   4x3 5x3 =   12 15

So we now have:

4 5 -      8  15 =   12 15 -      8  15

Step 2)

Now the denominators are equal, all we need to do now is to subtract the second numerator from the first.

12 15 -      8  15 =   12-8  15 =    4  15

Step 3)

There are no common factors, so this fraction is already in simplest form.

Example 2)   6 7 -     3 5

Step 1)

The denominator of the first fraction is 7. The denominator of the second fraction is 5. These numbers are not multiples of one another.

We need to use Step 1b)

So we multiply the numerator and denominator of the first fraction by the second fraction's denominator (5).

This give us:

6 7 =   6x5 7x5 =   30 35

Next we multiply the second fraction's numerator and denominator by the first fraction's denominator (7).

This give us:

3 5 =   3x7 5x7 =   21 35

Step 2)

Now the denominators are equal, all we need to do now is to subtract the second numerator from the first.

6 7 -     3 5 =   30 35 -   21 35 =   30-21 35 =      9  35

Step 3)

There are no common factors, so this fraction is already in simplest form.

So let's remember the two important steps:

Step 1: convert both fractions to fractions with the same denominator

Step 2: subtract the second numerator from the first, keeping the denominator the same!