Subtracting Fractions

Make sure the denominators are the same, subtract the numerators, and simplify the fraction if necessary.


How does subtraction with fractions work?

When subtracting fractions, the numerators need to be subtracted and the denominators stay as they are. The denominators do need to be the same. If this is not the case, the denominators first need to be made the same before the numerators can be subtracted.
Subtraction with fraction is explained with several examples. The following subtractions with fractions are dealt with:
- Subtracting fractions with the same denominators
- Subtracting mixed fractions with the same denominators
- Subtracting fractions with different denominators
- Subtracting mixed fractions with different denominators

It's important to have equivalent fractions when subtracting fractions. If you don't remember how that works, have a look at the 'Equivalent Fractions' page.

On this page you will find examples and exercices. For an extensive practice go to one of the 5-step plans.

5-step plans


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Example 1

Subtracting fractions with the same denominators



In this example we explain the sum 34 - 14.

Step 1. Are the fractions equivalent?

Yes, the fractions are equivalent. They both have the denominator 4.
If the denominators weren't the same, the fractions would first need to be made equivalent.

Step 2. Subtracting the cardinal numbers and the numerators.

There are no cardinal numbers, so we only need to subtract the numerators. 3 - 1 = 2. We then get

34 - 14 = 24.

Step 3. Simplify if necessary.

24 can be simplified to 12, look at 'Simplifying Fractions' for more information.

The answer becomes 34 - 14 = 12

Example 2

Subtracting mixed fractions with the same denominator



In this example we explain the sum 4 35 + 2 25. ​

Step 1. Are the fractions equivalent?

Yes, the fractions are equivalent. They both have the denominator 5.

Step 2. Subtracting the cardinal numbers and the numerators.

First we subtract the cardinal numbers, that's 4 - 2 = 2.
Then the numerators, 3 - 2 = 1. The denominator stays 5.

The answer to the sum: 435 - 225 = 2 15.

Step 3. Simplify if necessary.

The answer can't be simplified.

Example 3

Subtracting fractions with the different denominators



In this example we explain the sum 23 - 14.


Step 1. Are the fractions equivalent?

The fractions 23 and 14 aren't equivalent. The denominators need to be made the same before the fractions can be added.

To make the fractions equivalent, both these fractions need to get the denominator 12.

2 x 4 = 83 x 4 = 12 and 1 x 3 = 34 x 3 = 12


You then get 812and 312.

Step 2. Subtracting the cardinal numbers and the numerators.

You now have equivalent fractions and you can subtract the numerators. 8 - 3 = 5. The answer is 812 - 312 = 512

Step 3. Simplify if necessary.

The answer can't be simplified.