Subtracting Fractions
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 5step plans.
5step plans

Subtracting Fractions 15step plan

Subtracting Fractions 25step plan

Subtracting Fractions 35step plan
Exercise 1:
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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.