Adding fractions
How does adding fractions work?
When you're adding fractions, you first need to make sure the denominators are the same and then you add the numerators together. If the denominators are not the same, you first need to make them equivalent.
Adding fraction is explained step by step with several examples. The following is discussed:
 Adding fractions with the same denominators
 Adding mixed fractions with the same denominators
 Adding fractions with different denominators
 Adding mixed fractions with different denominators
When adding fractions, it's important that they're equivalent 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

Adding Fractions 15step plan

Adding Fractions 25step plan

Adding Fractions 35step plan

Adding Fractions 45step plan
Example 1
Adding equivalent fractions
In this example we explain the sum 15 + 35.
Step 1. Are the fractions equivalent?
Yes, the fractions are equivalent. They both have the denominator 5.
Step 2. Adding the numerators.
At the second step we add the numerators, 1 + 3 = 4.
This makes the answer to the sum 15 + 35 = 45.
Make sure you only add the numerators and not the denominators.
Exercise 1:
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Example 2
Adding mixed fractions with the same denominator
In this example we explain the sum 1 25 + 4 15.
A mixed fraction is a fraction that's larger than 1. In this case both fractions are mixed fractions.
Step 1. Are the fractions equivalent?
Yes, they're equivalent. They both have the denominator 5. If the denominators weren't the same, they would first need to be made equivalent.
Step 2. Adding the whole numbers and the numerators.
First we add the whole numbers, here that is 1 + 4 = 5. Then we add the numerators, 2 + 1 = 3. The denominators remain the same.
The answer to the sum 1 25 + 4 15 = 5 35.
Example 3
Adding fractions with different denominators
In this example we explain the sum 14 + 13.
Nonequivalent fractions are fractions with different denominators.
Step 1. Are the fractions equivalent?
The fractions 14 and 13 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.
1 x 3 = 34 x 3 = 12 and 1 x 4 = 43 x 4 = 12
You then have 312and 412.
Look at the page Equivalent Fractions for more explanation and exercises about equivalent fractions.
Step 2. Adding the cardinal numbers and the numerators.
Now that the fractions are equivalent, all that's left is to add the numerators.
14 + 13 = 312+ 412 = 712
Example 4
Adding mixed fractions with different denominators
In this example we explain the sum 2 18 + 3 14
Step 1. Are the fractions equivalent?
The fractions 18 and 14 are not equivalent. These fractions need to have the same denominator before they can be added. In this case it's simple. The fraction with the denominator 4, can be changed into 8 by multiplying the numerator and the denominator by 2.
We then get 2 18 + 3 28
Step 2. Adding the cardinal numbers an the numerators
First add the cardinal numbers: 2 + 3 = 5
Then the fractions: 18 + 28 = 38.
The answer:
2 18 + 3 14 = 2 18 + 3 28 = 5 38
Exercise 2:
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