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Adding fractions calculator

Add fractions with this online fraction calculator. The calculator shows you step by step how to add fractions and how the result is reduced. Adding fractions can be tricky, especially if the fractions don't have the same denominators. This unique calculator shows you step by step how to add fractions. Enter your two fractions below (the numerator above the line and the denominator below the line) and click "Calculate" to add the fractions.

Add fractions calculator (with steps)

Simple fraction calculatorMixed fraction calculator

Work and steps of the calculation

The fraction calculator has not added fractions yet. Enter two fractions above (the numerators above the lines and the denominators below the lines) in order to add them. The result will be automatically reduced as a fraction in its simplest form. The calculation is explained step by step.

Adding fractions step by step

To add fractions, you first need to make sure that the denominators of both fractions are the same. This can be done by finding a common denominator for both fractions. You can find a common denominator by multiplying the numerator and denominator of one or both fractions by the same number. In this way you can ensure that the denominators of the fractions become the same. Below we show you an example of how to add fractions.

Example adding fractions

2
5
+
1
3
1
Make sure that the denominators of both fractions are the same.
The easiest way to create two fractions with the same denominators is to multiply the numerator and denominator of the first fraction by the denominator of the second fraction and multiply the numerator and denominator of the second fraction by the denominator of the first fraction (the common denominator for these fractions is the product of both denominators).
2 x 3
5 x 3
+
1 x 5
3 x 5
=
6
15
+
5
15
2
Add the numerators.
Because the denominators are the same, we can add the numerators.
6 + 5
15
=
11
15
3
Simplify the result if possible.
To simplify a fraction, look for the greatest common factor of the numerator and the denominator. The greatest common factor of 11 and 15 is 1. This is therefore already the simplest form of the fraction. So we cannot simplify this fraction any further.
11
15
=
11
15
4
In summary
2
5
+
1
3
=
2 x 3
5 x 3
+
1 x 5
3 x 5
=
6
15
+
5
15
=
6 + 5
15
=
11
15

How to add fractions?

Here are the general steps and rules for adding fractions:

  1. Make sure the denominators are the same
    To add fractions, the denominators must be the same. If they're not already the same, find a common denominator.
  2. Find a common denominator
    Try to identify the least common multiple (LCM) of the denominators. The LCM is the smallest number that both denominators divide into evenly. Sometimes its not easy to find the LCM, in that case you can always multiply both denominators and use this result as common denominator.
  3. Adjust the fractions
    Express each fraction with the common denominator by multiplying the numerator and denominator of each fraction by the same factor. This ensures that the fractions have the same denominator.
  4. Add the numerators
    Once the fractions have the same denominator, add the numerators together and keep the common denominator unchanged.
  5. Simplify, if necessary
    Simplify the resulting fraction by reducing it to its simplest form. Divide both the numerator and the denominator by their greatest common factor.

Here's the process in mathematical terms:

a
b
+
c
d
=
ad + bc
bd

When you use the adding fractions calculator, the entire work and steps of the calculation are shown.

Simplify fractions

Each fraction can be reduced to it’s simplest form, in which the numerator and denominator are as small as possible. Try this reduce fraction calculator to simplify your fraction and find the Greatest Common Factor (GCF).

Simplify fractions calculator

Long division calculator

A long division is a method for dividing multidigit numbers by hand. It breaks down the division of two numbers into a series of easier steps. From the makers of the fraction calculator:

Try our long division calculator