Sum of fractions calculator

With our fraction addition calculator you will be able to apply this simple operation automatically and without mistakes. Its algorithm will give you the result of a sum of simple or mixed fractions.

For example:

  • Simple fraction: 1/2 + 1/2 = 1
  • Mixed fraction1 1/2 + 1 1/2 = 3 (Note that in this case, we are adding 1 and 1/2 twice).

Finally, click on the button represented by the equal sign or on the calculate button and you will get the result for add the two fractions together you have entered.

How to add fractions with the same denominator

Addition of fractions with equal denominator

For adding fractions with equal denominatorIf we do not add the numerators, the only thing we have to do is to add the numerators, keeping the denominator fixed.

In the example you have in this section you can see how we add three fractions whose common denominator is 5.

If we apply what we have said in the first paragraph, we will make the sum of the numerators (7 + 3 + 4) but keeping the denominator unchangedThis results in a fraction of 14/5 that we cannot reduce any further because the resulting denominator and numerator do not share any common factor that would allow us to simplify the result further.

How to add fractions with different denominators

Exercise of addition of fractions with different denominator

In case you want to adding fractions with different denominatorsIf we do this, we will have to do some more calculations. In any case, the process is summarized in the following steps:

  1. Finding a common denominator to the fractions involved in the sum, something that can be done by the method of the least common multiple. In the link we have left you can see what the MCM search consists of.
  2. With the least common multiple of the denominators found, we substitute it in the denominators of the equivalent fractions.
  3. Now we have to replace the numerator of each fraction by its corresponding equivalent. In this case we have to divide the resulting denominator by the initial denominator. The resulting value is multiplied by the initial numerator and thus we obtain the new numerator of the fraction.

Fraction addition calculator

By example.In the proposed example we see that we have as denominator the numbers 4, 3 and 5. After finding the least common multiple of these values, we arrive at the value 60 as a result.

Now we need to find the equivalent numerators, for which we apply what was described in point 3:

  1. We divide the final denominator by the initial denominator: 60 / 4 = 15
  2. Multiply the result by the value of the initial numerator: 15 x 2 = 30
  3. Substitute to obtain the resulting fraction: 2/4 = 30 / 60

We repeat with the rest of the fractions and when they all have common denominator, we simply have to to make the sum of the numerators.

Easy, isn't it? If you have any questions, leave us a comment and we will try to help you. If you have found this calculator for adding fractions useful, we would be very grateful if you could share it on your social networks.

Remember that if you need to carry out any other operation, we have at your disposal a online fraction calculator.

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