Subtraction of fractions

Do you need subtract fractions? With our online calculator you can do this operation automatically by entering the value of a fraction. To do this, you simply use the "/" symbol to specify the value of the numerator and denominator. For example, a half is written as 1/2.

Each field also supports the possibility of working with mixed fractionsthat is, fractions with whole numbers. For example, you can write an operation like 2 2/3 - 4 5/3, which would be something like the following (2+2/3)-(4+5/3).

In both cases, you will obtain the subtraction of two fractions in irreducible format to solve any mathematical problem.

How to subtract fractions with the same denominator

Example of subtracting fractions

For subtract fractions with equal denominatorIf the denominator is the same, we have to keep the denominator the same and subtract the numerators keeping their original order.

In the example that we propose in the picture you can see three fractions with denominator 6 that we have to subtract. What we do is to keep the six as the common denominator and proceed with the subtraction of the numeratorsresulting in the fraction 3/6 which is not irreducible.

If we want to simplify it further, we can divide the numerator and denominator by 3 (a common factor of both), resulting in 1/2. If there had been no common factor, it could not be simplified any further but this is something you can check with our irreducible fraction calculator.

How to subtract fractions with different denominator

Subtraction of fractions with different denominator

If what we want is subtract fractions with different denominatorIf you are not sure, you will have to do some more calculations. Anyway, the process to follow is summarized in the following steps:

  1. Search for a common denominator to the fractions involved in the subtraction, something that can be achieved by searching the least common multiple.
  2. Once we have the least common multiple of the denominators, we substitute it in the denominators of the equivalent fractions.
  3. Now we have to replace the numerator of each fraction by its equivalent. This consists of dividing the resulting denominator by the initial denominator. The value we obtain must be multiplied by the initial numerator and thus we get the new numerator of the fraction. At the end of this step we will have a new fraction that is equivalent to the initial one, therefore, they are worth the same.

Subtraction of fractions calculator

In the proposed example we see that we have as denominator the numbers 4, 3 and 5. find the least common multiple of these values, we arrive at the number 60 as the result. This means that the three equivalent fractions will have that value in their denominator.

Now we have to look for the equivalent numeratorsFor this purpose, we apply the procedure described in the third point:

  1. We apply the division of the final denominator by the initial denominator: 60 / 3 = 20
  2. We multiply the result by the value of the initial numerator: 20 x 6 = 120
  3. We substitute in the numerator to obtain the resulting fraction. At the end, we will have gone from having 6/3 to having 120/60.

This has to be repeated with all the fractions involved in the operation and when they all have a common denominator, we simply have to subtract the numerators. It does not matter if we are left with a negative numerator, it is a completely valid result.

In the proposed example we see that the resulting fraction can be simplified a little more. If we enter the irreducible fraction calculator and enter its value, we will see that -126/60 is equivalent to -21/10. It is always convenient to express the final result as simplified as possible.

Online Fraction Calculator

In case you need to continue doing operations with fractions and it is not a subtraction, we have a calculator for you that will allow you to perform numerical conversions or calculate addition, multiplication, division and other operations with numerators and denominators.

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