Subtracting fractions calculator

Because subtracting fractions can be difficult, we developed this subtracting fractions calculator. With this fraction calculator you can simply subtract a fraction from another one. Fill in two fractions below (the numerator above the scoreline and the denominator below the scoreline) and click "Calculate" to subtract the fractions.

Subtract fractions calculator (with steps)

Work and steps of the calculation

No fractions have been subtracted yet by the fraction calculator. Enter two fractions above (the numerators above the lines and the denominators below the lines) in order to subtract them. The result will be automatically simplified as an irreducible fraction. A step by step explanation of the calculation is shown.

Subtracting fractions step by step

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

Example subtracting fractions

2
3
-
1
4
1
Equalize the denominators of both fractions.
One way to create two fractions with the same denominators is multiplying the numerator and denominator of the first fraction by the denominator of the second fraction and multiplying 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 4
3 x 4
-
1 x 3
4 x 3
=
8
12
-
3
12
2
Subtract the numerators.
Because the denominators are the same, we can subtract the numerators.
8 - 3
12
=
5
12
3
Reduce the result fraction if possible.
To reduce a fraction, find the greatest common factor of the numerator and the denominator. The greatest common factor of 5 and 12 is 1. In this case we already have a fraction in its simples form. We cannot reduce this fraction any further.
5
12
=
5
12
4
In summary
2
3
-
1
4
=
2 x 4
3 x 4
+
1 x 3
4 x 3
=
8
12
+
3
12
=
8 - 3
12
=
5
12

How to subtract fractions?

General steps and rules for subtracting fractions:

  1. Ensure that the denominators are the same
    To subtract fractions, both denominators have to be the same. If they differ, find a common denominator.
  2. Find a common denominator
    Try to find the least common multiple (LCM) of the denominators. The LCM is defined as the smallest number that both denominators divide into evenly. It will not always be easy to find the LCM. If that is the 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 both numerator and denominator of each fraction by the same factor. This gives the fractions the same denominator.
  4. Subtract the numerators
    Once the fractions have the same denominator, you can subtract the numerators and keep the common denominator unchanged.
  5. Reduce the result fraction, if necessary
    Reduce the result fraction to its simplest form by dividing both numerator and denominator by their greatest common factor (GCF).

This is what the process looks like in mathematical terms:

a
b
-
c
d
=
ad - bc
bd

The subtracting fractions calculator will show the entire work and steps of the calculation.

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