Fraction rules

On this page you will find a brief overview of the calculation rules for fractions.

Simplifying fractions

To write a fraction in its simplest form, find the greatest common divisor of the numerator and denominator. Example:

25

30

The numerator (25) and the denominator (30) are both divisible by 5 (greatest common divisor). If you divide both numerator and denominator by five, you can rewrite the fraction as:

25 / 5

30 / 5

=

5

6

More about: Simplifying fractions

Add and subtract fractions

When adding or subtracting fractions, both fractions must have the same denominator. To create two fractions with the same denominators, 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.

2

5

+

1

3

=

2 * 3

5 * 3

+

1 * 5

3 * 5

=

6

15

+

5

15

=

11

15

More about: adding fractions and subtracting fractions.

Multiplying fractions

When multiplying fractions, you multiply the numerators together and the denominators together. For example:

2

3

×

3

4

=

×

2 * 3

3 * 4

=

6

12

=

1

2

To simplify the fraction find the greatest common divisor of the numerator and denominator. In this example, the greatest common divisor is 6, so both the numerator and the denominator can be divided by 6.

More about: multiplying fractions

Dividing fractions

When you divide fractions, you swap the numerator and denominator of the second fraction. Then multiply the first fraction by this reversed second fraction. For example:

1

8

÷

3

4

=

×

1 * 4

8 * 3

=

4

24

=

1

6

To simplify the fraction find the greatest common divisor of the numerator and denominator. In this example, the largest common denominator is 4, so both the numerator and the denominator can be divided by 4.

More about: dividing fractions