# Fraction or ratio in simplest form

A fraction or ratio is in simplest form when the greatest common factor of the numerator ( number on top ) and the denominator ( number at the bottom) is 1.

To write a ratio in simplest form, we can use the same method that we use to write a fraction in simplest form.

Find the greatest common factor and divide both the number on top
( numerator ) and the number at the bottom ( denominator ) by the  greatest common factor.

Example #1

Write 10:12 ( ratio ) or 10/12 ( fraction ) in simplest form.

Find the greatest common factor of 10 and 12

The greatest common factor of 10 and 12 is 2.

Divide 10 and 12 by 2

The simplest form is 5:6 or 5/6

Since the greatest common factor of 5 and 6 is 1, 5:6 or 5/6 is indeed the simplest form of 10:12 or 10/12

Example #2

Write 25:50 or 25/50 in simplest form.

Find the greatest common factor of 25 and 50

The greatest common factor of 25 and 50 is 25.

Divide 25 and 50 by 25

The simplest form is 1:2 or 1/2

Since the greatest common factor of 1 and 2 is 1, 1:2 or 1/2 is indeed the simplest form of 25:50 or 25/50