Each fraction can be reduced to itâ€™s simplest form, in which the numerator and denominator are as small as possible. To simplify a fraction you have to first find the greatest common factor of the numerator and denominator. You then have to divide the numerator and denominator by the biggest possible integer (whole number).

For example, we have the following fraction:
^{12}⁄_{18}

The numerator (12) and the denominator (18) are both divisible by 6 (so the largest number that goes exactly into both 12 and 18 is 6 and therefore the greatest common factor is 6). Therefore if you divide the numerator and denominator by 6, you can write the fraction as:

^{12}⁄_{6} / ^{18}⁄_{6} = ^{2}⁄_{3}

You can also simplify a fraction in steps. So ^{12}⁄_{18} can also be written as ^{6}⁄_{9} (the numerator and denominator can both be divided by 2). However, both 6 and 9 can also be divided by 3, so you can write ^{6}⁄_{9} as ^{2}⁄_{3}. ^{2}⁄_{3} is the simplest form.

^{12}⁄_{18} = ^{6}⁄_{9} = ^{2}⁄_{3}