In lowest terms - Definition and Overview

An irreducible fraction is a fraction a/b, where the numerator a is an integer and the denominator b is a positive integer, such that there is not another fraction c/d with c smaller in absolute value than a and 0<d<b, and c and d are integers, that represents the same number. To say that a fraction is irreducible and to say that it is in lowest terms are synonymous.

For example the fraction 2/4 is equal to 1/2 and therefore not irreducible, but the fractions 1/4, 5/6 and -101/100 are irreducible.

It can be shown that a fraction a/b is irreducible if, and only if, a and b are coprime.

If the numerator is 0 then the denominator is 1, i.e. 0 is written as 0/1.

A fraction that is not irreducible can be reduced by using the Euclidean algorithm to find the greatest common divisor of the numerator and the denominator, and then dividing both the numerator and the denominator by the greatest common divisor.