Irreducible fraction
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An irreducible fraction (or fraction in lowest terms) is a vulgar fraction in which the numerator and denominator are smaller than those in any other equivalent fraction.
Stating it more formally, a fraction a⁄b is irreducible if there is no other equivalent fraction c⁄d with c having an absolute value less than the absolute value of a (where a, b, c, and d are all integers).
For example, 1⁄4, 5⁄6, and -101⁄100 are all irreducible fractions. On the other hand, 2⁄4 is not irreducible since it is equal in value to 1⁄2, and the numerator of the latter (1) is less than the numerator of the former (2).
It can be shown that a fraction a⁄b is irreducible if, and only if, a and b are coprime (relatively prime), that is, if a and b have a greatest common divisor of 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 it.
