Arithmetic : Fractions

Reduction of Fractions to Lowest Terms

A fraction has been simplified or reduced to lowest terms when there are no common factors in its numerator and denominator except 1.
For example, 2/7 is in its simplest form (because 2 and 7 have no common factors), but 6/21 is not (because 3 is a common factor of 6 and 21).

To simplify a fraction or reduce it to an equivalent fraction in lowest terms, cancel all common factors in the numerator and denominator.
For example to simplify 30/105, divide both numerator and denominator by 5 and 3 as follows.

To reduce a fraction to lowest terms, divide both numerator and denominator by their greatest common divisor (GCD). The GCD of 30 and 105 is 15.

Note that to ensure a fraction is in its simplest form, the numerator and denominator may be written as the product of primes with no common factors.
After fractions are added, subtracted, multiplied or divided, the result is usually expressed in lowest terms.