An algorithm for reducing fractions

Abstract

In the teaching of elementary mathematics, one of the areas that seems to give the most trouble is that of the reduction of simple fractions. For example, let us consider a proper fraction of the form a/b. We can reduce a/b to lowest terms by finding the greatest common divisor of a and b, denoted by GCD (a, b), and factoring it out of both numerator and denominator. This method, of course, calls for an understanding of factoring. Factoring is not beyond the realm of understanding of the students, but the method is so time-consuming and laborious that most students, especially the slower ones, are disenchanted with it and do not use it. Students then resort to the old standby method of trial-and-error, accompanied by a few rules of divisibility, which is, of course, also very time-consuming and laborious on many fractions. Too many students become discouraged with the whole process and tend to give up, thereby retarding their learning of how to properly reduce fractions.