What Happens When We Reduce Fractions to Lowest Terms

Many mathematical algorithms are performed so routinely that we sometimes do not think about why we do them or why the method works. One example of such routine algorithm is reducing fractions to lowest terms. Why do we always perform this procedure? What is really happening when we reduce fraction to lowest terms?

One of the basic reasons why we reduce fraction to lowest terms is to lessen the burden of calculating large numbers. Of course, we would rather add or multiply \frac{1}{2} and \frac{1}{4} than \frac{12}{24} and \frac{9}{36}. So you see, the effort of multiplying the same fraction is lessen when they are reduced to lowest terms.

But what really happens when we reduce fraction to lowest terms? Why is it possible and why does it work? » Read more