How to add two fractions:

Get a common denominator.  How do you do that?

Third grade way:  Involves a least common (or lowest common denominator).  This involves breaking up the two denominators into prime factors.



My way:  a/b + c/d = (ad + bc) / bd.

This gives you the fraction, but it may not be reduced.  So, then you have to reduce the 
fraction, which means you will have to find the greatest common factor.

This is ridiculously easy to do with a short recursive method.

GCF (a,0) is a.

GCF (a,b) = GCF (b,a%b).

For example, GCF (100,52) = GCF (52,48) = GCF (48,4) = GCF (4,0) = 4.

GCF (13,8) = GCF (8,5) = GCF (5,3) = GCF (3,2) = GCF (2,1) = GCF (1,0) = 1.