Technically, you should work it this way (although practice makes this step unnecessary for many fractions :P)
Find the greatest common denominator which will be the product of the shared primes from the prime factorization of both numbers...
60=2*2*3*5, 65=5*13 so the only shared prime is 5, so that is the greatest common denominator or factor. You then divide both the numerator and denominator by 5 to get:
12/13
