Many people know about crazy fraction reduction: 16/64 is 1/4 by normal arithmetic, but if you cancel the 6s, you get 1/4 as well. Right answer, wrong method.
I was just introduced to the inverse of crazy fraction reduction. 32/24 = 4/3, but if you cancel the 2s, 32/24 = 3/4. For some reason, this is more alarming to me than standard crazy fraction reduction.