Teacher: You say you got (a + b)/(a – b) to reduce to 1 by cancelling.

Teacher: You say you got (a + b)/(a – b) to reduce to 1 by cancelling. But if you just cancelled the ‘a’s and the ‘b’s, wouldn’t it be more logical for you to get just “+” divided by “-” ? Student: Yes sir. Then the “-” would cancel out in both places, leaving the “1”.

— Alan Wayne (1909-1996, mathematics author, puzzler, member of the American Mathematical Society)