Right Answer, Wrong Reason

Of course, everyone knows that many fractions can be reduced by cancelling:

16/64 = 1/4
(cancel the 6’s)

19/95 = 1/5
(cancel the 9’s)

266/665 = 2/5
(cancel the 6’s)

But all of those are examples of getting the right answer for the wrong reason. Sort of like the third patient in this joke…

The doctor at a mental hospital is testing three of his patients to determine if they are ready to be released. He asks the first guy, “What is 3 × 3?”

“274,” says the first guy.

The doctor asks the second guy, “What is 3 × 3?”

“Tuesday,” replies the second guy.

The doctor turns to the third guy. “Okay, your turn. What is 3 × 3?”

“Nine,” says the third guy proudly.

“That’s great!” says the doctor. “How did you get your answer?”

“Simple,” says the third guy. “I subtracted 274 from Tuesday.”