Dumb Arithmetic

You can divide 12 into 3rds or 4ths evenly.

But, if you take 1/3rd from 12 (= 4) and add it to 12, you get 16, which can't evenly divide into 3rds (but can into 4ths.) If you take 1/4th of 12 (= 3) and add it to 12, you get 15, which can't evenly divide into 4ths (but can into 3rds.)

Does this point at anything interesting, or am I just a dingus?