When professor Levik was very young he didn't care too much for mathematics, especially fractions. One day his teacher asked him to find the smaller of 2/5 and 3/7 and he jumped at what he though was a shortcut in solving the problem. He replaced 2/5 with 2/3 (2/(5-2)) and replaced 3/7 with 3/4 (3/(7-3)). He then replaced each of the two new fractions with 2/1 (2/(3-2)) and 3/1 (3/(4-3)), respectively, and concluded that the first fraction, 2/5, was the smaller of the two.
Was young Levik's method valid or was this case a lucky fluke?
Another Method
