Which is greater 31 out of 46 or 4 out of 13?

Answer 1

31/46 > 4/13

Besides just obtaining floating-point approximations with a calculator, one can simply refactor the two fractions into common denominators (usually based on the least-common multiple). In this case, though, 46 and 13 don't share common factors, so we'll take the simple approach: multiply them together to get 598.

And with that, we can prove that

31/46 (403/598) > 4/13 (184/598)