Which is greater, $\frac{11}{12}$ or $\frac{12}{13}$?

Explanation

1. 01

   Cross-multiply: $12 \times 12 = 144$ and $11 \times 13 = 143$.

2. 02

   $144 > 143$, so $\frac{12}{13} > \frac{11}{12}$: each falls short of 1 by $\frac{1}{13}$ and $\frac{1}{12}$.