2) 11 - 10

1. Convert mixed numbers to improper fractions: $$11\frac{5}{18} = \frac{203}{18}$$, $$10\frac{31}{54} = \frac{571}{54}$$.
2. Find a common denominator (54): $$\frac{203}{18} = \frac{203 \times 3}{18 \times 3} = \frac{609}{54}$$.
3. Subtract the fractions: $$\frac{609}{54} - \frac{571}{54} = \frac{38}{54} = \frac{19}{27}$$.