$$1\frac{51}{93} \div 1\frac{5}{31} = \frac{144}{93} \div \frac{36}{31} = \frac{144}{93} \cdot \frac{31}{36} = \frac{144 \cdot 31}{93 \cdot 36} = \frac{4 \cdot 1}{3 \cdot 1} = \frac{4}{3} = 1\frac{1}{3}$$
Ответ: $$1\frac{1}{3}$$.