511:1=

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

Ответ: $$1\frac{1}{3}$$