Решение:

1. а) $$1\frac{1}{8}:\frac{3}{4} = \frac{9}{8}:\frac{3}{4} = \frac{9}{8} \cdot \frac{4}{3} = \frac{9 \cdot 4}{8 \cdot 3} = \frac{36}{24} = \frac{3}{2} = 1\frac{1}{2}$$
2. б) $$3\frac{3}{5}:2\frac{7}{10} = \frac{18}{5}:\frac{27}{10} = \frac{18}{5} \cdot \frac{10}{27} = \frac{18 \cdot 10}{5 \cdot 27} = \frac{180}{135} = \frac{4}{3} = 1\frac{1}{3}$$
3. в) $$4\frac{3}{7}:\frac{1}{7}-1\frac{5}{6} \cdot 3 = \frac{31}{7}:\frac{1}{7} - \frac{11}{6} \cdot 3 = \frac{31}{7} \cdot \frac{7}{1} - \frac{11}{6} \cdot \frac{3}{1} = \frac{31 \cdot 7}{7 \cdot 1} - \frac{11 \cdot 3}{6 \cdot 1} = 31 - \frac{33}{6} = 31 - \frac{11}{2} = 31 - 5\frac{1}{2} = 25\frac{1}{2}$$

Ответ: а) $$1\frac{1}{2}$$; б) $$1\frac{1}{3}$$; в) $$25\frac{1}{2}$$