Решение:

$$3:3\frac{3}{4}+2\frac{2}{5}\cdot 2\frac{1}{2}-3\frac{5}{6} = 3:\frac{15}{4}+\frac{12}{5}\cdot \frac{5}{2}-\frac{23}{6} = 3\cdot \frac{4}{15} + \frac{12}{1} \cdot \frac{1}{2} - \frac{23}{6} = \frac{4}{5} + 6 - \frac{23}{6} = \frac{4}{5} + \frac{36}{6} - \frac{23}{6} = \frac{4}{5} + \frac{13}{6} = \frac{24}{30} + \frac{65}{30} = \frac{89}{30} = 2\frac{29}{30}$$

Ответ:

$$2\frac{29}{30}$$