е) $$6\frac{1}{4}\cdot8-3\frac{2}{3}\cdot5\frac{1}{2}+2\frac{2}{5}\cdot4\frac{7}{12}$$

Выполним вычисления по действиям:

1. $$6\frac{1}{4}\cdot8=\frac{25}{4}\cdot8=\frac{25\cdot8}{4}=25\cdot2=50$$
2. $$3\frac{2}{3}\cdot5\frac{1}{2}=\frac{11}{3}\cdot\frac{11}{2}=\frac{11\cdot11}{3\cdot2}=\frac{121}{6}=20\frac{1}{6}$$
3. $$2\frac{2}{5}\cdot4\frac{7}{12}=\frac{12}{5}\cdot\frac{55}{12}=\frac{12\cdot55}{5\cdot12}=\frac{55}{5}=11$$
4. $$50-20\frac{1}{6}+11=61-20\frac{1}{6}=41-\frac{1}{6}=\frac{41 \cdot 6}{6}-\frac{1}{6}=\frac{246}{6}-\frac{1}{6}=\frac{245}{6}=40\frac{5}{6}$$

Ответ: $$40\frac{5}{6}$$