Начинаю решение.
д) Решим пример по действиям:
1) $$2\frac{1}{2}:3\frac{3}{4} = \frac{5}{2}:\frac{15}{4} = \frac{5}{2} \cdot \frac{4}{15} = \frac{5 \cdot 4}{2 \cdot 15} = \frac{20}{30} = \frac{2}{3}$$
2) $$2\frac{1}{2} - 1\frac{1}{3} = \frac{5}{2} - \frac{4}{3} = \frac{5 \cdot 3}{2 \cdot 3} - \frac{4 \cdot 2}{3 \cdot 2} = \frac{15}{6} - \frac{8}{6} = \frac{15-8}{6} = \frac{7}{6}$$
3) $$\frac{7}{6} \cdot 6 = \frac{7 \cdot 6}{6} = \frac{42}{6} = 7$$
4) $$10 - \frac{2}{3} + 7 = 17 - \frac{2}{3} = \frac{17 \cdot 3}{3} - \frac{2}{3} = \frac{51}{3} - \frac{2}{3} = \frac{51-2}{3} = \frac{49}{3} = 16\frac{1}{3}$$
Ответ: $$16\frac{1}{3}$$
e) Решим пример по действиям:
1) $$6\frac{1}{4} \cdot 8 = \frac{25}{4} \cdot 8 = \frac{25 \cdot 8}{4} = \frac{200}{4} = 50$$
2) $$3\frac{2}{3} \cdot 5\frac{1}{2} = \frac{11}{3} \cdot \frac{11}{2} = \frac{11 \cdot 11}{3 \cdot 2} = \frac{121}{6} = 20\frac{1}{6}$$
3) $$2\frac{2}{5} \cdot 4\frac{7}{12} = \frac{12}{5} \cdot \frac{55}{12} = \frac{12 \cdot 55}{5 \cdot 12} = \frac{660}{60} = 11$$
4) $$50 - 20\frac{1}{6} + 11 = 61 - 20\frac{1}{6} = 41 - \frac{1}{6} = \frac{41 \cdot 6}{6} - \frac{1}{6} = \frac{246}{6} - \frac{1}{6} = \frac{246-1}{6} = \frac{245}{6} = 40\frac{5}{6}$$
Ответ: $$40\frac{5}{6}$$