Вычислите: $$(3 - 9\frac{3}{8} \cdot \frac{4}{5}) : (2\frac{2}{5} - 2\frac{1}{8})$$

Решение:

1. $$9\frac{3}{8} = \frac{9 \cdot 8 + 3}{8} = \frac{75}{8}$$
2. $$2\frac{2}{5} = \frac{2 \cdot 5 + 2}{5} = \frac{12}{5}$$
3. $$2\frac{1}{8} = \frac{2 \cdot 8 + 1}{8} = \frac{17}{8}$$
4. $$\frac{75}{8} \cdot \frac{4}{5} = \frac{75 \cdot 4}{8 \cdot 5} = \frac{300}{40} = \frac{30}{4} = \frac{15}{2} = 7\frac{1}{2}$$
5. $$3 - 7\frac{1}{2} = 3 - \frac{15}{2} = \frac{3 \cdot 2}{2} - \frac{15}{2} = \frac{6}{2} - \frac{15}{2} = \frac{6 - 15}{2} = -\frac{9}{2} = -4\frac{1}{2}$$
6. $$\frac{12}{5} - \frac{17}{8} = \frac{12 \cdot 8}{5 \cdot 8} - \frac{17 \cdot 5}{8 \cdot 5} = \frac{96}{40} - \frac{85}{40} = \frac{96 - 85}{40} = \frac{11}{40}$$
7. $$-4\frac{1}{2} : \frac{11}{40} = -\frac{9}{2} : \frac{11}{40} = -\frac{9}{2} \cdot \frac{40}{11} = -\frac{9 \cdot 40}{2 \cdot 11} = -\frac{360}{22} = -\frac{180}{11} = -16\frac{4}{11}$$

Ответ: $$-16\frac{4}{11}$$