8. Вычислите: \frac{17}{12}: 3\frac{2}{5} - \frac{2}{5} \cdot (2 - 1\frac{1}{12}). Запишите полностью решение и ответ.

Решение:

1) $$3\frac{2}{5} = \frac{3 \cdot 5 + 2}{5} = \frac{17}{5}$$

2) $$1\frac{1}{12} = \frac{1 \cdot 12 + 1}{12} = \frac{13}{12}$$

3) $$2 - 1\frac{1}{12} = 2 - \frac{13}{12} = \frac{24}{12} - \frac{13}{12} = \frac{11}{12}$$

4) $$\frac{2}{5} \cdot \frac{11}{12} = \frac{2 \cdot 11}{5 \cdot 12} = \frac{22}{60} = \frac{11}{30}$$

5) $$\frac{17}{12} : \frac{17}{5} = \frac{17}{12} \cdot \frac{5}{17} = \frac{17 \cdot 5}{12 \cdot 17} = \frac{5}{12}$$

6) $$\frac{5}{12} - \frac{11}{30} = \frac{5 \cdot 5}{12 \cdot 5} - \frac{11 \cdot 2}{30 \cdot 2} = \frac{25}{60} - \frac{22}{60} = \frac{3}{60} = \frac{1}{20}$$

Ответ: $$\frac{1}{20}$$