Вычислите: $$4\frac{1}{2}-1\frac{1}{5} \cdot (2\frac{2}{3}+3\frac{1}{4})$$. Запишите полностью решение и ответ.

Решение:

1. $$2\frac{2}{3}+3\frac{1}{4} = \frac{8}{3} + \frac{13}{4} = \frac{8 \cdot 4 + 13 \cdot 3}{12} = \frac{32+39}{12} = \frac{71}{12}$$
2. $$1\frac{1}{5} \cdot \frac{71}{12} = \frac{6}{5} \cdot \frac{71}{12} = \frac{1}{5} \cdot \frac{71}{2} = \frac{71}{10} = \frac{71}{5 \cdot 2} = \frac{71}{10} = 7\frac{1}{10}$$
3. $$4\frac{1}{2} - 7\frac{1}{10} = \frac{9}{2} - \frac{71}{10} = \frac{9 \cdot 5 - 71}{10} = \frac{45 - 71}{10} = \frac{-26}{10} = -\frac{13}{5} = -2\frac{3}{5}$$

Ответ: $$-2\frac{3}{5}$$