6. Вычислите: \(\frac{5}{4} + \left(-7\frac{3}{4} + \frac{7}{4} \cdot 2\frac{2}{7}\right) : \frac{5}{9}\). Запишите полностью решение.

Решение: \begin{aligned} \frac{5}{4} + \left(-7\frac{3}{4} + \frac{7}{4} \cdot 2\frac{2}{7}\right) : \frac{5}{9} &= \frac{5}{4} + \left(-\frac{31}{4} + \frac{7}{4} \cdot \frac{16}{7}\right) : \frac{5}{9} \\ &= \frac{5}{4} + \left(-\frac{31}{4} + \frac{7 \cdot 16}{4 \cdot 7}\right) : \frac{5}{9} \\ &= \frac{5}{4} + \left(-\frac{31}{4} + \frac{16}{4}\right) : \frac{5}{9} \\ &= \frac{5}{4} + \left(-\frac{31}{4} + \frac{16}{4}\right) : \frac{5}{9} \\ &= \frac{5}{4} + \left(-\frac{15}{4}\right) : \frac{5}{9} \\ &= \frac{5}{4} + \left(-\frac{15}{4}\right) \cdot \frac{9}{5} \\ &= \frac{5}{4} - \frac{15 \cdot 9}{4 \cdot 5} \\ &= \frac{5}{4} - \frac{3 \cdot 9}{4 \cdot 1} \\ &= \frac{5}{4} - \frac{27}{4} \\ &= \frac{5 - 27}{4} \\ &= \frac{-22}{4} \\ &= -\frac{11}{2} \\ &= -5\frac{1}{2} \end{aligned} Ответ: \(-5\frac{1}{2}\)