6 Найдите значение выражения: ((\(\frac{2}{3}\) + \(\frac{4}{5}\)) \(\cdot\) \(\frac{10}{11}\)) + (2\(\frac{6}{7}\) : \(\frac{2}{5}\)) - 6.

Решение:

1. \(\frac{2}{3} + \frac{4}{5} = \frac{2 \cdot 5 + 4 \cdot 3}{15} = \frac{10 + 12}{15} = \frac{22}{15}\)
2. \(\frac{22}{15} \cdot \frac{10}{11} = \frac{22 \cdot 10}{15 \cdot 11} = \frac{220}{165} = \frac{4}{3}\)
3. \(2\frac{6}{7} = \frac{2 \cdot 7 + 6}{7} = \frac{14+6}{7} = \frac{20}{7}\)
4. \(\frac{20}{7} : \frac{2}{5} = \frac{20}{7} \cdot \frac{5}{2} = \frac{20 \cdot 5}{7 \cdot 2} = \frac{100}{14} = \frac{50}{7}\)
5. \(\frac{4}{3} + \frac{50}{7} = \frac{4 \cdot 7 + 50 \cdot 3}{21} = \frac{28 + 150}{21} = \frac{178}{21}\)
6. \(\frac{178}{21} - 6 = \frac{178 - 6 \cdot 21}{21} = \frac{178 - 126}{21} = \frac{52}{21} = 2\frac{10}{21}\)

Ответ: \(2\frac{10}{21}\)