4. Вычислите: \(\frac{9}{10}\) + \(\frac{4}{9}\) : (2-\(\frac{11}{21}\)) - 1\(\frac{2}{3}\). Запишите полностью решение и ответ.

Решение:

1. \(2 - \frac{11}{21} = \frac{42}{21} - \frac{11}{21} = \frac{31}{21}\)
2. \(\frac{4}{9} : \frac{31}{21} = \frac{4}{9} \times \frac{21}{31} = \frac{4 \times 7}{3 \times 31} = \frac{28}{93}\)
3. \(\frac{9}{10} + \frac{28}{93} = \frac{9 \times 93}{10 \times 93} + \frac{28 \times 10}{93 \times 10} = \frac{837}{930} + \frac{280}{930} = \frac{1117}{930}\)
4. \(\frac{1117}{930} - 1\frac{2}{3} = \frac{1117}{930} - \frac{5}{3} = \frac{1117}{930} - \frac{5 \times 310}{3 \times 310} = \frac{1117}{930} - \frac{1550}{930} = -\frac{433}{930}\)

Ответ: -\(\frac{433}{930}\)