5. Вычислите: \(\frac{9}{22}\) - \(\frac{4}{9}\) : (3-\(\frac{8}{15}\)) + \(\frac{8}{11}\). Запишите полностью решение и ответ.

Решение:

1. \(3 - \frac{8}{15} = \frac{45}{15} - \frac{8}{15} = \frac{37}{15}\)
2. \(\frac{4}{9} : \frac{37}{15} = \frac{4}{9} \times \frac{15}{37} = \frac{4 \times 5}{3 \times 37} = \frac{20}{111}\)
3. \(\frac{9}{22} - \frac{20}{111} = \frac{9 \times 111}{22 \times 111} - \frac{20 \times 22}{111 \times 22} = \frac{999}{2442} - \frac{440}{2442} = \frac{559}{2442}\)
4. \(\frac{559}{2442} + \frac{8}{11} = \frac{559}{2442} + \frac{8 \times 222}{11 \times 222} = \frac{559}{2442} + \frac{1776}{2442} = \frac{2335}{2442}\)

Ответ: \(\frac{2335}{2442}\)