4. Выполните действия: (10-\(\frac{17}{27}\): \(\frac{22}{45}\)): \(\frac{4}{9}\).

Решение:

1) 10 - \(\frac{17}{27}\) = \(\frac{10}{1}\) - \(\frac{17}{27}\) = \(\frac{10*27}{1*27}\) - \(\frac{17}{27}\) = \(\frac{270}{27}\) - \(\frac{17}{27}\) = \(\frac{270-17}{27}\) = \(\frac{253}{27}\)

2) \(\frac{253}{27}\) : \(\frac{22}{45}\) = \(\frac{253}{27}\) * \(\frac{45}{22}\) = \(\frac{253 * 45}{27 * 22}\) = \(\frac{23 * 5}{3 * 2}\) = \(\frac{115}{6}\)

3) \(\frac{115}{6}\) : \(\frac{4}{9}\) = \(\frac{115}{6}\) * \(\frac{9}{4}\) = \(\frac{115 * 9}{6 * 4}\) = \(\frac{115 * 3}{2 * 4}\) = \(\frac{345}{8}\) = 43\(\frac{1}{8}\)

Ответ: 43\(\frac{1}{8}\)