4. Выполните действия: \(\left(10-1\frac{17}{27}:\frac{22}{45}\right):\frac{4}{9}\).

1) \(1\frac{17}{27}:\frac{22}{45}=\frac{1\cdot 27+17}{27}:\frac{22}{45}=\frac{44}{27}:\frac{22}{45}=\frac{44}{27}\cdot \frac{45}{22}=\frac{44 \cdot 45}{27 \cdot 22}=\frac{2 \cdot 5}{3 \cdot 1}=\frac{10}{3}=3\frac{1}{3}\)

2) \(10-3\frac{1}{3}=10-\frac{10}{3}=\frac{10}{1}-\frac{10}{3}=\frac{10 \cdot 3}{1 \cdot 3}-\frac{10}{3}=\frac{30}{3}-\frac{10}{3}=\frac{30-10}{3}=\frac{20}{3}=6\frac{2}{3}\)

3) \(6\frac{2}{3}:\frac{4}{9}=\frac{6\cdot 3+2}{3}:\frac{4}{9}=\frac{20}{3}:\frac{4}{9}=\frac{20}{3}\cdot \frac{9}{4}=\frac{20 \cdot 9}{3 \cdot 4}=\frac{5 \cdot 3}{1 \cdot 1}=15\)

Ответ: 15.