I. Вычислить: 1) \((17-1\frac{5}{9}:\frac{7}{24}):\frac{20}{27}\); 2) \(1\frac{31}{35}:(2-\frac{8}{9}:1\frac{19}{45})\); 3) \(4\frac{1}{3}\cdot5+2,4:(-0,1)-\frac{14}{15}:1\frac{2}{5}\); 4) \(3\frac{1}{7}\cdot(-4)-1,8:(-0,1)+\frac{20}{27}:1\frac{2}{3}\).

1) \(\left(17-1\frac{5}{9}:\frac{7}{24}\right):\frac{20}{27}\)

\(1\frac{5}{9}=\frac{14}{9}\), поэтому \(\frac{14}{9}:\frac{7}{24}=\frac{14}{9}\cdot\frac{24}{7}=\frac{16}{3}\).

\(17-\frac{16}{3}=\frac{35}{3}\).

\(\frac{35}{3}:\frac{20}{27}=\frac{35}{3}\cdot\frac{27}{20}=\frac{63}{4}=15\frac{3}{4}\).

2) \(1\frac{31}{35}:\left(2-\frac{8}{9}:1\frac{19}{45}\right)\)

\(1\frac{31}{35}=\frac{66}{35}\), \(1\frac{19}{45}=\frac{64}{45}\).

\(\frac{8}{9}:\frac{64}{45}=\frac{8}{9}\cdot\frac{45}{64}=\frac{5}{8}\).

\(2-\frac{5}{8}=\frac{11}{8}\).

\(\frac{66}{35}:\frac{11}{8}=\frac{66}{35}\cdot\frac{8}{11}=\frac{48}{35}=1\frac{13}{35}\).

3) \(4\frac{1}{3}\cdot5+2,4:(-0,1)-\frac{14}{15}:1\frac{2}{5}\)

\(4\frac{1}{3}\cdot5=\frac{13}{3}\cdot5=\frac{65}{3}\), \(2,4:(-0,1)=-24\), \(\frac{14}{15}:\frac{7}{5}=\frac{2}{3}\).

\(\frac{65}{3}-24-\frac{2}{3}=21-24=-3\).

4) \(3\frac{1}{7}\cdot(-4)-1,8:(-0,1)+\frac{20}{27}:1\frac{2}{3}\)

\(3\frac{1}{7}\cdot(-4)=-\frac{22}{7}\cdot4=-\frac{88}{7}\), \(1,8:(-0,1)=-18\), поэтому \(-1,8:(-0,1)=18\).

\(\frac{20}{27}:\frac{5}{3}=\frac{4}{9}\).

\(-\frac{88}{7}+18+\frac{4}{9}=\frac{350}{63}=\frac{50}{9}=5\frac{5}{9}\).

Ответ: 1) \(15\frac{3}{4}\); 2) \(1\frac{13}{35}\); 3) \(-3\); 4) \(5\frac{5}{9}\).