Вычислите: 1) \(\frac{7}{9}-\frac{5}{6}\cdot\frac{4}{15}\); 2) \(\left(\frac{2}{3}-\frac{4}{9}\right)\cdot\frac{3}{8}\); 3) \(\frac{2}{7}+\frac{3}{8}:\frac{7}{32}\); 4) \(\frac{5}{9}:\left(\frac{7}{9}+\frac{11}{18}\right)\); 5) \(1-\frac{4}{7}:\frac{16}{21}\); 6) \(\frac{5}{12}\cdot\left(\frac{1}{5}+\frac{3}{25}\right)\); 7) \(\frac{9}{14}\cdot\left(\frac{17}{24}-\frac{5}{12}\right)\); 8) \(\frac{24}{49}:\frac{6}{7}+\frac{1}{14}\).

1. \[\frac{7}{9}-\frac{5}{6}\cdot\frac{4}{15}=\frac{7}{9}-\frac{2}{9}=\frac{5}{9}.\]
2. \[\left(\frac{2}{3}-\frac{4}{9}\right)\cdot\frac{3}{8}=\frac{2}{9}\cdot\frac{3}{8}=\frac{1}{12}.\]
3. \[\frac{2}{7}+\frac{3}{8}:\frac{7}{32}=\frac{2}{7}+\frac{3}{8}\cdot\frac{32}{7}=\frac{2}{7}+\frac{12}{7}=2.\]
4. \[\frac{5}{9}:\left(\frac{7}{9}+\frac{11}{18}\right)=\frac{5}{9}:\frac{25}{18}=\frac{5}{9}\cdot\frac{18}{25}=\frac{2}{5}.\]
5. \[1-\frac{4}{7}:\frac{16}{21}=1-\frac{4}{7}\cdot\frac{21}{16}=1-\frac{3}{4}=\frac{1}{4}.\]
6. \[\frac{5}{12}\cdot\left(\frac{1}{5}+\frac{3}{25}\right)=\frac{5}{12}\cdot\frac{8}{25}=\frac{2}{15}.\]
7. \[\frac{9}{14}\cdot\left(\frac{17}{24}-\frac{5}{12}\right)=\frac{9}{14}\cdot\frac{7}{24}=\frac{3}{16}.\]
8. \[\frac{24}{49}:\frac{6}{7}+\frac{1}{14}=\frac{24}{49}\cdot\frac{7}{6}+\frac{1}{14}=\frac{4}{7}+\frac{1}{14}=\frac{9}{14}.\]

Ответ: 1) \(\frac{5}{9}\); 2) \(\frac{1}{12}\); 3) \(2\); 4) \(\frac{2}{5}\); 5) \(\frac{1}{4}\); 6) \(\frac{2}{15}\); 7) \(\frac{3}{16}\); 8) \(\frac{9}{14}\).