8. Вычислить: 1) (3 1/5 · 1 1/24 + 6 · 5/12) · 4/21 − 1 5/6; 2) (2 1/4 · 1/18)(1 2/15 · 2 1/17) · 5/24 · 6/25; 3) (5 5/14 − 4 · 17/42) · 1 1/5; 4) (3 1/6 + 4 5/6 · 11/29) · 1/15.

1) \(\left(3\frac{1}{5}\cdot1\frac{1}{24}+6\cdot\frac{5}{12}\right)\cdot\frac{4}{21}-1\frac{5}{6}\)

\(=\left(\frac{16}{5}\cdot\frac{25}{24}+\frac{5}{2}\right)\cdot\frac{4}{21}-\frac{11}{6}\)

\(=\left(\frac{10}{3}+\frac{5}{2}\right)\cdot\frac{4}{21}-\frac{11}{6}=\frac{35}{6}\cdot\frac{4}{21}-\frac{11}{6}\)

\(=\frac{10}{9}-\frac{11}{6}=\frac{20}{18}-\frac{33}{18}=-\frac{13}{18}\).

Ответ: \(-\frac{13}{18}\).

2) \(\left(2\frac{1}{4}\cdot\frac{1}{18}\right)\left(1\frac{2}{15}\cdot2\frac{1}{17}\right)\cdot\frac{5}{24}\cdot\frac{6}{25}\)

\(=\left(\frac{9}{4}\cdot\frac{1}{18}\right)\left(\frac{17}{15}\cdot\frac{35}{17}\right)\cdot\frac{5}{24}\cdot\frac{6}{25}\)

\(=\frac{1}{8}\cdot\frac{7}{3}\cdot\frac{5}{24}\cdot\frac{6}{25}=\frac{7}{240}\).

Ответ: \(\frac{7}{240}\).

3) \(\left(5\frac{5}{14}-4\cdot\frac{17}{42}\right)\cdot1\frac{1}{5}\)

\(=\left(\frac{75}{14}-\frac{68}{42}\right)\cdot\frac{6}{5}=\left(\frac{225}{42}-\frac{68}{42}\right)\cdot\frac{6}{5}\)

\(=\frac{157}{42}\cdot\frac{6}{5}=\frac{157}{35}\).

Ответ: \(\frac{157}{35}=4\frac{17}{35}\).

4) \(\left(3\frac{1}{6}+4\frac{5}{6}\cdot\frac{11}{29}\right)\cdot1\frac{1}{15}\)

\(=\left(\frac{19}{6}+\frac{29}{6}\cdot\frac{11}{29}\right)\cdot\frac{16}{15}\)

\(=\left(\frac{19}{6}+\frac{11}{6}\right)\cdot\frac{16}{15}=5\cdot\frac{16}{15}=\frac{16}{3}=5\frac{1}{3}\).

Ответ: \(\frac{16}{3}=5\frac{1}{3}\).