8. Вычислите наиболее удобным способом.

Решение:

1. \( \frac{1}{6} + \frac{5}{9} + \frac{5}{6} + \frac{4}{9} = (\frac{1}{6} + \frac{5}{6}) + (\frac{5}{9} + \frac{4}{9}) = \frac{6}{6} + \frac{9}{9} = 1 + 1 = 2 \)
2. \( \frac{2}{17} + \frac{3}{8} + \frac{5}{17} + \frac{10}{8} = (\frac{2}{17} + \frac{5}{17}) + (\frac{3}{8} + \frac{10}{8}) = \frac{7}{17} + \frac{13}{8} = \frac{56}{136} + \frac{221}{136} = \frac{277}{136} \)
3. \( \frac{1}{12} + \frac{1}{16} + \frac{5}{12} + \frac{7}{16} = (\frac{1}{12} + \frac{5}{12}) + (\frac{1}{16} + \frac{7}{16}) = \frac{6}{12} + \frac{8}{16} = \frac{1}{2} + \frac{1}{2} = 1 \)
4. \( \frac{3}{17} + \frac{4}{5} + \frac{1}{15} + \frac{14}{17} = (\frac{3}{17} + \frac{14}{17}) + (\frac{4}{5} + \frac{1}{15}) = \frac{17}{17} + (\frac{12}{15} + \frac{1}{15}) = 1 + \frac{13}{15} = 1\frac{13}{15} \)

Ответ: \( 2, \frac{277}{136}, 1, 1\frac{13}{15} \).