5.491. Найдите значение выражения: a) \( \frac{61}{64} - (\frac{7}{12} - \frac{5}{14}) \cdot (\frac{13}{16} + \frac{1}{2}) \) b) \( (1 - \frac{11}{17}) \cdot (\frac{3}{4} - \frac{5}{12} + \frac{11}{18}) \) c) \( 1 - \frac{1}{2} + \frac{1}{3} - \frac{1}{4} + \frac{1}{5} - \frac{1}{6} \) d) \( \frac{1}{8} + \frac{3}{8} + \frac{1}{12} + \frac{5}{12} + \frac{1}{16} + \frac{7}{16} + \frac{1}{20} + \frac{9}{20} \)

а) \( \frac{61}{64} - (\frac{7}{12} - \frac{5}{14}) \cdot (\frac{13}{16} + \frac{1}{2}) = \frac{61}{64} - (\frac{49}{84} - \frac{30}{84}) \cdot (\frac{13}{16} + \frac{8}{16}) = \frac{61}{64} - \frac{19}{84} \cdot \frac{21}{16} = \frac{61}{64} - \frac{19 \cdot 21}{84 \cdot 16} = \frac{61}{64} - \frac{399}{1344} = \frac{1281}{1344} - \frac{399}{1344} = \frac{882}{1344} = \frac{147}{224} = \frac{21}{32} \) b) \( (1 - \frac{11}{17}) \cdot (\frac{3}{4} - \frac{5}{12} + \frac{11}{18}) = \frac{6}{17} \cdot (\frac{27}{36} - \frac{15}{36} + \frac{22}{36} ) = \frac{6}{17} \cdot (\frac{27 - 15 + 22}{36}) = \frac{6}{17} \cdot \frac{34}{36} = \frac{6}{17} \cdot \frac{17}{18} = \frac{6 \cdot 17}{17 \cdot 18} = \frac{1}{3} \) c) \( 1 - \frac{1}{2} + \frac{1}{3} - \frac{1}{4} + \frac{1}{5} - \frac{1}{6} = \frac{60 - 30 + 20 - 15 + 12 - 10}{60} = \frac{37}{60} \) d) \( \frac{1}{8} + \frac{3}{8} + \frac{1}{12} + \frac{5}{12} + \frac{1}{16} + \frac{7}{16} + \frac{1}{20} + \frac{9}{20} = (\frac{1}{8} + \frac{3}{8}) + (\frac{1}{12} + \frac{5}{12}) + (\frac{1}{16} + \frac{7}{16}) + (\frac{1}{20} + \frac{9}{20}) = \frac{4}{8} + \frac{6}{12} + \frac{8}{16} + \frac{10}{20} = \frac{1}{2} + \frac{1}{2} + \frac{1}{2} + \frac{1}{2} = 2 \) Ответ: а) \( \frac{21}{32} \), б) \( \frac{1}{3} \), в) \( \frac{37}{60} \), г) \( 2 \)