а) \(\frac{61}{64} - (\frac{7}{12} - \frac{5}{14}) \cdot (\frac{13}{16} + \frac{1}{2});\) б) \((1 - \frac{11}{17}) \cdot (\frac{3}{4} - \frac{5}{12} + \frac{11}{18});\) в) \(1 - \frac{1}{2} + \frac{1}{3} - \frac{1}{4} + \frac{1}{5} - \frac{1}{6};\) г) \(\frac{1}{8} + \frac{3}{8} + \frac{1}{12} + \frac{5}{12} + \frac{1}{16} + \frac{7}{16} + \frac{1}{20} + \frac{9}{20}.\)

Решим данные выражения:

1. а) \(\frac{61}{64} - (\frac{7}{12} - \frac{5}{14}) \cdot (\frac{13}{16} + \frac{1}{2});\)

   1) \(\frac{7}{12} - \frac{5}{14} = \frac{7 \cdot 14 - 5 \cdot 12}{12 \cdot 14} = \frac{98 - 60}{168} = \frac{38}{168} = \frac{19}{84};\)

   2) \(\frac{13}{16} + \frac{1}{2} = \frac{13 + 1 \cdot 8}{16} = \frac{13 + 8}{16} = \frac{21}{16};\)

   3) \(\frac{19}{84} \cdot \frac{21}{16} = \frac{19 \cdot 21}{84 \cdot 16} = \frac{19 \cdot 1}{4 \cdot 16} = \frac{19}{64};\)

   4) \(\frac{61}{64} - \frac{19}{64} = \frac{61 - 19}{64} = \frac{42}{64} = \frac{21}{32}.\)

   Ответ: \(\frac{21}{32}\)

2. б) \((1 - \frac{11}{17}) \cdot (\frac{3}{4} - \frac{5}{12} + \frac{11}{18});\)

   1) \(1 - \frac{11}{17} = \frac{17 - 11}{17} = \frac{6}{17};\)

   2) \(\frac{3}{4} - \frac{5}{12} + \frac{11}{18} = \frac{3 \cdot 9 - 5 \cdot 3 + 11 \cdot 2}{36} = \frac{27 - 15 + 22}{36} = \frac{34}{36} = \frac{17}{18};\)

   3) \(\frac{6}{17} \cdot \frac{17}{18} = \frac{6 \cdot 17}{17 \cdot 18} = \frac{6}{18} = \frac{1}{3}.\)

   Ответ: \(\frac{1}{3}\)

3. в) \(1 - \frac{1}{2} + \frac{1}{3} - \frac{1}{4} + \frac{1}{5} - \frac{1}{6};\)

   \(1 - \frac{1}{2} + \frac{1}{3} - \frac{1}{4} + \frac{1}{5} - \frac{1}{6} = \frac{60 - 30 + 20 - 15 + 12 - 10}{60} = \frac{37}{60}.\)

   Ответ: \(\frac{37}{60}\)

4. г) \(\frac{1}{8} + \frac{3}{8} + \frac{1}{12} + \frac{5}{12} + \frac{1}{16} + \frac{7}{16} + \frac{1}{20} + \frac{9}{20}.\)

   1) \(\frac{1}{8} + \frac{3}{8} = \frac{4}{8} = \frac{1}{2};\)

   2) \(\frac{1}{12} + \frac{5}{12} = \frac{6}{12} = \frac{1}{2};\)

   3) \(\frac{1}{16} + \frac{7}{16} = \frac{8}{16} = \frac{1}{2};\)

   4) \(\frac{1}{20} + \frac{9}{20} = \frac{10}{20} = \frac{1}{2};\)

   5) \(\frac{1}{2} + \frac{1}{2} + \frac{1}{2} + \frac{1}{2} = \frac{4}{2} = 2.\)

   Ответ: 2