5.491 Найдите значение выражения: а) \(\frac{61}{64} - (\frac{7}{12} - \frac{5}{14}) \cdot (\frac{13}{16} + \frac{1}{2})\); б) \((1 - \frac{11}{17}) \cdot (\frac{3}{4} - \frac{5}{12} + \frac{11}{18})\)

Пошаговое решение:

1. Шаг 1 (а):
   \((\frac{7}{12} - \frac{5}{14}) = \frac{49 - 30}{84} = \frac{19}{84}\)
   \((\frac{13}{16} + \frac{1}{2}) = \frac{13 + 8}{16} = \frac{21}{16}\)
   \(\frac{19}{84} \cdot \frac{21}{16} = \frac{19 \cdot 1}{4 \cdot 16} = \frac{19}{64}\)
   \(\frac{61}{64} - \frac{19}{64} = \frac{42}{64} = \frac{21}{32}\)
2. Шаг 2 (б):
   \((1 - \frac{11}{17}) = \frac{6}{17}\)
   \((\frac{3}{4} - \frac{5}{12} + \frac{11}{18}) = \frac{27 - 15 + 22}{36} = \frac{34}{36} = \frac{17}{18}\)
   \(\frac{6}{17} \cdot \frac{17}{18} = \frac{6}{18} = \frac{1}{3}\)

Ответ: а) \(\frac{21}{32}\), б) \(\frac{1}{3}\)