5.491 Найдите значение выражения: a) \(\frac{61}{64} - (\frac{7}{12} - \frac{5}{14}) \cdot (\frac{13}{16} + \frac{1}{2})\); в) \(1 - \frac{1}{2} + \frac{1}{3} - \frac{1}{4} + \frac{1}{5} - \frac{1}{6}\);

a) \(\frac{61}{64} - (\frac{7}{12} - \frac{5}{14}) \cdot (\frac{13}{16} + \frac{1}{2})\) = \(\frac{61}{64} - (\frac{7\cdot7 - 5\cdot6}{84}) \cdot (\frac{13 + 1\cdot 8}{16})\) = \(\frac{61}{64} - (\frac{49 - 30}{84}) \cdot (\frac{13 + 8}{16})\) = \(\frac{61}{64} - \frac{19}{84} \cdot \frac{21}{16}\) = \(\frac{61}{64} - \frac{19}{4\cdot 21} \cdot \frac{21}{16}\) = \(\frac{61}{64} - \frac{19}{4} \cdot \frac{1}{16}\) = \(\frac{61}{64} - \frac{19}{64}\) = \(\frac{61 - 19}{64}\) = \(\frac{42}{64}\) = \(\frac{21}{32}\)

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

Ответ: a) \(\frac{21}{32}\); в) \(\frac{37}{60}\)