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

a) Найдём значение выражения:

1. \(\frac{7}{12} - \frac{5}{14}\)
\(\frac{7}{12} - \frac{5}{14} = \frac{7 \cdot 7 - 5 \cdot 6}{84} = \frac{49 - 30}{84} = \frac{19}{84}\)
2. \(\frac{13}{16} + \frac{1}{2}\)
\(\frac{13}{16} + \frac{1}{2} = \frac{13 + 1 \cdot 8}{16} = \frac{13 + 8}{16} = \frac{21}{16}\)
3. \(\frac{19}{84} \cdot \frac{21}{16}\)
\(\frac{19}{84} \cdot \frac{21}{16} = \frac{19 \cdot 21}{84 \cdot 16} = \frac{19 \cdot 1}{4 \cdot 16} = \frac{19}{64}\)
4. \(\frac{61}{64} - \frac{19}{64}\)
\(\frac{61}{64} - \frac{19}{64} = \frac{61 - 19}{64} = \frac{42}{64} = \frac{21}{32}\)

б) Найдём значение выражения:

1. \(1 - \frac{11}{17}\)
\(1 - \frac{11}{17} = \frac{17 - 11}{17} = \frac{6}{17}\)
2. \(\frac{3}{4} - \frac{5}{12} + \frac{11}{18}\)
\(\frac{3}{4} - \frac{5}{12} + \frac{11}{18} = \frac{3 \cdot 9 - 5 \cdot 3 + 11 \cdot 2}{36} = \frac{27 - 15 + 22}{36} = \frac{34}{36} = \frac{17}{18}\)
3. \(\frac{6}{17} \cdot \frac{17}{18}\)
\(\frac{6}{17} \cdot \frac{17}{18} = \frac{6 \cdot 17}{17 \cdot 18} = \frac{6}{18} = \frac{1}{3}\)

Ответ: a) \(\frac{21}{32}\); б) \(\frac{1}{3}\)