§5. Обыкновенные дроби — Упражнения — 5.491 — стр. 78

\( \frac{61}{64} - \left( \frac{7}{12} - \frac{5}{14} \right) \cdot \left( \frac{13}{16} + \frac{1}{2} \right) \):

\(= \frac{61}{64} - \left( \frac{49}{84} - \frac{30}{84} \right) \cdot \left( \frac{13}{16} + \frac{8}{16} \right)\)\(\= frac{61}{64} - \frac{19}{84} \cdot \frac{21}{16} = \frac{61}{64} - \frac{19}{64}=\frac{42}{64}=\frac{21}{32}\)

Ответ: \( \frac{21}{32} \).

\( \left( 1 - \frac{11}{17} \right) \cdot \left( \frac{3}{4} - \frac{5}{12} + \frac{11}{18} \right) \):

\(= \frac{6}{17} \cdot \left( \frac{27}{36} - \frac{15}{36} + \frac{22}{36} \right) = \frac{6}{17} \cdot \frac{34}{36} = \frac{6 \cdot 34}{17 \cdot 36} = \frac{204}{612} = \frac{1}{3}.\)

Ответ: \( \frac{1}{3} \).

\( 1 - \frac{1}{2} + \frac{1}{3} - \frac{1}{4} + \frac{1}{5} - \frac{1}{6} \):

\(= \frac{60}{60} - \frac{30}{60} + \frac{20}{60} - \frac{15}{60} + \frac{12}{60} - \frac{10}{60} = \frac{37}{60}.\)

Ответ: \( \frac{37}{60} \).

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

\(= \frac{4}{8} + \frac{6}{12} + \frac{8}{16} + \frac{10}{20} = \frac{1}{2} + \frac{1}{2} + \frac{1}{2} + \frac{1}{2} = 2.\)

Ответ: \( 2 \).