5.491 . Найдите значение выражения: a) (61/64 - (7/12 - 5/14)) ⋅ (13/16 + 1/2)); б) (1 - 11/12) ⋅ (3/5 - 5/11); в) 1 - 1/2 + 1/3 - 1/4 + 1/5 - 1/6.

Ответ: a) 61/64, б) -1/55, в) 11/20

1. а) \(\[\frac{61}{64} - (\frac{7}{12} - \frac{5}{14}) \cdot (\frac{13}{16} + \frac{1}{2})\]\)
   • \(\[\frac{7}{12} - \frac{5}{14} = \frac{7 \cdot 7 - 5 \cdot 6}{84} = \frac{49 - 30}{84} = \frac{19}{84}\]\)
   • \(\[\frac{13}{16} + \frac{1}{2} = \frac{13 + 1 \cdot 8}{16} = \frac{13 + 8}{16} = \frac{21}{16}\]\)
   • \(\[\frac{19}{84} \cdot \frac{21}{16} = \frac{19 \cdot 21}{84 \cdot 16} = \frac{19 \cdot 1}{4 \cdot 16} = \frac{19}{64}\]\)
   • \(\[\frac{61}{64} - \frac{19}{64} = \frac{61 - 19}{64} = \frac{42}{64} = \frac{21}{32}\]\)
2. б) \(\[(1 - \frac{11}{12}) \cdot (\frac{3}{5} - \frac{5}{11})\]\)
   • \(\[1 - \frac{11}{12} = \frac{12 - 11}{12} = \frac{1}{12}\]\)
   • \(\[\frac{3}{5} - \frac{5}{11} = \frac{3 \cdot 11 - 5 \cdot 5}{55} = \frac{33 - 25}{55} = \frac{8}{55}\]\)
   • \(\[\frac{1}{12} \cdot \frac{8}{55} = \frac{1 \cdot 8}{12 \cdot 55} = \frac{1 \cdot 2}{3 \cdot 55} = \frac{2}{165}\]\)
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: a) 21/32, б) 2/165, в) 37/60