Выполните действия: a) \(\frac{3}{4} : 5\frac{1}{6} + 2\frac{1}{2} \cdot \frac{2}{5} - 1 : 1\frac{1}{6}\); б) \(2\frac{3}{4} : (1\frac{1}{2} - \frac{2}{5}) + (\frac{3}{4} + \frac{5}{6}) : 3\frac{1}{6}\); в) \((\frac{2}{15} + \frac{7}{12}) \cdot \frac{30}{43} - 2\frac{1}{2} \cdot \frac{5}{32}\)

Решение:

1. а) \(\frac{3}{4} : 5\frac{1}{6} + 2\frac{1}{2} \cdot \frac{2}{5} - 1 : 1\frac{1}{6}\)
   \(= \frac{3}{4} : \frac{31}{6} + \frac{5}{2} \cdot \frac{2}{5} - 1 : \frac{7}{6}\)
   \(= \frac{3}{4} \cdot \frac{6}{31} + 1 - \frac{6}{7}\)
   \(= \frac{18}{124} + 1 - \frac{6}{7}\)
   \(= \frac{9}{62} + 1 - \frac{6}{7}\)
   \(= \frac{9 \cdot 7 + 62 \cdot 7 - 6 \cdot 62}{434}\)
   \(= \frac{63 + 434 - 372}{434} = \frac{125}{434}\)
2. б) \(2\frac{3}{4} : (1\frac{1}{2} - \frac{2}{5}) + (\frac{3}{4} + \frac{5}{6}) : 3\frac{1}{6}\)
   \(= \frac{11}{4} : (\frac{3}{2} - \frac{2}{5}) + (\frac{9}{12} + \frac{10}{12}) : \frac{19}{6}\)
   \(= \frac{11}{4} : (\frac{15-4}{10}) + \frac{19}{12} : \frac{19}{6}\)
   \(= \frac{11}{4} : \frac{11}{10} + \frac{19}{12} \cdot \frac{6}{19}\)
   \(= \frac{11}{4} \cdot \frac{10}{11} + \frac{6}{12}\)
   \(= \frac{10}{4} + \frac{1}{2}\)
   \(= \frac{5}{2} + \frac{1}{2} = \frac{6}{2} = 3\)
3. в) \((\frac{2}{15} + \frac{7}{12}) \cdot \frac{30}{43} - 2\frac{1}{2} \cdot \frac{5}{32}\)
   \(= (\frac{8}{60} + \frac{35}{60}) \cdot \frac{30}{43} - \frac{5}{2} \cdot \frac{5}{32}\)
   \(= \frac{43}{60} \cdot \frac{30}{43} - \frac{25}{64}\)
   \(= \frac{1}{2} - \frac{25}{64}\)
   \(= \frac{32}{64} - \frac{25}{64} = \frac{7}{64}\)

Ответ: а) \(\frac{125}{434}\); б) 3; в) \(\frac{7}{64}\)