635. Выполните действия: a) \frac{3}{4} : \frac{5}{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 : 2\frac{1}{2} \cdot \frac{5}{32}; г) (3\frac{1}{2} : 4\frac{2}{3} + 4\frac{2}{3} : 3\frac{1}{2}) \cdot 4\frac{4}{5}; д) (11\frac{5}{11} - 8\frac{21}{22}) : 1\frac{2}{3}; e) ((1\frac{1}{2})^3 - \frac{3}{4}) : \frac{7}{8}.

Ответ:

a) \(\frac{3}{4} : \frac{5}{6} + 2\frac{1}{2} \cdot \frac{2}{5} - 1 : 1\frac{1}{6} = \frac{3}{4} \cdot \frac{6}{5} + \frac{5}{2} \cdot \frac{2}{5} - 1 : \frac{7}{6} = \frac{18}{20} + \frac{10}{10} - \frac{6}{7} = \frac{9}{10} + 1 - \frac{6}{7} = \frac{9}{10} + \frac{10}{10} - \frac{6}{7} = \frac{19}{10} - \frac{6}{7} = \frac{19 \cdot 7 - 6 \cdot 10}{70} = \frac{133 - 60}{70} = \frac{73}{70} = 1\frac{3}{70}\)

б) \(2\frac{3}{4} : (1\frac{1}{2} - \frac{2}{5}) + (\frac{3}{4} + \frac{5}{6}) : 3\frac{1}{6} = \frac{11}{4} : (\frac{3}{2} - \frac{2}{5}) + (\frac{3}{4} + \frac{5}{6}) : \frac{19}{6} = \frac{11}{4} : (\frac{15 - 4}{10}) + (\frac{9 + 10}{12}) : \frac{19}{6} = \frac{11}{4} : \frac{11}{10} + \frac{19}{12} : \frac{19}{6} = \frac{11}{4} \cdot \frac{10}{11} + \frac{19}{12} \cdot \frac{6}{19} = \frac{10}{4} + \frac{6}{12} = \frac{5}{2} + \frac{1}{2} = \frac{6}{2} = 3\)

в) \((\frac{2}{15} + \frac{7}{12}) \cdot \frac{30}{43} - 2 : 2\frac{1}{2} \cdot \frac{5}{32} = (\frac{8 + 35}{60}) \cdot \frac{30}{43} - 2 : \frac{5}{2} \cdot \frac{5}{32} = \frac{43}{60} \cdot \frac{30}{43} - 2 \cdot \frac{2}{5} \cdot \frac{5}{32} = \frac{1}{2} - \frac{4}{5} \cdot \frac{5}{32} = \frac{1}{2} - \frac{20}{160} = \frac{1}{2} - \frac{1}{8} = \frac{4 - 1}{8} = \frac{3}{8}\)

г) \((3\frac{1}{2} : 4\frac{2}{3} + 4\frac{2}{3} : 3\frac{1}{2}) \cdot 4\frac{4}{5} = (\frac{7}{2} : \frac{14}{3} + \frac{14}{3} : \frac{7}{2}) \cdot \frac{24}{5} = (\frac{7}{2} \cdot \frac{3}{14} + \frac{14}{3} \cdot \frac{2}{7}) \cdot \frac{24}{5} = (\frac{3}{4} + \frac{4}{3}) \cdot \frac{24}{5} = (\frac{9 + 16}{12}) \cdot \frac{24}{5} = \frac{25}{12} \cdot \frac{24}{5} = \frac{25 \cdot 24}{12 \cdot 5} = \frac{5 \cdot 2}{1} = 10\)

д) \((11\frac{5}{11} - 8\frac{21}{22}) : 1\frac{2}{3} = (\frac{126}{11} - \frac{197}{22}) : \frac{5}{3} = (\frac{252 - 197}{22}) : \frac{5}{3} = \frac{55}{22} : \frac{5}{3} = \frac{5}{2} \cdot \frac{3}{5} = \frac{3}{2} = 1\frac{1}{2}\)

e) \(((1\frac{1}{2})^3 - \frac{3}{4}) : \frac{7}{8} = ((\frac{3}{2})^3 - \frac{3}{4}) : \frac{7}{8} = (\frac{27}{8} - \frac{3}{4}) : \frac{7}{8} = (\frac{27 - 6}{8}) : \frac{7}{8} = \frac{21}{8} : \frac{7}{8} = \frac{21}{8} \cdot \frac{8}{7} = \frac{21}{7} = 3\)

Ответ: