Вычислите:
а) $(2\frac{5}{6} + 1\frac{7}{9}) * 3\frac{3}{5} + (2\frac{5}{6} - 1\frac{7}{9}) * (-2\frac{16}{19})$;
б) $(2\frac{2}{15} + 2\frac{7}{10}) : 1\frac{2}{27} - (2\frac{7}{10} - 2\frac{2}{15}) : 2\frac{3}{7}$;
в) $(1\frac{1}{12} + 1\frac{5}{8}) * (-1\frac{11}{13}) - (1\frac{1}{12} - 1\frac{5}{8}) * 1\frac{7}{26}$;
г) $(1\frac{2}{9} + 1\frac{7}{12}) : 1\frac{47}{54} + (1\frac{2}{9} - 1\frac{7}{12}) * 5\frac{7}{13}$.

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Решение

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Решение а

$(2\frac{5}{6} + 1\frac{7}{9}) * 3\frac{3}{5} + (2\frac{5}{6} - 1\frac{7}{9}) * (-2\frac{16}{19}) = (2\frac{15}{18} + 1\frac{14}{18}) * \frac{18}{5} + (2\frac{15}{18} - 1\frac{14}{18}) * (-\frac{54}{19}) = 3\frac{29}{18} * \frac{18}{5} + 1\frac{1}{18} * (-\frac{54}{19}) = \frac{83}{18} * \frac{18}{5} + \frac{19}{18} * (-\frac{54}{19}) = \frac{83}{1} * \frac{1}{5} + \frac{1}{1} * (-\frac{3}{1}) = \frac{83}{5} - 3 = 16\frac{3}{5} - 3 = 13\frac{3}{5}$

Решение б

$(2\frac{2}{15} + 2\frac{7}{10}) : 1\frac{2}{27} - (2\frac{7}{10} - 2\frac{2}{15}) : 2\frac{3}{7} = (2\frac{4}{30} + 2\frac{21}{30}) : \frac{29}{27} - (2\frac{21}{30} - 2\frac{4}{30}) : \frac{17}{7} = 4\frac{25}{30} * \frac{27}{29} - \frac{17}{30} * \frac{7}{17} = 4\frac{5}{6} * \frac{27}{29} - \frac{17}{30} * \frac{7}{17} = \frac{29}{6} * \frac{27}{29} - \frac{17}{30} * \frac{7}{17} = \frac{1}{2} * \frac{9}{1} - \frac{1}{30} * \frac{7}{1} = \frac{9}{2} - \frac{7}{30} = 4\frac{1}{2} - \frac{7}{30} = 4\frac{15}{30} - \frac{7}{30} = 4\frac{8}{30} = 4\frac{4}{15}$

Решение в

$(1\frac{1}{12} + 1\frac{5}{8}) * (-1\frac{11}{13}) - (1\frac{1}{12} - 1\frac{5}{8}) * 1\frac{7}{26} = (1\frac{2}{24} + 1\frac{15}{24}) * (-\frac{24}{13}) - (1\frac{2}{24} - 1\frac{15}{24}) * \frac{33}{26} = 2\frac{17}{24} * (-\frac{24}{13}) - (-\frac{13}{24}) * \frac{33}{26} = \frac{65}{24} * (-\frac{24}{13}) - (-\frac{13}{24}) * \frac{33}{26} = \frac{5}{1} * (-\frac{1}{1}) - (-\frac{1}{8}) * \frac{11}{2} = -5 + \frac{11}{16} = -4\frac{5}{16}$

Решение г

$(1\frac{2}{9} + 1\frac{7}{12}) : 1\frac{47}{54} + (1\frac{2}{9} - 1\frac{7}{12}) * 5\frac{7}{13} = (1\frac{8}{36} + 1\frac{21}{36}) : \frac{101}{54} + (1\frac{8}{36} - 1\frac{21}{36}) * \frac{72}{13} = 2\frac{29}{36} * \frac{54}{101} + (-\frac{13}{36}) * \frac{72}{13} = \frac{101}{36} * \frac{54}{101} + (-\frac{13}{36}) * \frac{72}{13} = \frac{1}{2} * \frac{3}{1} + (-\frac{1}{1}) * \frac{2}{1} = \frac{3}{2} - 2 = 1\frac{1}{2} - 2 = -\frac{1}{2}$