5.29 Вычислите значение выражения: a) $4\frac{2}{15} - 3\frac{3}{10} - 2\frac{1}{6}$; б) $7\frac{5}{21} - 14\frac{1}{7} + 6\frac{1}{14}$; в) $24\frac{2}{35} - 18\frac{5}{14} - 5\frac{3}{10}$; г) $1\frac{2}{9} + 2\frac{5}{6} - 35\frac{1}{5}$; е) $-5\frac{4}{7} + ( -\frac{1}{14} );$

Решение: а) $4\frac{2}{15} - 3\frac{3}{10} - 2\frac{1}{6} = 4\frac{4}{30} - 3\frac{9}{30} - 2\frac{5}{30} = (4 - 3 - 2) + (\frac{4}{30} - \frac{9}{30} - \frac{5}{30}) = -1 + \frac{4-9-5}{30} = -1 + \frac{-10}{30} = -1 - \frac{1}{3} = -1\frac{1}{3}$ Ответ: **-1$\frac{1}{3}$** б) $7\frac{5}{21} - 14\frac{1}{7} + 6\frac{1}{14} = 7\frac{10}{42} - 14\frac{6}{42} + 6\frac{3}{42} = (7 - 14 + 6) + (\frac{10}{42} - \frac{6}{42} + \frac{3}{42}) = -1 + \frac{10-6+3}{42} = -1 + \frac{7}{42} = -1 + \frac{1}{6} = -\frac{6}{6} + \frac{1}{6} = -\frac{5}{6}$ Ответ: **-\frac{5}{6}** в) $24\frac{2}{35} - 18\frac{5}{14} - 5\frac{3}{10} = 24\frac{4}{70} - 18\frac{25}{70} - 5\frac{21}{70} = (24 - 18 - 5) + (\frac{4}{70} - \frac{25}{70} - \frac{21}{70}) = 1 + \frac{4-25-21}{70} = 1 + \frac{-42}{70} = 1 - \frac{3}{5} = \frac{5}{5} - \frac{3}{5} = \frac{2}{5}$ Ответ: **$\frac{2}{5}$** г) $1\frac{2}{9} + 2\frac{5}{6} - 35\frac{1}{5} = 1\frac{4}{18} + 2\frac{15}{18} - 35\frac{1}{5} = (1 + 2 - 35) + (\frac{4}{18} + \frac{15}{18} - \frac{1}{5}) = -32 + (\frac{19}{18} - \frac{1}{5}) = -32 + (\frac{95}{90} - \frac{18}{90}) = -32 + \frac{77}{90} = -32 + \frac{77}{90} = -31\frac{90}{90} + \frac{77}{90} = -31\frac{13}{90}$ Ответ: **-31$\frac{13}{90}$** е) $-5\frac{4}{7} + ( -\frac{1}{14} ) = -5\frac{8}{14} - \frac{1}{14} = -5\frac{9}{14}$ Ответ: **-5$\frac{9}{14}$**