Выполни, пожалуйста, действия: a) 6 5/6 + 4 1/4

- a) $6\frac{5}{6} + 4\frac{1}{4} = 6 + \frac{5}{6} + 4 + \frac{1}{4} = (6+4) + (\frac{5}{6} + \frac{1}{4}) = 10 + (\frac{5*2}{6*2} + \frac{1*3}{4*3}) = 10 + (\frac{10}{12} + \frac{3}{12}) = 10 + \frac{13}{12} = 10 + 1\frac{1}{12} = 11\frac{1}{12}$ - б) $7\frac{8}{6} - 5\frac{6}{8} = 7 + \frac{8}{6} - 5 - \frac{6}{8} = (7-5) + (\frac{8}{6} - \frac{6}{8}) = 2 + (\frac{8*4}{6*4} - \frac{6*3}{8*3}) = 2 + (\frac{32}{24} - \frac{18}{24}) = 2 + \frac{14}{24} = 2 + \frac{7}{12} = 2\frac{7}{12}$ - в) $10\frac{3}{10} - 15\frac{4}{15}$. **Допущение:** Нужно вычесть $10\frac{3}{10}$ из $15\frac{4}{15}$. $15\frac{4}{15} - 10\frac{3}{10} = 15 + \frac{4}{15} - 10 - \frac{3}{10} = (15 - 10) + (\frac{4}{15} - \frac{3}{10}) = 5 + (\frac{4*2}{15*2} - \frac{3*3}{10*3}) = 5 + (\frac{8}{30} - \frac{9}{30}) = 5 - \frac{1}{30} = 4\frac{30}{30} - \frac{1}{30} = 4\frac{29}{30}$ - г) $5 - 3\frac{2}{7} = 5 - (3 + \frac{2}{7}) = 5 - 3 - \frac{2}{7} = 2 - \frac{2}{7} = 1\frac{7}{7} - \frac{2}{7} = 1\frac{5}{7}$ - д) $9\frac{4}{8} : 6\frac{3}{5} = \frac{9*8 + 4}{8} : \frac{6*5 + 3}{5} = \frac{76}{8} : \frac{33}{5} = \frac{76}{8} * \frac{5}{33} = \frac{76*5}{8*33} = \frac{380}{264} = \frac{95}{66} = 1\frac{29}{66}$ - e) $8\frac{5}{10} : 9\frac{3}{10} = \frac{8*10 + 5}{10} : \frac{9*10 + 3}{10} = \frac{85}{10} : \frac{93}{10} = \frac{85}{10} * \frac{10}{93} = \frac{85}{93}$ - ж) $2\frac{6}{7} : 1\frac{3}{7} = \frac{2*7 + 6}{7} : \frac{1*7 + 3}{7} = \frac{20}{7} : \frac{10}{7} = \frac{20}{7} * \frac{7}{10} = \frac{20}{10} = 2$ - з) $6\frac{3}{5} * 3\frac{6}{10} = \frac{6*5 + 3}{5} * \frac{3*10 + 6}{10} = \frac{33}{5} * \frac{36}{10} = \frac{33 * 36}{5 * 10} = \frac{1188}{50} = 23\frac{38}{50} = 23\frac{19}{25}$