3. Вычислите a) \(-8 \cdot 3\frac{6}{7} =\) б) \(-5\frac{12}{15}:1\frac{7}{12}=\) б) \(2\frac{1}{8}*(-3\frac{5}{12})=\) г) \(-7\frac{4}{8} \cdot (-2\frac{1}{6})=\)

Решение:

a) \(-8 \cdot 3\frac{6}{7} = -8 \cdot \frac{3 \cdot 7+6}{7} = -8 \cdot \frac{27}{7} = -\frac{8 \cdot 27}{7} = -\frac{216}{7} = -30\frac{6}{7}\)

б) \(-5\frac{12}{15}:1\frac{7}{12} = -5\frac{4}{5}:1\frac{7}{12} = -\frac{5 \cdot 5 + 4}{5}:\frac{1 \cdot 12 + 7}{12} = -\frac{29}{5}:\frac{19}{12} = -\frac{29}{5} \cdot \frac{12}{19} = -\frac{29 \cdot 12}{5 \cdot 19} = -\frac{348}{95} = -3\frac{63}{95}\)

б) \(2\frac{1}{8}*(-3\frac{5}{12}) = \frac{2 \cdot 8 + 1}{8} \cdot (-\frac{3 \cdot 12 + 5}{12}) = \frac{17}{8} \cdot (-\frac{41}{12}) = -\frac{17 \cdot 41}{8 \cdot 12} = -\frac{697}{96} = -7\frac{25}{96}\)

г) \(-7\frac{4}{8} \cdot (-2\frac{1}{6}) = -7\frac{1}{2} \cdot (-2\frac{1}{6}) = -\frac{7 \cdot 2 + 1}{2} \cdot (-\frac{2 \cdot 6 + 1}{6}) = \frac{15}{2} \cdot \frac{13}{6} = \frac{15 \cdot 13}{2 \cdot 6} = \frac{195}{12} = \frac{65}{4} = 16\frac{1}{4}\)

Ответ: a) \(-30\frac{6}{7}\); б) \(-3\frac{63}{95}\); б) \(-7\frac{25}{96}\); г) \(16\frac{1}{4}\)