5.470 Найдите значение выражения: 6 1 1 в) 11.5 a) 7 12 3 ; 33 10' 3 10 39 6) 4 13 40', r) 3.4.5.12.

a) \(\frac{6}{7} \cdot 1\frac{1}{12} : \frac{3}{5} = \frac{6}{7} \cdot \frac{13}{12} : \frac{3}{5} = \frac{6}{7} \cdot \frac{13}{12} \cdot \frac{5}{3} = \frac{6 \cdot 13 \cdot 5}{7 \cdot 12 \cdot 3} = \frac{2 \cdot 3 \cdot 13 \cdot 5}{7 \cdot 3 \cdot 4 \cdot 3} = \frac{2 \cdot 13 \cdot 5}{7 \cdot 4 \cdot 3} = \frac{130}{84} = \frac{65}{42} = 1\frac{23}{42}\)

б) \(\frac{3}{4} \cdot \frac{10}{13} : \frac{39}{40} = \frac{3}{4} \cdot \frac{10}{13} \cdot \frac{40}{39} = \frac{3 \cdot 10 \cdot 40}{4 \cdot 13 \cdot 39} = \frac{3 \cdot 2 \cdot 5 \cdot 4 \cdot 10}{4 \cdot 13 \cdot 3 \cdot 3 \cdot 13} = \frac{2 \cdot 5 \cdot 10}{13 \cdot 3 \cdot 13} = \frac{100}{507}\)

в) \(11 \cdot \frac{5}{33} - \frac{1}{10} = \frac{11 \cdot 5}{33} - \frac{1}{10} = \frac{55}{33} - \frac{1}{10} = \frac{5}{3} - \frac{1}{10} = \frac{5 \cdot 10 - 1 \cdot 3}{30} = \frac{50 - 3}{30} = \frac{47}{30} = 1\frac{17}{30}\)

г) \(3 \cdot \frac{4}{5} \cdot \frac{6}{12} = 3 \cdot \frac{4}{5} \cdot \frac{1}{2} = \frac{3 \cdot 4 \cdot 1}{5 \cdot 2} = \frac{12}{10} = \frac{6}{5} = 1\frac{1}{5}\)

Ответ: а) \(1\frac{23}{42}\); б) \(\frac{100}{507}\); в) \(1\frac{17}{30}\); г) \(1\frac{1}{5}\)