701. Вычислить: 1) \(\frac{27}{32} \cdot \frac{8}{162} \cdot \frac{72}{69}\) 3) \(\left(\frac{5}{8} + \frac{7}{12}\right) \cdot \left(\frac{3}{23} - \frac{9}{58}\right)\) 5) \(34,17 : 1,7 + \left(2\frac{3}{4} + 0,15\right) : \frac{4}{5} - 23\frac{3}{8}\) 7) \(\frac{12\frac{4}{5} \cdot 3\frac{3}{4} - 4\frac{4}{11} \cdot 4\frac{1}{8}}{11\frac{2}{3} \cdot 2\frac{4}{7}}\)

Решение:

1. 1) \(\frac{27}{32} \cdot \frac{8}{162} \cdot \frac{72}{69} = \frac{27 \cdot 8 \cdot 72}{32 \cdot 162 \cdot 69} = \frac{15552}{357048} = \frac{1}{22.6\)
2. 3) \(\left(\frac{5}{8} + \frac{7}{12}\right) \cdot \left(\frac{3}{23} - \frac{9}{58}\right) = \left(\frac{15+14}{24}\right) \cdot \left(\frac{6-9}{58}\right) = \frac{29}{24} \cdot \left(-\frac{3}{58}\right) = \frac{29}{24} \cdot \left(-\frac{3}{2 \cdot 29}\right) = -\frac{3}{24 \cdot 2} = -\frac{3}{48} = -\frac{1}{16}\)
3. 5) \(34,17 : 1,7 + \left(2\frac{3}{4} + 0,15\right) : \frac{4}{5} - 23\frac{3}{8}\)
   \(34,17 : 1,7 = 20,1\)
   \(2\frac{3}{4} + 0,15 = 2,75 + 0,15 = 2,9\)
   \(2,9 : \frac{4}{5} = 2,9 \cdot \frac{5}{4} = \frac{14,5}{4} = 3,625\)
   \(20,1 + 3,625 - 23,375 = 23,725 - 23,375 = 0,35\)
4. 7) \(\frac{12\frac{4}{5} \cdot 3\frac{3}{4} - 4\frac{4}{11} \cdot 4\frac{1}{8}}{11\frac{2}{3} \cdot 2\frac{4}{7}}\)
   Числитель: \(\frac{64}{5} \cdot \frac{15}{4} - \frac{48}{11} \cdot \frac{33}{8} = \frac{64 \cdot 15}{5 \cdot 4} - \frac{48 \cdot 33}{11 \cdot 8} = \frac{16 \cdot 3}{1} - \frac{6 \cdot 3}{1} = 48 - 18 = 30\)
   Знаменатель: \(\frac{35}{3} \cdot \frac{18}{7} = \frac{35 \cdot 18}{3 \cdot 7} = \frac{5 \cdot 6}{1} = 30\)
   \(\frac{30}{30} = 1\)

Ответ: 1) \(\frac{1}{22.6}\) 3) \(-\frac{1}{16}\) 5) \(0,35\) 7) \(1\)