1.4 Вычислите: 1) 11 \(\cdot\) 1 \(\frac{17}{55}\) - 15,3; 2) 3 \(\frac{4}{7}\) \(\cdot\) 4,5 \(\cdot\) \(\frac{7}{35}\) \(\cdot\) 8,75 : \(\frac{2}{5}\) : \(\frac{9}{32}\); 3) 19 \(\cdot\) 2 \(\frac{55}{76}\) - 39,4; 4) 6,8 \(\cdot\) \(\frac{5}{13}\) \(\cdot\) 2,7 \(\cdot\) 3 \(\frac{3}{25}\) : 5 \(\frac{2}{5}\) : \(\frac{1}{175}\).

Решение:

1. \( 11 \cdot 1 \frac{17}{55} - 15,3 = 11 \cdot \frac{72}{55} - 15,3 = \frac{72}{5} - 15,3 = 14,4 - 15,3 = -0,9 \)
2. \( 3 \frac{4}{7} \cdot 4,5 \cdot \frac{7}{35} \cdot 8,75 : \frac{2}{5} : \frac{9}{32} = \frac{25}{7} \cdot \frac{9}{2} \cdot \frac{7}{35} \cdot \frac{35}{4} : \frac{2}{5} : \frac{9}{32} \)
3. \( = \frac{25}{7} \cdot \frac{7}{35} \cdot \frac{9}{2} \cdot \frac{35}{4} \cdot \frac{5}{2} \cdot \frac{32}{9} = \frac{25}{35} \cdot \frac{9}{2} \cdot \frac{35}{4} \cdot \frac{5}{2} \cdot \frac{32}{9} = \frac{5}{7} \cdot \frac{9}{2} \cdot \frac{35}{4} \cdot \frac{5}{2} \cdot \frac{32}{9} = 5 \cdot \frac{1}{2} \cdot 5 \cdot \frac{5}{2} \cdot \frac{32}{9} \)
4. \( = \frac{25}{2} \cdot \frac{5}{2} \cdot \frac{32}{9} = \frac{125}{4} \cdot \frac{32}{9} = 125 \cdot \frac{8}{9} = \frac{1000}{9} \approx 111,11 \)
5. \( 19 \cdot 2 \frac{55}{76} - 39,4 = 19 \cdot \frac{152 + 55}{76} - 39,4 = 19 \cdot \frac{207}{76} - 39,4 = \frac{207}{4} - 39,4 = 51,75 - 39,4 = 12,35 \)
6. \( 6,8 \cdot \frac{5}{13} \cdot 2,7 \cdot 3 \frac{3}{25} : 5 \frac{2}{5} : \frac{1}{175} = \frac{68}{10} \cdot \frac{5}{13} \cdot \frac{27}{10} \cdot \frac{78}{25} : \frac{27}{5} : \frac{1}{175} \)
7. \( = \frac{34}{5} \cdot \frac{5}{13} \cdot \frac{27}{10} \cdot \frac{78}{25} \cdot \frac{5}{27} \cdot 175 = \frac{34}{13} \cdot \frac{1}{10} \cdot \frac{78}{25} \cdot 5 \cdot 175 = \frac{34}{13} \cdot \frac{78}{25} \cdot \frac{5}{10} \cdot 175 = \frac{34}{13} \cdot \frac{78}{25} \cdot \frac{1}{2} \cdot 175 \)
8. \( = 34 \cdot \frac{6}{25} \cdot \frac{1}{2} \cdot 175 = 34 \cdot \frac{3}{25} \cdot 175 = 34 \cdot 3 \cdot 7 = 102 \cdot 7 = 714 \)

Ответ: 1) -0,9; 2) \(\frac{1000}{9}\); 3) 12,35; 4) 714.