4. Вычислите: 1) 11 · 1 17/55 - 15,3; 2) 3 4/7 · 4,5 · 7/35 · 8,75 : 2/5 : 9/32; 3) 19 · 2 55/76 - 39,4; 4) 6,8 · 5/13 · 2,7 · 3/25.

Решение:

1. 1) \( 11 \cdot 1 \frac{17}{55} - 15.3 \)
   \( 1 \frac{17}{55} = \frac{72}{55} \)
   \( 11 \cdot \frac{72}{55} = \frac{11 \cdot 72}{55} = \frac{1 \cdot 72}{5} = \frac{72}{5} = 14.4 \)
   \( 14.4 - 15.3 = -0.9 \)
2. 2) \( 3 \frac{4}{7} \cdot 4.5 \cdot \frac{7}{35} \cdot 8.75 : \frac{2}{5} : \frac{9}{32} \)
   \( 3 \frac{4}{7} = \frac{25}{7} \)
   \( 4.5 = \frac{9}{2} \)
   \( 8.75 = \frac{875}{100} = \frac{35}{4} \)
   \( \frac{25}{7} \cdot \frac{9}{2} \cdot \frac{7}{35} \cdot \frac{35}{4} = \frac{25 \cdot 9 \cdot 7 \cdot 35}{7 \cdot 2 \cdot 35 \cdot 4} = \frac{25 \cdot 9}{2 \cdot 4} = \frac{225}{8} \)
   \( \frac{225}{8} : \frac{2}{5} = \frac{225}{8} \cdot \frac{5}{2} = \frac{1125}{16} \)
   \( \frac{1125}{16} : \frac{9}{32} = \frac{1125}{16} \cdot \frac{32}{9} = \frac{1125 \cdot 2}{9} = 125 \cdot 2 = 250 \)
3. 3) \( 19 \cdot 2 \frac{55}{76} - 39.4 \)
   \( 2 \frac{55}{76} = \frac{152 + 55}{76} = \frac{207}{76} \)
   \( 19 \cdot \frac{207}{76} = \frac{19 \cdot 207}{76} = \frac{1 \cdot 207}{4} = \frac{207}{4} = 51.75 \)
   \( 51.75 - 39.4 = 12.35 \)
4. 4) \( 6.8 \cdot \frac{5}{13} \cdot 2.7 \cdot \frac{3}{25} \)
   \( 6.8 = \frac{68}{10} = \frac{34}{5} \)
   \( 2.7 = \frac{27}{10} \)
   \( \frac{34}{5} \cdot \frac{5}{13} \cdot \frac{27}{10} \cdot \frac{3}{25} = \frac{34 \cdot 5 \cdot 27 \cdot 3}{5 \cdot 13 \cdot 10 \cdot 25} = \frac{34 \cdot 27 \cdot 3}{13 \cdot 10 \cdot 25} = \frac{2754}{3250} = \frac{1377}{1625} \)

Ответ: 1) -0.9; 2) 250; 3) 12.35; 4) 1377/1625.