4) 19,44: \(\left\)(\(\frac{5}{6}\) \(\cdot\) 2,4 - 1,5 : \(\left\)\(2\frac{3}{7} - 1\frac{5}{14}\right\)\(\right\)) : \(\frac{4,04}\){\(\left\)\(0,52 + 2,005\right\)}

Решение:

Вычислим по действиям.

1. \(2\frac{3}{7} - 1\frac{5}{14} = \frac{17}{7} - \frac{19}{14} = \frac{34}{14} - \frac{19}{14} = \frac{15}{14}\)
2. \(\frac{5}{6} \cdot 2,4 = \frac{5}{6} \cdot \frac{24}{10} = \frac{5 \cdot 24}{6 \cdot 10} = \frac{120}{60} = 2\)
3. \(1,5 : \frac{15}{14} = \frac{3}{2} : \frac{15}{14} = \frac{3}{2} \cdot \frac{14}{15} = \frac{3 \cdot 14}{2 \cdot 15} = \frac{42}{30} = \frac{7}{5} = 1,4\)
4. \(2 - 1,4 = 0,6\)
5. \(0,52 + 2,005 = 2,525\)
6. \(4,04 : 2,525 = \frac{4040}{2525} = \frac{1616}{1010} = \frac{808}{505} = 1,6\)
7. \(0,6 : 1,6 = \frac{6}{10} : \frac{16}{10} = \frac{6}{10} \cdot \frac{10}{16} = \frac{6}{16} = \frac{3}{8} = 0,375\)
8. \(19,44 : 0,375 = \frac{1944}{100} : \frac{375}{1000} = \frac{1944}{100} \cdot \frac{1000}{375} = \frac{1944000}{37500} = \frac{19440}{375} = 51,84\)

Ответ: 51,84