Вычислить:
$$14. \frac{(58\frac{4}{15} - 56\frac{7}{24}) : 0,8 + 2\frac{1}{9} \cdot 0,225}{8\frac{3}{4} \cdot \frac{3}{5}}.$$

Решение:
\(14. \frac{(58\frac{4}{15} - 56\frac{7}{24}) : 0,8 + 2\frac{1}{9} \cdot 0,225}{8\frac{3}{4} \cdot \frac{3}{5}} = \frac{157}{280}.\)

\(
1) 58\frac{4}{15} - 56\frac{7}{24} = 58\frac{32}{120} - 56\frac{35}{120} = 57 + 1 + \frac{32}{120} - 56\frac{35}{120} = 57 + \frac{120}{120} + \frac{32}{120} - 56\frac{35}{120} = 57 -
\)

\(
- 56 + (\frac{120}{120} + \frac{32}{120} - \frac{35}{120}) = 1 + \frac{120 + 32 - 35}{120} = 1\frac{117}{120};
\)

\(
2) 1\frac{117}{120} : 0,8 = \frac{237}{120} : \frac{8}{10} = \frac{237}{120} : \frac{4}{5} = \frac{237}{120} \cdot \frac{5}{4} = \frac{237 \cdot 5}{120 \cdot 4} = \frac{237 \cdot 1}{24 \cdot 4} = \frac{237}{96} = \frac{79}{32} = 2\frac{15}{32};
\)

\(
3) 2\frac{1}{9} \cdot 0,225 = \frac{19}{9} \cdot \frac{225}{1000} = \frac{19}{9} \cdot \frac{9}{40} = \frac{19 \cdot 9}{9 \cdot 40} = \frac{19 \cdot 1}{1 \cdot 40} = \frac{19}{40};
\)

\(
4) 2\frac{15}{32} + \frac{19}{40} = 2\frac{75}{160} + \frac{76}{160} = 2\frac{151}{160};
\)

\(
5) 8\frac{3}{4} \cdot \frac{3}{5} = \frac{35}{4} \cdot \frac{3}{5} = \frac{35 \cdot 3}{4 \cdot 5} = \frac{7 \cdot 3}{4 \cdot 1} = \frac{21}{4} = 5\frac{1}{4};
\)

\(
6) 2\frac{151}{160} : 5\frac{1}{4} = \frac{471}{160} \cdot \frac{4}{21} = \frac{471 \cdot 4}{160 \cdot 21} = \frac{157 \cdot 1}{40 \cdot 7} = \frac{157}{280}.
\)
Ответ: \(\frac{157}{280}.\)