Вычислить:
$$23.\quad (10 : 2\frac{2}{3} + 7,5 : 10) \cdot (\frac{3}{40} - \frac{7}{30} \cdot 0,25 + \frac{157}{360}).$$
Решение:
\(23. (10 : 2\frac{2}{3} + 7,5 : 10) \cdot (\frac{3}{40} - \frac{7}{30} \cdot 0,25 + \frac{157}{360}) = 2\frac{3}{80}.\)

\(
1) 10 : 2\frac{2}{3} = 10 : \frac{8}{3} = 10 \cdot \frac{3}{8} = \frac{10 \cdot 3}{8} = \frac{5 \cdot 3}{4} = \frac{15}{4} = 3\frac{3}{4} = 3,75;
\)

\(
2) 7,5 : 10 = 0,75;
\)

\(
3) 3,75 + 0,75 = 4,5;
\)

\(
4) \frac{7}{30} \cdot 0,25 = \frac{7}{30} \cdot \frac{25}{100} = \frac{7}{30} \cdot \frac{1}{4} = \frac{7 \cdot 1}{30 \cdot 4} = \frac{7}{120};
\)

\(
5) \frac{3}{40} - \frac{7}{120} = \frac{9}{120} - \frac{7}{120} = \frac{2}{120} = \frac{1}{60};
\)

\(
6) \frac{1}{60} + \frac{157}{360} = \frac{6}{360} + \frac{157}{360} = \frac{163}{360};
\)

\(
7) 4,5 \cdot \frac{163}{360} = 4\frac{5}{10} \cdot \frac{163}{360} = 4\frac{1}{2} \cdot \frac{163}{360} = \frac{9}{2} \cdot \frac{163}{360} = \frac{9 \cdot 163}{2 \cdot 360} = \frac{1 \cdot 163}{2 \cdot 40} = \frac{163}{80} = 2\frac{3}{80}.
\)
Ответ: \(2\frac{3}{80}\).