Вычислить:
$$38. (41\frac{23}{84} - 40\frac{49}{60})\{[4 - 3\frac{1}{2}(2\frac{1}{7} - 1\frac{1}{5})] : 0,16\}.$$
Решение:
\(38. (41\frac{23}{84} - 40\frac{49}{60}){[4 - 3\frac{1}{2}(2\frac{1}{7} - 1\frac{1}{5})] : 0,16} = 2.\)

\(
1) 41\frac{23}{84} - 40\frac{49}{60} = 41\frac{115}{420} - 40\frac{343}{420} = 40 + 1 + \frac{115}{420} - 40 + \frac{343}{420} = 40 + \frac{420}{420} + \frac{115}{420} - 40 - \frac{343}{420} =
\)

\(
= 40 - 40 + \frac{420 + 115 - 343}{420} = \frac{192}{420} = \frac{16}{35};
\)

\(
2) 2\frac{1}{7} - 1\frac{1}{5} = 2\frac{5}{35} - 1\frac{7}{35} = 1 + 1 + \frac{5}{35} - 1 - \frac{7}{35} = 1 + \frac{35}{35} + \frac{5}{35} - 1 - \frac{7}{35} = 1 - 1 + \frac{35 + 5 - 7}{35} = \frac{33}{35};
\)

\(
3) 3\frac{1}{2} \cdot \frac{33}{35} = \frac{7}{2} \cdot \frac{33}{35} = \frac{7 \cdot 33}{2 \cdot 35} = \frac{1 \cdot 33}{2 \cdot 5} = \frac{33}{10} = 3\frac{3}{10} = 3,3;
\)

\(
4) 4 - 3,3 = 0,7;
\)

\(
5) 0,7 : 0,16 = \frac{7}{10} \cdot \frac{100}{16} = \frac{7}{10} \cdot \frac{25}{4} = \frac{7 \cdot 25}{10 \cdot 4} = \frac{7 \cdot 5}{2 \cdot 4} = \frac{35}{8} = 4\frac{3}{8};
\)

\(
6) \frac{16}{35} \cdot 4\frac{3}{8} = \frac{16}{35} \cdot \frac{35}{8} = \frac{16 \cdot 35}{35 \cdot 8} = \frac{2 \cdot 1}{1 \cdot 1} = \frac{2}{1} = 2.
\)
Ответ: 2.