Вычислить:
$$24. (\frac{0,216}{0,15} + \frac{2}{3} : \frac{4}{15}) + (\frac{196}{225} - \frac{7,7}{24\frac{3}{4}}) + 0,695 : 1,39.$$
Решение:
\(24. (\frac{0,216}{0,15} + \frac{2}{3} : \frac{4}{15}) + (\frac{196}{225} - \frac{7,7}{24\frac{3}{4}}) + 0,695 : 1,39 = 5.\)

\(
1) \frac{0,216}{0,15} = 0,216 : 0,15 = 1,44;
\)

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

\(
3) 1,44 + 2,5 = 3,94;
\)

\(
4) 7,7 : 24\frac{3}{4} = 7\frac{7}{10} : \frac{99}{4} = \frac{77}{10} \cdot \frac{4}{99} = \frac{77 \cdot 4}{10 \cdot 99} = \frac{7 \cdot 2}{5 \cdot 9} = \frac{14}{45};
\)

\(
5) \frac{196}{225} - \frac{14}{45} = \frac{196}{225} - \frac{70}{225} = \frac{126}{225} = \frac{42}{75};
\)

\(
6) 0,695 : 1,39 = 0,5;
\)

\(
7) 3,94 + \frac{42}{75} = 3\frac{94}{100} + \frac{42}{75} = 3\frac{47}{50} + \frac{42}{75} = 3\frac{141}{150} + \frac{84}{150} = 3\frac{225}{150} = 3 + \frac{225}{150} = 3 + 1 + \frac{75}{150} =
\)

\(
= 4 + \frac{1}{2} = 4\frac{1}{2} = 4,5;
\)

\(
8) 4,5 + 0,5 = 5.
\)
Ответ: 5.