Вычислить:
$$8. \frac{(49\frac{5}{24} - 46\frac{7}{20}) \cdot 2\frac{1}{3} + 0,6}{0,2}.$$
Решение:
\(8. \frac{(49\frac{5}{24} - 46\frac{7}{20}) \cdot 2\frac{1}{3} + 0,6}{0,2} = 36\frac{25}{72}.\)
\(
1) 49\frac{5}{24} - 46\frac{7}{20} = 49\frac{25}{120} - 46\frac{42}{120} = 48 + 1 + \frac{25}{120} - 46\frac{42}{120} = 48 + \frac{120}{120} + \frac{25}{120} - 46\frac{42}{120} = 48 -
\)
\(
- 46 + (\frac{120}{120} + \frac{25}{120} - \frac{42}{120}) = 2 + \frac{120 + 25 - 42}{120} = 2\frac{103}{120};
\)
\(
2) 2\frac{103}{120} \cdot 2\frac{1}{3} = \frac{343}{120} \cdot \frac{7}{3} = \frac{2401}{360} = 6\frac{241}{360};
\)
\(
3) 6\frac{241}{360} + 0,6 = 6\frac{241}{360} + \frac{3}{5} = 6\frac{241}{360} + \frac{216}{360} = 6 + \frac{241 + 216}{360} = 6 + \frac{457}{360} = 6 + 1\frac{97}{360} = 7\frac{97}{360};
\)
\(
4) 7\frac{97}{360} : 0,2 = \frac{2617}{360} : \frac{1}{5} = \frac{2617}{360} \cdot \frac{5}{1} = \frac{2617 \cdot 5}{360 \cdot 1} = \frac{2617 \cdot 1}{72 \cdot 1} = \frac{2617}{72} = 36\frac{25}{72}.
\)
Ответ: \(36\frac{25}{72}.\)
