3. Найдите значение выражения \(\left(4 - \frac{14}{33} \cdot 1\frac{1}{21}\right) \cdot \frac{5}{8}.\)

Решение:

1. \(1\frac{1}{21} = \frac{1 \cdot 21 + 1}{21} = \frac{22}{21}\)
2. \(\frac{14}{33} \cdot \frac{22}{21} = \frac{14 \cdot 22}{33 \cdot 21} = \frac{2 \cdot 2}{3 \cdot 3} = \frac{4}{9}\)
3. \(4 - \frac{4}{9} = \frac{4 \cdot 9}{9} - \frac{4}{9} = \frac{36}{9} - \frac{4}{9} = \frac{32}{9}\)
4. \(\frac{32}{9} \cdot \frac{5}{8} = \frac{32 \cdot 5}{9 \cdot 8} = \frac{4 \cdot 5}{9 \cdot 1} = \frac{20}{9} = 2\frac{2}{9}\)