2. Выполните действия a) \(1 \frac{5}{19} \cdot (6 - 3 \frac{5}{8})\) б) \((6,3:1,4 - 2,05) \cdot 1,8\)

Решение:

а) \(1 \frac{5}{19} \cdot (6 - 3 \frac{5}{8}) = \frac{24}{19} \cdot (6 - \frac{29}{8}) = \frac{24}{19} \cdot (\frac{48 - 29}{8}) = \frac{24}{19} \cdot \frac{19}{8} = \frac{24 \cdot 19}{19 \cdot 8} = \frac{24}{8} = 3\)

б) \((6,3:1,4 - 2,05) \cdot 1,8 = (\frac{63}{10} : \frac{14}{10} - \frac{205}{100}) \cdot \frac{18}{10} = (\frac{63}{10} \cdot \frac{10}{14} - \frac{41}{20}) \cdot \frac{9}{5} = (\frac{63}{14} - \frac{41}{20}) \cdot \frac{9}{5} = (\frac{9}{2} - \frac{41}{20}) \cdot \frac{9}{5} = (\frac{90 - 41}{20}) \cdot \frac{9}{5} = \frac{49}{20} \cdot \frac{9}{5} = \frac{441}{100} = 4,41\)

Ответ: а) 3; б) 4,41.