2. Вычислите \((7,42 - \frac{5}{9} - (-11,48): 1\frac{4}{5}) : 0,35\)

Вычислим значение выражения: \((7,42 - \frac{5}{9} - (-11,48): 1\frac{4}{5}) : 0,35\)

1. \(1\frac{4}{5} = \frac{1 \cdot 5 + 4}{5} = \frac{9}{5}\)
2. \((-11,48) : \frac{9}{5} = -11,48 \cdot \frac{5}{9} = -\frac{1148}{100} \cdot \frac{5}{9} = -\frac{287}{25} \cdot \frac{5}{9} = -\frac{287}{5} \cdot \frac{1}{9} = -\frac{287}{45}\)
3. \(\frac{5}{9} = \frac{5 \cdot 5}{9 \cdot 5} = \frac{25}{45}\)
4. \(7,42 = \frac{742}{100} = \frac{371}{50}\)
5. \(\frac{371}{50} - \frac{25}{45} = \frac{371 \cdot 9}{50 \cdot 9} - \frac{25 \cdot 10}{45 \cdot 10} = \frac{3339}{450} - \frac{250}{450} = \frac{3339 - 250}{450} = \frac{3089}{450}\)
6. \(\frac{3089}{450} - ( - \frac{287}{45}) = \frac{3089}{450} + \frac{287}{45} = \frac{3089}{450} + \frac{287 \cdot 10}{45 \cdot 10} = \frac{3089}{450} + \frac{2870}{450} = \frac{3089 + 2870}{450} = \frac{5959}{450}\)
7. \(0,35 = \frac{35}{100} = \frac{7}{20}\)
8. \(\frac{5959}{450} : \frac{7}{20} = \frac{5959}{450} \cdot \frac{20}{7} = \frac{5959}{45 \cdot 10} \cdot \frac{2 \cdot 10}{7} = \frac{5959}{45} \cdot \frac{2}{7} = \frac{5959 \cdot 2}{45 \cdot 7} = \frac{11918}{315}\)
9. \(\frac{11918}{315} = 37,834920634920635 \approx 37,83\)

Ответ: 37,83