5.542 Выполните действия: а) \(\frac{3}{8} + (3\frac{1}{3} - 2\frac{3}{5}) : \frac{7}{15}\);

а) \(\frac{3}{8} + (3\frac{1}{3} - 2\frac{3}{5}) : \frac{7}{15}\)

1. \(3\frac{1}{3} - 2\frac{3}{5} = \frac{10}{3} - \frac{13}{5} = \frac{10 \cdot 5 - 13 \cdot 3}{15} = \frac{50 - 39}{15} = \frac{11}{15}\)
2. \(\frac{11}{15} : \frac{7}{15} = \frac{11}{15} \cdot \frac{15}{7} = \frac{11 \cdot 15}{15 \cdot 7} = \frac{11}{7} = 1\frac{4}{7}\)
3. \(\frac{3}{8} + 1\frac{4}{7} = \frac{3}{8} + \frac{11}{7} = \frac{3 \cdot 7 + 11 \cdot 8}{56} = \frac{21 + 88}{56} = \frac{109}{56} = 1\frac{53}{56}\)

Ответ: \(1\frac{53}{56}\)