5.543 Найдите значение выражения: a) (\frac{5}{6} + \frac{4}{9}) - \frac{5}{6} \cdot \frac{4}{9}; б) \frac{2}{8} + (3\frac{1}{3}-2\frac{3}{5}): \frac{7}{15}.

1. $$\left(\frac{5}{6} + \frac{4}{9}\right) - \frac{5}{6} \cdot \frac{4}{9} = \left(\frac{5 \cdot 3}{6 \cdot 3} + \frac{4 \cdot 2}{9 \cdot 2}\right) - \frac{5 \cdot 4}{6 \cdot 9} = \left(\frac{15}{18} + \frac{8}{18}\right) - \frac{20}{54} = \frac{23}{18} - \frac{20}{54} = \frac{23 \cdot 3}{18 \cdot 3} - \frac{20}{54} = \frac{69}{54} - \frac{20}{54} = \frac{49}{54}$$
2. $$\frac{2}{8} + \left(3\frac{1}{3} - 2\frac{3}{5}\right) : \frac{7}{15} = \frac{2}{8} + \left(\frac{10}{3} - \frac{13}{5}\right) : \frac{7}{15} = \frac{2}{8} + \left(\frac{10 \cdot 5}{3 \cdot 5} - \frac{13 \cdot 3}{5 \cdot 3}\right) : \frac{7}{15} = \frac{2}{8} + \left(\frac{50}{15} - \frac{39}{15}\right) : \frac{7}{15} = \frac{2}{8} + \frac{11}{15} : \frac{7}{15} = \frac{2}{8} + \frac{11}{15} \cdot \frac{15}{7} = \frac{2}{8} + \frac{11}{7} = \frac{1}{4} + \frac{11}{7} = \frac{1 \cdot 7}{4 \cdot 7} + \frac{11 \cdot 4}{7 \cdot 4} = \frac{7}{28} + \frac{44}{28} = \frac{51}{28} = 1\frac{23}{28}$$

Ответ: a) $$\frac{49}{54}$$; б) $$1\frac{23}{28}$$