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

a) (\(\frac{5}{6} + \frac{4}{9}\)) - \(\frac{5}{6} \cdot \frac{4}{9}\) = (\(\frac{5 \cdot 3}{6 \cdot 3} + \frac{4 \cdot 2}{9 \cdot 2}\)) - \(\frac{5 \cdot 4}{6 \cdot 9}\) = (\(\frac{15}{18} + \frac{8}{18}\)) - \(\frac{20}{54}\) = \(\frac{23}{18}\) - \(\frac{20}{54}\) = \(\frac{23 \cdot 3}{18 \cdot 3}\) - \(\frac{20}{54}\) = \(\frac{69}{54}\) - \(\frac{20}{54}\) = \(\frac{49}{54}\)

Ответ: \(\frac{49}{54}\)

б) \(\frac{2}{8} \cdot \frac{8}{8} + (3\frac{1}{3} - 2\frac{3}{5}) : \frac{7}{15}\) = \(\frac{2}{8} \cdot \frac{8}{8} + (\frac{10}{3} - \frac{13}{5}) : \frac{7}{15}\) = \(\frac{2}{8} \cdot \frac{8}{8} + (\frac{10 \cdot 5}{3 \cdot 5} - \frac{13 \cdot 3}{5 \cdot 3}) : \frac{7}{15}\) = \(\frac{2}{8} \cdot \frac{8}{8} + (\frac{50}{15} - \frac{39}{15}) : \frac{7}{15}\) = \(\frac{2}{8} \cdot \frac{8}{8} + \frac{11}{15} : \frac{7}{15}\) = \(\frac{2}{8} \cdot \frac{8}{8} + \frac{11}{15} \cdot \frac{15}{7}\) = \(\frac{2}{8} \cdot \frac{8}{8} + \frac{11 \cdot 15}{15 \cdot 7}\) = \(\frac{2}{8} \cdot \frac{8}{8} + \frac{11}{7}\) = \(\frac{1}{4} + \frac{11}{7}\) = \(\frac{1 \cdot 7}{4 \cdot 7} + \frac{11 \cdot 4}{7 \cdot 4}\) = \(\frac{7}{28} + \frac{44}{28}\) = \(\frac{51}{28}\) = 1\(\frac{23}{28}\)

Ответ: 1\(\frac{23}{28}\)