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

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

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