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

Решение:

а) $$\left(\frac{5}{6} + \frac{4}{9}\right) - \frac{5}{6} \cdot \frac{4}{9} = \frac{5}{6} + \frac{4}{9} - \frac{20}{54} = \frac{5}{6} + \frac{4}{9} - \frac{10}{27} = \frac{5 \cdot 9}{6 \cdot 9} + \frac{4 \cdot 6}{9 \cdot 6} - \frac{10 \cdot 2}{27 \cdot 2} = \frac{45}{54} + \frac{24}{54} - \frac{20}{54} = \frac{45 + 24 - 20}{54} = \frac{49}{54}.$$

Ответ: $$\frac{49}{54}.$$

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

Ответ: $$1 \frac{23}{28}.$$