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

\begin{aligned} (\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} \end{aligned}

\begin{aligned} \frac{2}{8} \cdot \frac{8}{8} + (3\frac{1}{3}) &= \frac{2 \cdot 8}{8 \cdot 8} + \frac{3 \cdot 3 + 1}{3} = \frac{16}{64} + \frac{10}{3} = \frac{1}{4} + \frac{10}{3} = \frac{1 \cdot 3}{4 \cdot 3} + \frac{10 \cdot 4}{3 \cdot 4} = \frac{3}{12} + \frac{40}{12} = \frac{43}{12} = 3\frac{7}{12} \end{aligned}