85.5434 Найдите значение выражения: a) $$(\frac{5}{6}+\frac{4}{9})-\frac{5}{6} \cdot \frac{4}{9}$$; б) $$\frac{2}{8}:\frac{8}{8} + (3\frac{1}{3}-2\frac{3}{5}):\frac{7}{15}$$

а) $$(\frac{5}{6}+\frac{4}{9})-\frac{5}{6} \cdot \frac{4}{9}$$

$$\frac{5}{6}+\frac{4}{9} = \frac{5 \cdot 3}{6 \cdot 3} + \frac{4 \cdot 2}{9 \cdot 2} = \frac{15}{18} + \frac{8}{18} = \frac{15 + 8}{18} = \frac{23}{18}$$

$$\frac{5}{6} \cdot \frac{4}{9} = \frac{5 \cdot 4}{6 \cdot 9} = \frac{20}{54} = \frac{10 \cdot 2}{27 \cdot 2} = \frac{10}{27}$$

$$\frac{23}{18}-\frac{10}{27} = \frac{23 \cdot 3}{18 \cdot 3} - \frac{10 \cdot 2}{27 \cdot 2} = \frac{69}{54} - \frac{20}{54} = \frac{69 - 20}{54} = \frac{49}{54}$$

Ответ: $$\frac{49}{54}$$

б) $$\frac{2}{8}:\frac{8}{8} + (3\frac{1}{3}-2\frac{3}{5}):\frac{7}{15}$$

$$\frac{2}{8}:\frac{8}{8} = \frac{2}{8} : 1 = \frac{2}{8} = \frac{1}{4}$$

$$3\frac{1}{3}-2\frac{3}{5} = \frac{3 \cdot 3 + 1}{3} - \frac{2 \cdot 5 + 3}{5} = \frac{10}{3} - \frac{13}{5} = \frac{10 \cdot 5}{3 \cdot 5} - \frac{13 \cdot 3}{5 \cdot 3} = \frac{50}{15} - \frac{39}{15} = \frac{50 - 39}{15} = \frac{11}{15}$$

$$\frac{11}{15}:\frac{7}{15} = \frac{11}{15} \cdot \frac{15}{7} = \frac{11 \cdot 15}{15 \cdot 7} = \frac{11}{7}$$

$$\frac{1}{4} + \frac{11}{7} = \frac{1 \cdot 7}{4 \cdot 7} + \frac{11 \cdot 4}{7 \cdot 4} = \frac{7}{28} + \frac{44}{28} = \frac{7 + 44}{28} = \frac{51}{28} = 1\frac{23}{28}$$

Ответ: $$1\frac{23}{28}$$