Решение:

а)

$$\frac{5}{6} + \frac{4}{9} = \frac{5 \cdot 3}{6 \cdot 3} + \frac{4 \cdot 2}{9 \cdot 2} = \frac{15}{18} + \frac{8}{18} = \frac{23}{18}$$ $$\frac{5}{6} \cdot \frac{4}{9} = \frac{5 \cdot 4}{6 \cdot 9} = \frac{20}{54} = \frac{10}{27}$$ $$\frac{23}{18} - \frac{10}{27} = \frac{23 \cdot 3}{18 \cdot 3} - \frac{10 \cdot 2}{27 \cdot 2} = \frac{69}{54} - \frac{20}{54} = \frac{49}{54}$$

Ответ: $$\frac{49}{54}$$

б)

$$\frac{2}{8} \cdot \frac{8}{8} = \frac{2 \cdot 8}{8 \cdot 8} = \frac{16}{64} = \frac{1}{4}$$ $$3\frac{1}{3} = \frac{3 \cdot 3 + 1}{3} = \frac{10}{3}$$ $$2\frac{3}{5} = \frac{2 \cdot 5 + 3}{5} = \frac{13}{5}$$ $$\frac{10}{3} - \frac{13}{5} = \frac{10 \cdot 5}{3 \cdot 5} - \frac{13 \cdot 3}{5 \cdot 3} = \frac{50}{15} - \frac{39}{15} = \frac{11}{15}$$ $$\frac{11}{15} : \frac{7}{15} = \frac{11}{15} \cdot \frac{15}{7} = \frac{11 \cdot 15}{15 \cdot 7} = \frac{11}{7}$$ $$\frac{1}{4} + \frac{11}{7} = \frac{1 \cdot 7}{4 \cdot 7} + \frac{11 \cdot 4}{7 \cdot 4} = \frac{7}{28} + \frac{44}{28} = \frac{51}{28} = 1\frac{23}{28}$$

Ответ: $$1\frac{23}{28}$$

в)

$$\frac{2}{7} + \frac{1}{2} = \frac{2 \cdot 2}{7 \cdot 2} + \frac{1 \cdot 7}{2 \cdot 7} = \frac{4}{14} + \frac{7}{14} = \frac{11}{14}$$ $$\frac{3}{14} + \frac{11}{14} = \frac{3 + 11}{14} = \frac{14}{14} = 1$$

Ответ: $$1$$

г)

$$\frac{6}{7} - \frac{3}{8} = \frac{6 \cdot 8}{7 \cdot 8} - \frac{3 \cdot 7}{8 \cdot 7} = \frac{48}{56} - \frac{21}{56} = \frac{27}{56}$$ $$\frac{11}{56} + \frac{27}{56} = \frac{11 + 27}{56} = \frac{38}{56} = \frac{19}{28}$$

Ответ: $$\frac{19}{28}$$

д)

$$\frac{5}{8} + \frac{1}{6} = \frac{5 \cdot 3}{8 \cdot 3} + \frac{1 \cdot 4}{6 \cdot 4} = \frac{15}{24} + \frac{4}{24} = \frac{19}{24}$$ $$\frac{19}{24} - \frac{7}{24} = \frac{19 - 7}{24} = \frac{12}{24} = \frac{1}{2}$$

Ответ: $$\frac{1}{2}$$