5.486 Найдите произведение: a) $$\frac{8}{9} \cdot \frac{9}{22}$$; б) $$\frac{45}{11} \cdot \frac{11}{22}$$; в) $$\frac{51}{29} \cdot \frac{58}{85}$$; г) $$\frac{14}{121} \cdot \frac{11}{28}$$.

**Решение:** a) $$\frac{8}{9} \cdot \frac{9}{22} = \frac{8 \cdot 9}{9 \cdot 22} = \frac{8}{22} = \frac{4}{11}$$. **Ответ:** $$\frac{4}{11}$$ б) $$\frac{45}{11} \cdot \frac{11}{22} = \frac{45 \cdot 11}{11 \cdot 22} = \frac{45}{22} = 2\frac{1}{22}$$. **Ответ:** $$2\frac{1}{22}$$ в) $$\frac{51}{29} \cdot \frac{58}{85} = \frac{51 \cdot 58}{29 \cdot 85} = \frac{3 \cdot 17 \cdot 2 \cdot 29}{29 \cdot 5 \cdot 17} = \frac{3 \cdot 2}{5} = \frac{6}{5} = 1\frac{1}{5}$$. **Ответ:** $$1\frac{1}{5}$$ г) $$\frac{14}{121} \cdot \frac{11}{28} = \frac{14 \cdot 11}{121 \cdot 28} = \frac{2 \cdot 7 \cdot 11}{11 \cdot 11 \cdot 4 \cdot 7} = \frac{2}{11 \cdot 4} = \frac{1}{11 \cdot 2} = \frac{1}{22}$$. **Ответ:** $$\frac{1}{22}$$