Решение примеров:

1. $$\frac{14}{27} \cdot \frac{6}{7} = \frac{14 \cdot 6}{27 \cdot 7} = \frac{2 \cdot 6}{27 \cdot 1} = \frac{2 \cdot 2}{9 \cdot 1} = \frac{4}{9}$$
2. $$\frac{8}{9} \cdot \frac{1}{8} = \frac{8 \cdot 1}{9 \cdot 8} = \frac{1 \cdot 1}{9 \cdot 1} = \frac{1}{9}$$
3. $$4\frac{4}{7} \cdot \frac{3}{8} = \frac{4\cdot7+4}{7} \cdot \frac{3}{8} = \frac{32}{7} \cdot \frac{3}{8} = \frac{32 \cdot 3}{7 \cdot 8} = \frac{4 \cdot 3}{7 \cdot 1} = \frac{12}{7} = 1\frac{5}{7}$$
4. $$\frac{7}{8} \cdot 4 = \frac{7 \cdot 4}{8} = \frac{7 \cdot 1}{2} = \frac{7}{2} = 3\frac{1}{2}$$
5. $$\frac{5}{6} \cdot \frac{5}{9} = \frac{5 \cdot 5}{6 \cdot 9} = \frac{25}{54}$$

Ответы:

1. $$\frac{4}{9}$$
2. $$\frac{1}{9}$$
3. $$1\frac{5}{7}$$
4. $$3\frac{1}{2}$$
5. $$\frac{25}{54}$$