Решение:
1) $$3 \frac{3}{8} : \frac{1}{8} = \frac{3 \cdot 8 + 3}{8} : \frac{1}{8} = \frac{27}{8} : \frac{1}{8} = \frac{27}{8} \cdot \frac{8}{1} = 27$$
2) $$1 \frac{5}{14} \cdot 7 = \frac{1 \cdot 14 + 5}{14} \cdot 7 = \frac{19}{14} \cdot 7 = \frac{19 \cdot 7}{14} = \frac{19 \cdot 1}{2} = \frac{19}{2} = 9 \frac{1}{2}$$
3) $$27 - 9 \frac{1}{2} = 27 - 9 - \frac{1}{2} = 18 - \frac{1}{2} = 17 \frac{1}{2}$$
Ответ: $$17 \frac{1}{2}$$