Решение:
\[ 1 \frac{1}{8} = \frac{1 \times 8 + 1}{8} = \frac{9}{8} \]
\[ -3 \frac{3}{8} = -\frac{3 \times 8 + 3}{8} = -\frac{27}{8} \]
\[ \frac{9}{8} \div \left(-\frac{27}{8}\right) = \frac{9}{8} \times \left(-\frac{8}{27}\right) = -\frac{9 \times 8}{8 \times 27} = -\frac{9}{27} \]
\[ -\frac{9}{27} = -\frac{1}{3} \]
Ответ: - \frac{1}{3}