\( 1 \frac{1}{8} = \frac{8 \cdot 1 + 1}{8} = \frac{9}{8} \)
\( -3 \frac{3}{8} = -\frac{8 \cdot 3 + 3}{8} = -\frac{27}{8} \)
\( \frac{9}{8} : \left(-\frac{27}{8}\right) = \frac{9}{8} \times \left(-\frac{8}{27}\right) \)
\( \frac{9 \times (-8)}{8 \times 27} = \frac{9 \times (-1)}{1 \times 27} = \frac{-9}{27} \)
\( -\frac{1}{3} \)
Ответ: -\( \frac{1}{3} \)