\[\frac{2\frac{1}{4}}{1\frac{3}{8}} = 2\frac{1}{4}\ :1\frac{3}{8} = \frac{9}{4}\ :\frac{11}{8} = \frac{9}{4} \cdot \frac{8}{11} =\]
\[= \frac{9 \cdot 2 \cdot 4}{4 \cdot 11} = \frac{18}{11} = 1\frac{7}{11}\]