54. \(\frac{3}{8}\) : \(\frac{1}{9}\) : \(\frac{5}{16}\)

1. First division: $$\frac{3}{8} : \frac{1}{9} = \frac{3}{8} \cdot 9 = \frac{27}{8}$$.
2. Second division: $$\frac{27}{8} : \frac{5}{16} = \frac{27}{8} \cdot \frac{16}{5} = \frac{27 \cdot 2}{5} = \frac{54}{5}$$.
3. Convert to mixed number: $$\frac{54}{5} = 10 \frac{4}{5}$$.