$\text{a)}\frac{1}{4}:\frac{3}{8}=\frac{1}{{\sout{4}}^1}\cdot \frac{{\sout{8}}^2}{3}=\frac{2}{3}$

$\text{b)}\frac{4}{9}:\frac{8}{15}=\frac{{\sout{4}}^1}{{\sout{9}}^3}\cdot \frac{{\sout{15}}^5}{{\sout{8}}^2}=\frac{5}{6}$