Answer: $\frac7{15}$

All three fractions are just under $\frac{1}{2}$.

$\frac{7}{15}$ is $\frac{1}{2}-\frac{1}{30}$

$\frac{4}{9}$ is $\frac{1}{2}-\frac{1}{18}$

$\frac{5}{11}$ is $\frac{1}{2}-\frac{1}{22}$

So $\frac{7}{15}$ is the largest.