The value of $3\frac{1}{3}-[\frac{9}{4}+\begin{Bmatrix}\frac{5}{4}-\frac{1}{13}×(\frac{5}{2}-\frac{1}{3})\end{Bmatrix}]$ is:

0

$3\frac{1}{3}-[\frac{9}{4}+\begin{Bmatrix}\frac{5}{4}-\frac{1}{13}×(\frac{5}{2}-\frac{1}{3})\end{Bmatrix}]$

= $\frac{10}{3}-[\frac{9}{4}+\begin{Bmatrix}\frac{5}{4}--\frac{1}{13}×\frac{13}{6}\end{Bmatrix}]$

= $\frac{10}{3}-[\frac{9}{4}+\frac{13}{12}]$

= $\frac{10}{3}-[\frac{40}{12}]$

= 0