7. (10 points) If $\left[\frac{1}{1+\frac{24}{4}}-\frac{5}{9}\right] \times \frac{3}{2 \frac{5}{7}} \div \frac{2}{3 \frac{3}{4}}+2.25=4$, then the value of $A$ is
【Analysis】First, simplify the complex fraction, derive the equation about the unknown $A$, and then solve the equation according to the properties of equations.
【Solution】Solve: $\left[\frac{1}{1+\frac{5}{\mathrm{~A}}}-\frac{5}{9}\right] \times \frac{3}{2 \frac{5}{7}} \div \frac{2}{3 \frac{3}{4}}+2.25=4$
$$
\begin{array}{l}
{\left[\frac{24+\mathrm{A}}{5 \mathrm{~A}}-\frac{5}{9}\right] \times \frac{21}{19} \div \frac{8}{15}+2.25=4} \\
{\left[\frac{24+\mathrm{A}}{5 \mathrm{~A}}-\frac{5}{9}\right] \times \frac{21}{19} \div \frac{8}{15}=\frac{7}{4}} \\
{\left[\frac{24+\mathrm{A}}{5 \mathrm{~A}}-\frac{5}{9}\right] \times \frac{315}{152}=\frac{7}{4}}
\end{array}
$$
$$
\begin{array}{r}
\frac{24+A}{5 A}-\frac{5}{9}=\frac{7}{4} \times \frac{152}{315} \\
\frac{24+A}{5 A}-\frac{5}{9}=\frac{38}{45} \\
\frac{24+A}{5 A}=\frac{38}{45}+\frac{5}{9} \\
\frac{24+A}{5 A}=\frac{7}{5} \\
24=6 A \\
A=4
\end{array}
$$

Therefore, the answer is: 4.