1. (10 points) The value of the expression $\frac{3}{2} \times\left[2 \frac{2}{3} \times\left(1.875-\frac{5}{6}\right)\right] \div\left[\left(0.875+1 \frac{5}{6}\right) \div 3 \frac{1}{4}\right]$ is
5
【Analysis】Solve according to the order of operations for mixed arithmetic of fractions, note to convert mixed numbers to improper fractions, and decimals to fractions for easier calculation.
【Solution】Solve: $\frac{3}{2} \times\left[2 \frac{2}{3} \times\left(1.875-\frac{5}{6}\right)\right] \div\left[\left(0.875+1 \frac{5}{6}\right) \div 3 \frac{1}{4}\right]$
$$
\begin{array}{l}
=\frac{3}{2} \times \frac{8}{3} \times\left(\frac{15}{8}-\frac{5}{6}\right) \div\left[\left(\frac{7}{8}+\frac{11}{6}\right) \times \frac{4}{13}\right] \\
=4 \times \frac{25}{24} \div\left[\left(\frac{7}{8}+\frac{11}{6}\right) \times \frac{4}{13}\right] \\
=\frac{25}{6} \div\left[\frac{65}{24} \times \frac{4}{13}\right] \\
=\frac{25}{6} \div \frac{5}{6} \\
=5
\end{array}
$$

Therefore, the answer is: 5.