1. (6 points) Calculate: $\frac{2 \frac{1}{4}+0.25}{2 \frac{3}{4}-\frac{1}{2}}+\frac{2 \times 0.5}{2 \frac{1}{5}-\frac{2}{5}}=$
【Analysis】We can first simplify the original expression by calculating the numerator and denominator separately, and then obtain the final result.
【Solution】According to the analysis, the original expression is $=\frac{2 \frac{1}{4}+0.25}{2 \frac{3}{4}-\frac{1}{2}}+\frac{2 \times 0.5}{2 \frac{1}{5}-\frac{2}{5}}$
$$
\begin{array}{l}
=\frac{\frac{9}{4}+\frac{1}{4}}{\frac{11}{4}-\frac{1}{2}}+\frac{1}{\frac{11}{5}-\frac{2}{5}}=\frac{\frac{5}{2}}{\frac{11}{4}-\frac{2}{4}}+\frac{5}{9} \\
=\frac{5}{2} \times \frac{4}{9}+\frac{5}{9} \\
=\frac{10}{9}+\frac{5}{9} \\
=\frac{15}{9} \\
=\frac{5}{3}
\end{array}
$$

Therefore, the answer is: $\frac{5}{3}$.