1. (10 points) $84 \frac{4}{19} \times 1.375 + 105 \frac{5}{19} \times 0.9$.
【Analysis】In the four arithmetic operations, multiplication and division are performed before addition and subtraction. It is simpler to convert the decimals in this problem into fractions and then use the rules of fraction multiplication for calculation.

【Solution】Solution:
$$
\begin{array}{l}
84 \frac{4}{19} \times 1.375+105 \frac{5}{19} \times 0.9 . \\
=\frac{1600}{19} \times \frac{11}{8}+\frac{2000}{19} \times \frac{9}{10} \\
=\frac{2200}{19}+\frac{1800}{19} \\
=\frac{4000}{19} \\
=210 \frac{10}{19}
\end{array}
$$

Therefore, the answer is: $210 \frac{10}{19}$