2. (3 points) $a$ and $b$ are non-zero natural numbers. If $\frac{\mathrm{a}}{\mathrm{b}}<\frac{\mathrm{a}+1}{\mathrm{~b}+1}$, then ( )
A. $\frac{\mathrm{a}}{\mathrm{b}}$ is an improper fraction
B. $\frac{\mathrm{b}}{\mathrm{a}}$ is a proper fraction
C. $\frac{2012 \mathrm{a}}{\mathrm{b}}$ is an improper fraction
【Analysis】$a$ and $b$ are non-zero natural numbers. If $\frac{a}{b}<\frac{a+1}{b+1}$, after removing the denominators from the inequality, we get $a b+a<a b+b$. Subtracting $a b$ from both sides of the inequality, we can determine that $a<b$. Then, based on the relationship between $a$ and $b$, we can solve the problem.

【Solution】Solution: $\frac{a}{b}<\frac{a+1}{b+1}$,
$$
\begin{aligned}
a b+a & <a b+b, \\
a & <b ;
\end{aligned}
$$

Therefore, $\frac{a}{b}$ is a proper fraction; $\frac{b}{a}$ is an improper fraction, eliminating options $A$ and $B$, so the correct choice is $C$.

Hence, the answer is: $C$.