2. (7 points) As shown in the figure, the area of rectangle $A B C D$ is $1, M$ is the midpoint of side $A D$, and $N$ is on side $A B$ such that $A N=\frac{1}{2} B N$. Then, the area of the shaded part is $\qquad$

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【Solution】The area of $\triangle A N M$:
$$
1 \times \frac{1}{2} \times \frac{1}{2} \times \frac{1}{3}=\frac{1}{12} \text {; }
$$
The area of $\triangle_{A B D}$:
$$
1 \times \frac{1}{2}=\frac{1}{2} \text {; }
$$

The area of the shaded part:
$$
\frac{1}{2}-\frac{1}{12}=\frac{5}{12} \text {. }
$$

Therefore, the answer is: $\frac{5}{12}$.