jmc

The area of triangle $ADE$ is $\frac{1}{2}(10)(2)=10$ square units, and the area of rectangle $ABCD$ is $(6)(10)=60$ square units. Subtracting, we find that the area of $ABCE$ is 50 square units. Therefore, the ratio of the area of triangle $ADE$ to the area of quadrilateral $ABCE$ is $10/50=\boxed{\frac{1}{5}}$.