$AE$ divides rectangle $ABCD$ into two parts such that the ratio of the area of $\triangle ADE$ to the area of quadrilateral $ABCE$ is 1:4. Find the ratio of $DE$ to $EC$. Express your answer as a common fraction.

4 *Area of ADE = (1/2) AD * DE =

Area of quadrilateral ABCE = (1/2)(AD) (AB + EC)

4 (1/2) AD * DE = (1/2) (AD) (AB + EC)

4DE = AB + EC

4DE = (DE + EC) + EC

3 DE = 2 EC

DE / EC = 2 / 3