What is the ratio of the numerical value of the area, in square units, of an equilateral triangle of side length 4 units to the numerical value of its perimeter, in units? Express your answer as a common fraction in simplest radical form.
The area of this equilateral triangle is $\frac{4^2 \sqrt{3}}{4}$, and the perimeter is $3 \cdot 4 = 12$. Thus, the ratio of area to perimeter is $\frac{\frac{4^2 \sqrt{3}}{4}}{12}=\boxed{\frac{\sqrt{3}}{3}}$.