Arectangular park has an area of 2/3 square mile. the length of the park is 2 2/3 the width of the park. what is the width of the park?

The width is 1/2 mi.

We know that area of a rectangle is length times width:

A = lw

The length is 2 2/3 the width, so 
l = 2 2/3w

We will change this to an improper fraction; multiply the denominator by the whole number and add the numerator:
l = 8/3w

Using this for l in the area formula, we have:
A = (8/3w)(w) = 8/3w²
2/3 = 8/3w²

Divide both sides by 8/3:

2/3÷8/3 = 8/3w²÷8/3
2/3×3/8 = w²
2/8 = w²
0.25 = w²

Take the square root of both sides:
√0.25 = √w²
0.5 = w