<image>A square piece of paper, 4 inches on a side, is folded in half vertically. Both layers are then cut in half parallel to the fold. Three new rectangles are formed, a large one and two small ones. What is the ratio of the perimeter of one of the small rectangles to the perimeter of the large rectangle?
A. $\frac{1}{3}$
B. $\frac{1}{2}$
C. $\frac{3}{4}$
D. $\frac{4}{5}$
E. $\frac{5}{6}$