Question

You have a 32 32 -foot fence around a square garden. There are 4 4 equal sections. You paint 13 1 3 of one section of the fence. What fraction of the fence did you paint?

Answer 1

Answer: The answer is one-twelveth.

Step-by-step explanation:  Given that we have a 32 feet fence around a square garden ABCD as shown in the attached figure.

There are four equal sections AB = BC = BD = DA of the fence.

If we paint one-third of one section, then we need to find what fraction of the total fence we painted.

Since ABCD is a square, so AB = BC = CD = DA = 8 feet.

Let we paint one-third of section AB. so, the part of AB we painted is

$P_{AB}=\dfrac{1}{3}\times AB=\dfrac{8}{3}~\textup{feet}.$

Therefore, the fraction of the fence that we painted is given by

$P_{fence}=\dfrac{\frac{8}{3}}{32}=\dfrac{8}{3}\times \dfrac{1}{32}=\dfrac{1}{12}.$  

Thus, we painted one -twelveth of the total fence.