Question

You have a 32-foot fence around a square garden. There are 4 equal sections. You paint 13 of one section of the fence.

What fraction of the fence did you paint?

Answer 1

Question:

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

Answer:

The fraction of the fence painted is $\frac{1}{12}$

Solution:

Given that:

You have a 32-foot fence around a square garden. There are 4 equal sections

Find the length of each section:

4 sections = 32 foot

$\text{ 1 section } = 32 \div 4 = 8 foot$

Find the length that is painted:

$\text{ Fence painted }= \frac{1}{3} \text{ of one section }\\\\\text{ Fence painted }= \frac{1}{3} \times 8 = \frac{8}{3} \text{ foot }$

Therefore $\frac{8}{3}$ foot of fence is painted

Find the fraction that that is painted:

Total length of fence = 32

$\text{ Fraction of the fence painted } = \frac{8}{3} \div 32 = \frac{8}{3} \times \frac{1}{32}\\\\\text{ Fraction of the fence painted } = \frac{1}{12}$

Therefore $\frac{1}{12}$ fraction of the fence is painted