An ant stands at one vertex of a rectangle sheet of paper. The ant then proceeds to walk all the way around the perimeter of the paper. The dimensions of the sheet of paper are 3 5/8 inches by 2 7/8 inches. How many inches does the ant travel? Show your work.
To find the perimeter of the rectangle, we add up the lengths of all four sides.
The length of the rectangle is 3 5/8 inches, or $\frac{29}{8}$ inches.
The width of the rectangle is 2 7/8 inches, or $\frac{23}{8}$ inches.
The perimeter is then $2\left(\frac{29}{8}\right) + 2\left(\frac{23}{8}\right) = \frac{58}{8} + \frac{46}{8} = \frac{104}{8} = \boxed{13}$ inches.
To find the total distance the ant travels around the perimeter of the paper, we need to calculate the sum of all four sides.
First, let's convert the dimensions of the paper to a common fraction.
The length is 3 5/8 inches, which is equal to (3 * 8 + 5) / 8 = 29/8 inches.
The width is 2 7/8 inches, which is equal to (2 * 8 + 7) / 8 = 23/8 inches.
Now let's calculate the distance traveled by the ant:
1. The ant walks along the length twice, so the distance traveled is 2 * length = 2 * 29/8 inches = 58/8 inches.
2. The ant walks along the width twice, so the distance traveled is 2 * width = 2 * 23/8 inches = 46/8 inches.
3. To find the total distance, we add the distances from step 1 and step 2: 58/8 inches + 46/8 inches = 104/8 inches.
Simplifying the fraction 104/8, we get 13/1 inches.
Therefore, the ant travels 13 inches around the perimeter of the paper.