An ant stands at one vertex of a rectangular 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.
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To find the distance the ant travels, we need to calculate the perimeter of the rectangle.
The length of the rectangle is 3 5/8 inches or 29/8 inches.
The width of the rectangle is 2 7/8 inches or 23/8 inches.
To find the perimeter, we add the lengths of all four sides of the rectangle:
Perimeter = 2 * (Length + Width)
Perimeter = 2 * (29/8 + 23/8)
Perimeter = 2 * (52/8)
Perimeter = 2 * 6.5
Perimeter = 13 inches
Therefore, the ant travels 13 inches around the perimeter of the rectangle.
can you make that easier
To find out how many inches the ant travels, we need to calculate the perimeter of the rectangular sheet of paper.
First, let's convert the dimensions of the sheet of paper from mixed numbers to improper fractions for easier calculation:
3 5/8 inches = (3 * 8 + 5)/8 = 29/8 inches
2 7/8 inches = (2 * 8 + 7)/8 = 23/8 inches
Now, we can calculate the perimeter of the rectangular sheet of paper:
Perimeter = 2 * (Length + Width)
Length = 29/8 inches
Width = 23/8 inches
Perimeter = 2 * (29/8 + 23/8)
= 2 * (29 + 23)/8
= 2 * 52/8
= 104/8
= 13 inches
Therefore, the ant travels 13 inches around the perimeter of the rectangular sheet of paper.
To find the total distance traveled by the ant, we need to calculate the perimeter of the rectangular sheet of paper. The perimeter of a rectangle is given by the formula P = 2L + 2W, where L is the length of the rectangle and W is the width.
In this case, the length (L) of the rectangular sheet is 3 5/8 inches and the width (W) is 2 7/8 inches.
To add mixed numbers, we need to convert them to improper fractions. 3 5/8 can be written as (3*8 + 5)/8 = 29/8, and 2 7/8 can be written as (2*8 + 7)/8 = 23/8.
Now we can substitute these values into the formula P = 2L + 2W:
P = 2(29/8) + 2(23/8)
P = 58/8 + 46/8
P = (58 + 46)/8
P = 104/8
P = 13
So the perimeter of the rectangular sheet of paper is 13 inches.
Therefore, the ant travels a total distance of 13 inches around the perimeter of the paper.