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.
Morgan
To find the perimeter of the rectangular sheet of paper, we need to add up the lengths of all four sides.
The length of the top side is 3 5/8 inches.
The length of the bottom side is also 3 5/8 inches.
The length of the left side is 2 7/8 inches.
The length of the right side is also 2 7/8 inches.
To find the perimeter, we add up all four side lengths:
Perimeter = 3 5/8 + 3 5/8 + 2 7/8 + 2 7/8
First, we add the whole numbers:
Perimeter = 3 + 3 + 2 + 2 = 10
Next, we add the fractions.
Perimeter = 5/8 + 5/8 + 7/8 + 7/8
Since the denominators of all four fractions are the same, we can simply add the numerators:
Perimeter = (5 + 5 + 7 + 7)/8 = 24/8
We can simplify 24/8 by dividing both the numerator and denominator by their greatest common factor, which is 8:
24 ÷ 8 = 3
Therefore, 24/8 = 3.
So, the perimeter of the rectangular sheet of paper is 10 inches.
Therefore, the ant travels 10 inches.
I apologize for the mistake in my previous response. Let's calculate the correct perimeter.
The length of the top side is 3 5/8 inches.
The length of the bottom side is also 3 5/8 inches.
The length of the left side is 2 7/8 inches.
The length of the right side is also 2 7/8 inches.
To find the perimeter, we add up all four side lengths:
Perimeter = 3 5/8 + 3 5/8 + 2 7/8 + 2 7/8
First, we add the whole numbers:
Perimeter = 3 + 3 + 2 + 2 = 10
Next, we add the fractions:
Perimeter = 5/8 + 5/8 + 7/8 + 7/8 = 24/8
We can simplify 24/8 by dividing both the numerator and denominator by their greatest common factor, which is 8:
24 ÷ 8 = 3
Therefore, 24/8 = 3.
So, the perimeter of the rectangular sheet of paper is 10 inches.
Therefore, the ant travels 10 inches.
are u sure
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 4 6/9 inches by 3 8/9 inches. How many inches does the ant travel? Show your work.
Morgan
To find the perimeter of the rectangular sheet of paper, add up the lengths of all four sides.
The length of the top side is 4 6/9 inches.
The length of the bottom side is also 4 6/9 inches.
The length of the left side is 3 8/9 inches.
The length of the right side is also 3 8/9 inches.
To find the perimeter, add up all four side lengths:
Perimeter = 4 6/9 + 4 6/9 + 3 8/9 + 3 8/9
First, add the whole numbers:
Perimeter = 4 + 4 + 3 + 3 = 14
Next, add the fractions:
Perimeter = 6/9 + 6/9 + 8/9 + 8/9
Since the denominators of all four fractions are the same, we can simply add the numerators:
Perimeter = (6 + 6 + 8 + 8)/9 = 28/9
We can simplify 28/9 by dividing both the numerator and denominator by their greatest common factor, which is 1:
28 ÷ 1 = 28
9 ÷ 1 = 9
Therefore, 28/9 cannot be further simplified.
So, the perimeter of the rectangular sheet of paper is 14 inches + 28/9 inches.
To convert the improper fraction 28/9 to a mixed number, divide the numerator (28) by the denominator (9):
28 ÷ 9 = 3 remainder 1
So, 28/9 can be written as 3 1/9.
Now, add the mixed number 3 1/9 to the whole number 14:
14 + 3 1/9 = 17 1/9
Therefore, the ant travels 17 1/9 inches.
what is 3 5/8 increased by one inch
To find 3 5/8 increased by one inch, we add 1 inch to the whole number and fraction separately.
First, we increase the whole number:
3 + 1 = 4
Next, we increase the fraction:
5/8 + 1/8 = 6/8
Since the fraction 6/8 can be simplified, we divide both the numerator and denominator by their greatest common factor, which is 2:
6 ÷ 2 = 3
8 ÷ 2 = 4
Therefore, 6/8 simplifies to 3/4.
Now we have 4 + 3/4.
To combine the whole number and fraction, we convert the whole number 4 to a fraction with the same denominator as the fraction:
4 = 4/1
Now, we add the two fractions:
4/1 + 3/4 = 16/4 + 3/4 = 19/4
We can simplify 19/4 by dividing both the numerator and denominator by their greatest common factor, which is 1:
19 ÷ 1 = 19
4 ÷ 1 = 4
Therefore, 19/4 cannot be further simplified.
So, 3 5/8 increased by one inch is equal to 19/4 inches.