A rectangle is eleven and two-thirds centimeters long. Its width is seven and six-sevenths centimeters. The length of this rectangle is how much longer than its width?
We need to subtract the width from the length to find the difference.
Eleven and two-thirds minus seven and six-sevenths can be tricky to do in our head, so let's convert these mixed numbers to improper fractions first:
- Eleven and two-thirds can be written as 11 + 2/3 = (33/3) + (2/3) = 35/3
- Seven and six-sevenths can be written as 7 + (6/7) = (49/7) + (6/7) = 55/7
Now we can subtract:
35/3 - 55/7
To do this, we need to find a common denominator. One way to do this is to multiply the two denominators together:
3 × 7 = 21
So we need to convert both fractions to have a denominator of 21.
35/3 × 7/7 = 245/21
55/7 × 3/3 = 165/21
Now we can subtract:
245/21 - 165/21 = 80/21
This is the difference between the length and width of the rectangle. But we should also simplify the fraction:
80/21 = 3 and 17/21
So the length of the rectangle is three and seventeen twenty-firsts centimeters longer than its width.
To find out how much longer the length of the rectangle is than its width, we can subtract the width from the length.
Given:
Length = 11 and 2/3 centimeters
Width = 7 and 6/7 centimeters
Step 1: Convert the mixed numbers to improper fractions.
11 and 2/3 = (11 * 3 + 2) / 3 = 35/3
7 and 6/7 = (7 * 7 + 6) / 7 = 55/7
Step 2: Subtract the width from the length.
35/3 - 55/7
To subtract fractions, we need to find the common denominator, which is 3 * 7 = 21.
(35/3) * (7/7) = 245/21
(55/7) * (3/3) = 165/21
So, 35/3 - 55/7 = 245/21 - 165/21 = (245 - 165) / 21 = 80/21
Step 3: Simplify the fraction, if possible.
To simplify 80/21, we can find the greatest common divisor (GCD) of 80 and 21, which is 1.
80/21 ÷ 1/1 = 80/21
So, the length of the rectangle is 80/21 centimeters longer than its width.