A boy is mowing a rectangular lawn 40ft long and 30ft wide. He has cut all of it except for a rectangle that is 20ft long and 15ft wide. What fractional part of the lawn remains uncut?
I need helping figuring out how to solve this. My answer sheet says its 1/4 but I don't know how to solve for it. I need to know how to solve this problem. Please explain, thank you.
A = 40 * 30
A = 1,200 square feet
A = 20 * 15
A = 300 square feet uncut
300/1200 = 3/12 = 1/4
To solve this problem, we need to find the area of the uncut rectangle and then compare it to the total area of the lawn.
Step 1: Find the area of the uncut rectangle.
The area of a rectangle is calculated by multiplying its length by its width. In this case, the length of the uncut rectangle is 20ft and its width is 15ft. Therefore, the area of the uncut rectangle is:
Area of uncut rectangle = Length × Width = 20ft × 15ft = 300ft²
Step 2: Find the total area of the lawn.
The total area of the lawn is also obtained by multiplying its length by its width. In this case, the length of the lawn is 40ft and its width is 30ft. Therefore, the total area of the lawn is:
Total area of lawn = Length × Width = 40ft × 30ft = 1200ft²
Step 3: Find the fractional part of the lawn that remains uncut.
To find the fractional part, divide the area of the uncut rectangle by the total area of the lawn and simplify the result to its simplest form.
Area of uncut rectangle / Total area of lawn = 300ft² / 1200ft²
To simplify the fraction, we can divide both the numerator and denominator by their greatest common divisor, which is 100ft².
300ft² / 1200ft² = (300ft² ÷ 100ft²) / (1200ft² ÷ 100ft²) = 3/12
Since 3/12 can be further simplified, we divide both numerator and denominator by their greatest common divisor, which is 3.
3/12 = (3 ÷ 3) / (12 ÷ 3) = 1/4
Therefore, the fractional part of the lawn that remains uncut is 1/4.
To solve this problem, you'll need to find the area of the remaining uncut rectangle and compare it to the area of the entire lawn.
The area of a rectangle is found by multiplying its length by its width.
1. Calculate the area of the entire lawn:
Area of the entire lawn = 40 ft x 30 ft
2. Calculate the area of the remaining uncut rectangle:
Area of the remaining uncut rectangle = 20 ft x 15 ft
3. Divide the area of the remaining uncut rectangle by the area of the entire lawn to find the fractional part:
Fractional part = Area of the remaining uncut rectangle / Area of the entire lawn
Simplify the fraction if necessary.
Let's calculate everything step by step:
1. Calculate the area of the entire lawn:
Area of the entire lawn = 40 ft x 30 ft
Area of the entire lawn = 1200 square feet
2. Calculate the area of the remaining uncut rectangle:
Area of the remaining uncut rectangle = 20 ft x 15 ft
Area of the remaining uncut rectangle = 300 square feet
3. Divide the area of the remaining uncut rectangle by the area of the entire lawn:
Fractional part = Area of the remaining uncut rectangle / Area of the entire lawn
Fractional part = 300 sq ft / 1200 sq ft
Simplify the fraction:
Fractional part = 1/4
So, the fractional part of the lawn that remains uncut is 1/4.