If the rise of a roof is 8 feet and the run is 2 feet 8 inches, what is the pitch of the roof in lowest terms when written as a FRACTION?

change both measures to inches, then form rise/run and reduce to lowest terms

8 feet = 96 inches

2 feet 8 inches = 24+8= 32

so is it 32/96

which equals 1/3

To find the pitch of a roof in lowest terms when written as a fraction, we need to determine the ratio of the rise (vertical height) to the run (horizontal distance).

Given that the rise of the roof is 8 feet and the run is 2 feet 8 inches, we need to ensure that the units are consistent. Since 2 feet 8 inches is equivalent to 2.67 feet (1 foot = 12 inches), we can proceed with the calculation.

The pitch of the roof is calculated by dividing the rise (in feet) by the run (in feet). Therefore, the pitch can be determined as follows:

Pitch = Rise / Run

Pitch = 8 feet / 2.67 feet

To simplify this fraction, we can divide both the numerator and denominator by their greatest common divisor (GCD). In this case, the GCD of 8 and 2.67 is 1.

Pitch = (8 / 1) / (2.67 / 1)

Pitch = 8 / 2.67

Converting the decimal to a fraction, we have:

Pitch ≈ 8 / (2 67/100)

Multiplying both the numerator and denominator by 100 to remove the decimal:

Pitch ≈ (8 * 100) / (2 * 67)

Pitch ≈ 800 / 134

Finally, we should simplify the fraction by dividing both the numerator and denominator by their GCD, which is 2:

Pitch = (800 / 2) / (134 / 2)

Pitch ≈ 400 / 67

Hence, the pitch of the roof, when written as a fraction in lowest terms, is 400/67.