A ridge beam rises 18 in. over a horizontal run of 72 in. Calculate the pitch of the roof and express it as a fraction with a denominator of 12.
To calculate the pitch of the roof, we need to find the vertical rise per horizontal run, which is commonly expressed as a ratio. In this case, the rise is 18 in., and the run is 72 in.
To convert this ratio to a fraction, we need to simplify it down to the lowest terms. First, let's divide both the rise and run by their greatest common divisor (GCD). In this case, the GCD of 18 and 72 is 18. So, dividing both by 18, we get:
18 in. ÷ 18 = 1 in.
72 in. ÷ 18 = 4 in.
Now, we have a rise of 1 in. over a run of 4 in.
To express it as a fraction with a denominator of 12, we need to find an equivalent fraction by multiplying both the numerator and denominator by the same factor. In this case, we can multiply both by 3 to get:
1 in. * 3 = 3 in.
4 in. * 3 = 12 in.
Therefore, the pitch of the roof is 3/12 when expressed as a fraction with a denominator of 12.