Question

you're on a residential construction team doing Roofing. the pitch of a roof is 1 / 3 rise over run. Find the rise if the horizontal run of the roof is 15 ft 3/4 in.

Answer 1

first off, let's conver the mixed fraction to an improper one, and then check the proportions.

$\bf \stackrel{mixed}{15\frac{3}{4}}\implies \cfrac{15\cdot 4+3}{4}\implies \stackrel{improper}{\cfrac{63}{4}}\\\\ -------------------------------$

$\bf \cfrac{rise}{run}=\cfrac{1}{3}\qquad \qquad \cfrac{\quad rise\quad }{\stackrel{run}{\frac{63}{4}}}=\cfrac{1}{3}\implies \cfrac{\quad \frac{rise}{1}\quad }{\frac{63}{4}}=\cfrac{1}{3} \\\\\\ \cfrac{rise}{1}\cdot \cfrac{4}{63}=\cfrac{1}{3}\implies \cfrac{4rise}{63}=\cfrac{1}{3}\implies rise=\cfrac{63}{4\cdot 3} \\\\\\ rise=\cfrac{21}{4}\implies rise=5\frac{1}{4}$

Answer 2

The rise is 60 1/4 in. Hope this helps.