Question

allen is building birdhouses that require 1/2-ft-long boards. How many piece that are exactly 1/2 ft long can be made from a board that is 8 1/4 ft long?

Answer 1

You can get 9 boards at 1\2 ft each

Answer 2

Namely, how many times does ½ goes into 8¼.

well, we'll first change the mixed fraction to an "improper" one and then do the division,

$\bf \stackrel{mixed}{8\frac{1}{4}}\implies\cfrac{8\cdot 4+1}{4}\implies \stackrel{improper}{\cfrac{33}{4}} \\\\\\ \cfrac{\quad \frac{33}{4}\quad }{\frac{1}{2}}\implies \cfrac{33}{4}\cdot \cfrac{2}{1}\implies \cfrac{33}{2}\cdot \cfrac{1}{1}\implies \cfrac{33}{2}\implies 16\frac{1}{2}$

so, nevermind the fraction bit, only 16 whole ones.