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(1)/(4)}\implies\cfrac{8\cdot 4+1}{4}\implies \stackrel{improper}{\cfrac{33}{4}} \\\\\\ \cfrac{\quad (33)/(4)\quad }{(1)/(2)}\implies \cfrac{33}{4}\cdot \cfrac{2}{1}\implies \cfrac{33}{2}\cdot \cfrac{1}{1}\implies \cfrac{33}{2}\implies 16(1)/(2)`

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