Allen is building birdhouses that require 1/2-foot-long boards. how many pieces that are exactly 1/2 ft long can be made from a board that is 8 1/4 ft long?

Hello!

Since you have a board that is 8 and 1/4 feet long, the easy way to calculate how many 1/2 feet are on 8 feet is two multiply 8 x 2, since there are two halves of a foot, in one foot (because two halves equal one whole). Now this may sound confusing but we can double check.
   
   |       |          As we can see here, there are two rows, each with 8 halves.
  V      V          So now we multiply 8 x 2 and get 16.
1/2 + 1/2 = 1
1/2 + 1/2 = 1
1/2 + 1/2 = 1
1/2 + 1/2 = 1
1/2 + 1/2 = 1      
1/2 + 1/2 = 1
1/2 + 1/2 = 1
1/2 + 1/2 = 1
                  ^-- Now if you add all of these, it's 8, proving that you can do 8 x 2

Yes, you may be asking, "What about the 1/4?" Don't worry about it! Questions like this try to trick you into making it more complicated, it asks how many halves are in 8 and 1/4, but 1/4 isn't enough to make a half so we leave it alone.