Pop Question #1

    An algorithm for interconverting degrees C and degrees F.


     You have (hopefully) learned the formulas for temperature
conversion:

               deg C = 5/9(deg F - 32)

               deg F = 9/5 deg C  + 32

     These are relatively simple, but unless you have the formula
memorized, it is easy to forget whether you add or subtract 32
before multiplying by 5/9 or 9/5.  Following is an algorithm (i.e.
stepwise calculation) that avoids that problem.  All you have to
remember is that going from C to F, you multiply by 9/5 (F degrees
are smaller, so there are more of them), and in going from F to C
you multiply by 5/9.

          Algorithm

     Add 40 
     Multiply by 9/5 if changing deg C to deg F
  or Multiply by 5/9 if changing deg F to deg C
     Subtract 40 

     Now, explain in fairly simple terms why this algorithm works.