Simple Example of Canceling Units

If you know the units of conversion factors, and that anything divided by itself is equal to 1, with a little common sense you can figure out a lot. For example, maybe you can't remember the equation to compute gas mileage, but you know you are looking for "miles per gallon." So if you went 200 miles on 10 gallons, you would divide 200 miles by 10 gallons (or multiply by the inverse of 10) for your miles-per-gallon result.

   200 miles  X   ----------  =  20 miles per gallon
                  10 gallons   
That's simple enough, but let's say you are in Europe and they put in 40 liters. You're guide book says there are 3.785 liters per gallon. You want to get gallons in the denominator (you know, because it's "per"), so you multiply by this conversion factor. Then you have to get rid of liters, so you have to divide by the number of liters put in the car (or multiply by the "inverse"). i.e.,

                 3.785 liters         1
   200 miles  X  ------------  X  ---------  =  18.925 miles per gallon
                   1 gallon       40 liters

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