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.
1
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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