# Don’t multiply yet!

Suppose you are trying to solve the following problem:

If , what is the value of ?

Here is one (bad) option for solving the problem:  (Multiply everything together) (Divide both sides by 2184) (Divide both sides by ) (Simplify.)

This method produces the correct answer, 8, but it requires a lot of complex arithmetic, which wastes time and increases the likelihood of mistakes.

Here is a better way to solve it:  (Divide both sides by } (Divide both sides by ) (Simplify.)

Notice that in the last line of this solution, I divided the bottom numbers into the top numbers first instead of multiplying everything together. Dividing 24 by 12, 26 by 13, and 28 by 14 is a whole lot easier than multiplying 12 by 13 by 14 and 24 by 26 by 28 and then dividing 17,472 by 2,184. Â The principle that we are exploiting is simple: smaller numbers are easier to work with. Â And, generally, division produces smaller numbers than multiplication. Â Hence, the title of this entry. Â Don’t be in a rush to multiply everything together. Keep the numbers in factored form, and simplify anything you can with division first. Â Don’t multiply until the end.