The Factor Label Method of Problem Solving

The factor label method of problem solving is the backbone of most chemistry calculations. This method can be used to do everything from converting 16.8 feet to meters to determining the mass of sodium sulfate needed to precipitate all of the barium from 120.0mL of 3.88 M solution of barium nitrate. (No, you aren’t supposed to have any idea what that means right now. I bring it up because I want you to be just scared enough to pay attention to this section, since it is, perhaps, the most important part of this unit.)

The big idea

There are several ideas behind the Factor Label method. The most important is that

If you have an amount of something and you want to change the unit, you do NOT want to change the amount.

As a specific example, If you have 18 g of table salt and you want to determine how many milligrams of table salt that is you do not want to change the amount of salt. You know enough math that this point to know that if you don't want a number to change, the only thing you can multiply by is the number 1. Any other math will change the amount.

The next idea

The next idea is that a fraction that has the same thing on the top and bottom is equal to 1. In other words,

It is important to note that things don’t have to look the same to be the same. In other words 1 dozen donuts = 12 donuts, or 1 hundred cents = 1 dollar. That means that 

The last idea

The last idea is that when the same thing (like a unit) appears on the top and bottom of an algebraic or mathematical equation it can be divided (or cancelled) out.

To see how this works, we need to look at some sample problems