In the previous reading, I explained how to create conversion factors, but being able to create a conversion factor is only half the battle. Now you need to be able to put those fractions to use in doing an actual conversion. Here's an example: let's suppose you wanted to convert 36 inches into feet. You're probably thinking, "I don't need a conversion factor to do that; you just divide by 12, because there are twelve inches in a foot!"

And you're right. But let's do it using our conversion factors. Later you'll have problems that aren't quite so simple, and you'll be glad you learned to do this with conversion factors. We start by taking the quantity (36 inches) and multiplying it by our conversion factor (1 foot)/(12 inches). Remember that the reason we're allowed to do this is because our conversion factor is a fraction that's equal to one, so we can multiply it by anything we want to, without changing its value. So here we go:

(36 inches) x (1 foot)/(12 inches). 

Why would we do this? Well, do you remember, from studying fractions, that when you multiply fractions, something in the numerator of one fraction can cancel the same thing in the denominator of another? Well, guess what! That is true of units as well as numbers and variables. I can cancel units if there's a matching unit in the numerator and denominator:

(36 inches ) x (1 foot)/(12 inches)

Inches is in the top and the bottom, so it cancels!

Now just do the fraction multiplication, and what have you got? You have the answer: 3 feet.

The only thing left to talk about is: How did I know what conversion factor to use? That's not too difficult to answer. First, since we started with inches, and wanted to end up in feet, I needed to use a conversion factor that involved both feet and inches. There are two conversion factors involving feet and inches, so how did I know which one to use? Well, since the original quantity had inches for its unit, and I wanted to get rid of inches, I needed to use the conversion factor which would cause the inch unit to cancel out. That led me to pick the conversion factor that had inches in the denominator.

Example Two - Convert 5 weeks to days.

Answer - The conversion factors for days and weeks are (7 days)/(1 week) and (1 week)/(7 days). Which one do we use? Well, we're starting with a quantity that has a unit of weeks, and we want to get rid of that unit, so we'll put weeks in the denominator:

(5 weeks) x (7 days)/(1 week) =
(5 weeks) x (7 days)/(1 week) =
35 days

Example Three - Convert 45 seconds to minutes.

Answer - The conversion factors for seconds and minutes are (1 minute)/(60 seconds) and (60 seconds)/(1 minute). Since we're starting with a quantity that has a unit of seconds, and we want to get rid of that unit, we put seconds in the denominator:

(45 seconds) x (1 minute)/(60 seconds) =
(45 seconds) x (1 minute)/(60 seconds) =
0.75 minutes