One more trivial example ...

 

We're still on that same long drive - and yeah - it does seem to be dragging on ....

In fact your buddy Bob  is thinking just that and says, "Judy live 96 more miles from here. How long is this gonna take?". Well, since you have your factor-label hat on you immediately think :

What I want to know is time, that is hours, so :

 

 

And what else you know that has time in it is your speed - still cruising along at 64 mi/hr - so remembering that you need to take the thing you know that has the same unit as what you want to know and write it so the unit is in the same position :

 

 

 

And then multiply it by the other thing we know, namely Judy is STILL 96 miles away ....

 

 

Now we just have to cancel (common denominator = 32) & solve  :

 

 

 

Now, knowing that Bob is such a precise kind of fellow, he's probably  going to make some smart remark, so maybe giving the answer in minutes is better .... but none of the things we KNOW about the problem have minutes in them.  Here is where another little "trick" of using the factor-label method comes in. 

Units don't just exist individually. There are actually classes of units.  For example linear units, for measuring distance, such as miles, feet, inches, and so forth. Or units of volume, such as gallon, quart, cup, milliliter and so forth. And of course there are units of time, like hours, minutes, and seconds. Or units of weight like pounds, kilograms, milligrams, etc. You get the idea.

  In cases where what we want to know (minutes in this case) is in the same unit class as what we do know, or what was given (hours in this case) for the purpose of setting up a problem, we can pretend they are the same.   We can do that because (almost) without exception, there are conversion factors among units of the same class. More about those later when we define what a conversion factor is.

So how does this help us?  For this problem, we want to know minutes :

 

 

and take the thing we know that has a unit in the same CLASS and write in so it is in the same position :

 

 

And again we're going to multiply by the other thing we know :

 

 

 

Now we're still missing something because our units aren't quite right.   If we cancel now, our answer is in hours - we have minutes on the left (want to know) side & hours on the right side.

 

 

This is our clue that we need a conversion factor - and it tells us which conversion factor we need!  We need one that has minutes and hours in it. And the problem itself tells us which way to orient the conversion factor : we always add a factor with the common unit opposite.

 

 

 

 

Now when we factor & solve :

 

 

We know we've correctly set up the problem because we have only the same unit on each side of the equation.  If you've followed this far, you'll find no problem with dosage calculations ....

So on to the nursing math ......

 

©1997-2006 Dale Sampson, RN