One math prob that could help please regarding infusion rate

chuckster, ADN, BSN, RN, EMT-B · Nov 18, 2010

TJG21 --

I'm new to nursing but have a quasi-technical background (econ and quantitative analysis undergrad, work in industrial engineering/production planning). My nursing program had a provision allowing new students to test out of the nursing math requirement which I found fairly easy (the only tough part was that you had to get 100%, so no room for error). Because I found the math questions relatively easy, I didn't understand at first why my fellow nursing students were anxious about the nursing math questions on our tests, not to mention the NCLEX. As I progressed through the program, it occurred to me that the reason so many were anxious and had trouble was because of the overreliance on application of formulas to solve the problems. I was always bad at memorizing formulas and so learned to solve things without relying on them. I suspect that this also true for lot of other nursing students.

My approach is look at the problem as a whole first, then determine what units the answer should be in before proceding. Most of the nursing questions involve flow rates, typically this is drops per minute or milliliters per minute/hour. Once I know what unit I'm looking for, I usually go step by step, one equation at a time - and this is important - paying attention to units involved and canceling or combining as appropriate in each equation, until I have what I think is the right answer. At each step, you can and should perform a test of reasonableness; basically looking to see if what you've done makes sense.

Here's a fairly simple problem from an NCLEX review:

Normal saline 50mL is to be given by IV infusion over a 15-minute period. The drop factor for the tubing is 10 gtt per mL. The nurse sets the flow rate at how many drops per minute?

You're looking for the number of drops per minute however, the medication is given in volume (in this case mL). Also, the period you're given is 15 minutes. So first determine how much volume per minute is needed. In this case you're giving 50mL in 15 minutes, so you divide the amount by the time involved:

50 mL = 3.33 mL/min

15 mins

When you combine the terms as above, you can easily see that the value you've gotten is the number of milliliters needed for each minuteYou would expect that value per minute would be less than that per hour - or in this case, less than one quarter of an hour - and it is. Things pass the first test of reasonableness. You've been told that the drop rate is 10 gtt per mL, so now all you need to do is multiply the terms, remembering to cancel/combine as appropriate:

10 gtt/mL x 3.33 mL/min = 33.3 gtt/min

You can see that the volume (mL) cancels and your answer now is in the form of drops per minute. Since you can't deliver a fractional drop, your answer should be rounded to 33 gtt/min. Our test of reasonableness is applied: 1) the answer is in the right terms, gtt/min and we know that this is correct because we can see how we canceled and combined terms; 2) our answer ot 33 drops makes sense because we know that each mL is comprised of 10 drops and we need a little bit more than 3 mL.

A slightly more difficult problem:

Gentamycin sulfate 80 mg in 100mL normal saline is to be administered over 45 minutes. The drop factor is 15 drops per mL. The nurse sets the flow rate at how many drops per minute?

In this problem, you still are solving for drops per minute but the medication unit is mass (milligrams in this case). Just as in the previous problem, we can first determine how much medication per minute we need to administer (and our final answer also needs to be in units per minute)

80 mg = 1.78 mg/min

45 mins

A quick appraisal and things pass the test of reasonableness (things are in milligrams per minute, as expected and the value per minute is smaller than that per 45 minutes).

Since flow rate is in volume, you need to know how much mass (mg) is each unit of volume (mL). Set up another simple equation:

80 mg = 0.8 mg/mL

100 mL

Applying the reasonableness test, we've gotten the answer is in the terms we expected and it also makes mathematical sense at 1/100th of the original value.

Now we need to get our mass per minute into volume per minute - something we didn't need to do in the first problem. We need 1.78 mg each minute (1.78 mg/min) and we know that there are 0.8 milligrams in each milliliter (0.8 mg/mL). It's easy to get confused about whether you need to multiply or divide - by setting up a simple equation, paying attention to the terms and checking the result for reasonableness, you can fairly easily see if you've done things correctly. In this case, if you multiplied, it would look like this:

1.78 mg/mL x 0.8 mg/min = 1.4 mg2/mL/min.

You can easily see that the terms are not what we wanted (or expected) so we've clearly done something wrong. Doesn't pass the reasonableness test.

When we divide, this is what things look like:

1.78 mg/min = 2.22 mL/min

0.8 mg/mL

The mass (mg) cancels out, leaving volume (mL) and time (min). Check for reasonableness: 1) the answer is in the units we expected and the arithmetic works (since we divided by a value less than 1 we know that the result of the division will be greater than the number we started with.

Now all we need to do, just like the simpler problem, is multiply by our drop factor:

2.22 mL/min x 15 gtt/mL = 33.3 gtt/min.

Again you can see that the volume (mL) cancels and your answer now is in the form of drops per minute. Since you can't deliver a fractional drop, your answer should be rounded to 33 gtt/min - just like we did on the first problem. Our test of reasonableness is applied and things pass muster (as for the problem above, 1) the answer is in the right terms, gtt/min and we know that this is correct because we can see how we canceled and combined terms; 2) our answer ot 33 drops makes sense because we know that each mL is comprised of 15 drops and we need a little bit more than 2 mL.

You may want to stop reading now and try to solvethings on your own - in case not, here's what I would do:

Step 1) 500 ml / 4 hrs = 125 ml/hr

Step 2) 125 mL/hr / 60 min/hr = 2.08 mL/min

Step 3) 2.08 mL/min x 15 gtt/mL = 31.2 gtt/min - round to 31 gtt/min

The obvious advantage of using this method is that you don't have to worry about memorizing formulas(though you do have to be familiar with mathematical operations) and you can easily see if you are on the right track by paying attention to the terms in each equation. The just as obvious disadvantage is that at least at first, this method takes longer. Over time though, as you become familiar with doing things this way, you can actually combine equations and do things in one step. I don't usually bother however, since each equation is simple and takes very little time to set up and solve. Also I have the opportunity to quickly check things at each step to make sure I'm on the right road to the solution needed by doing things in multiple steps.

Keep in mind however that this advice is worth every penny you paid for it.

shaas, ASN, RN · Nov 19, 2010

Hi, there.

I hope that you practice repeatedly and, if you feel that you have a math block, you must take some time to work on that. You can definitely overcome fear of math.

1. First, let's look at what they want. They want the answer to have

gtt/min as its unit. Please, write them out on a piece of paper to see how the units are set up and, thus, can cancel out.

2. When writing this out, use a horizontal, straight line for fractions, not the slanted line like the following. It's visually better to grasp with horizontal lines. :)

3. You start with a conversion factor (a set of numbers) that has the unit of 'gtt' on top, because the answer requires gtt on top.

4. Then carefully observe how each unit cancels out because they are arranged diagonally or oppositely - top unit always has to match the bottom unit of the next conversion factor. Don't forget not to separate each number with its unit. Number and its unit are always a package deal!

gtt / min = (15 gtt/1 mL) x (500 mL/4 h) x (1 h/60 min) = 31.25 gtt/min (the numbers not quite final!)

This gives you the ballpark numbers and the exact units that the question is asking for.

Now, the proper rounding - if this is a machine calibrating the drops, then it can take more precise figures. However, if this is a person calibrating, I doubt they could count a 0.25 or 0.3 of a drop. So, this requires the answer in whole, humanly countable numbers, which is 31 gtt/min.

Good luck!

Shaas