Conquering Nursing Math on the NCLEX®: Part 1

Many students find mastering dose calculation a challenge, especially since they are often expected to answer all the questions correctly. If allowed to miss any questions, it is limited to one. They seem extreme, doesn’t it? But think about it like this: Every math problem you answer is a medication you are going to administer to a client. Get the problem wrong….you just made a medication error! So even one incorrect answer is one medication error! Now I know that you do not want to make an error.

Medication errors can exacerbate a medical crisis, sometimes with tragic consequences. On average, a U.S. hospital client is exposed to at least one medication error per day. Medication errors contribute to over 7,000 deaths per year in the United States. The most common types of reported errors were wrong dosage and infusion rate. This risk to patient safety can occur at the prescribing, transcribing, dispensing or administration stage, but it’s registered nurses (RNs) who are most likely to identify and intercept medication errors before they reach the client (Flynn, Liang, Dickson, Xie, & Suh, 2012).

So every nurse must master dose calculation in order to prevent dispensing errors. So let’s get started! It is time to master dose calculations!

Ratio and Proportion

There are several different methods that one could use to complete a dose calculation. However, I have found that students who have difficulty mastering dose calculations can benefit from learning the ratio and proportion method. All medication calculations can be completed in this manner, so this is what we will focus on in this article.

Here is the basic formula:

What you know goes on this side : What you want to know goes on this side.

Here is the primary healthcare provider’s prescription: Furosemide 40 mg by mouth once a day.

What is available: Furosemide 20 mg tablets.

When using ratio and proportion, put what is known on the left side of the formula and what you are trying to determine on the right side of the formula:

20 mg : 1 tablet :: 40 mg : x tablets
(Read this formula as: 20 mg is to 1 tablet as 40 mg is to x tablets).

It is important to note to keep like measurements in the same place within the formula. For instance, the answer will be WRONG if you write the problem out like this: 20 mg : 1 tablet :: x tablets : 40 mg.

The next step is to multiple the extremes by extremes and means by means. What does this mean? Extremes are the numbers on the outside of the problem. In this case 20 mg times x tablets. Means are the numbers inside the equation: 1 tablet times 40 mg.

So now we have:

20 mg x X tablets = 1 tablet x 40 mg

When we multiply this out we have:

20 mg X = 40 mg tab

In order for X to be by itself on the left side, we need to divide 20 mg. When you divide on one side of the equation, you must divide the same number on the other side. So we now have this:

(20 mg X = 40 mg tab)/(20 mg)

When we divide 20 mg X by 20 mg, we are left with 1X or X.

When we divide 40 mg tab by 20 mg, we are left with 2 tabs.

2

~~20 mg~~ X = ~~40 mg~~ tab

X = 2 tabs

See, the formula is really rather simple! But that was a pretty easy calculation, right? Well, it works with harder ones as well, but we have to start with the basic and move to the complex. So today, let’s master the basic formula for ratio and proportion. Even if you can do the problem in your head, while you are learning, do it on paper using this formula so that you can master the steps for those harder problems.

Practice Makes Perfect!

Work these problems out using ratio and proportion, then check your answers against the answers found after the references.

Primary Healthcare Provider Prescription: Propranolol 40 mg by mouth at bedtime.

Available: Propranolol 80 mg tablets

Primary Healthcare Provider Prescription: Methylprednisolone sodium succinate 62.5 mg IVP now. Available: Methylprednisolone sodium succinate 125 mg/2 mL.

Primary Healthcare Provider Prescription: Potassium chloride 40 mg by mouth twice a day. Available: Potassium chloride 10 mg per 1 mL.

Primary Healthcare Provider Prescription: Furosemide 30 mg IVP now. Available: Furosemide 80 mg in 2 mL.

Primary Healthcare Provider Prescription: Phenytoin 0.2 grams per NG tube twice a day. Available: Phenytoin 40 mg / 5 mL

References

Flynn, L., Liang, Y., Dickson, G. L., Xie, M. and Suh, D.-C. (2012), Nurses’ Practice Environments, Error Interception Practices, and Inpatient Medication Errors. Journal of Nursing Scholarship, 44: 180–186. doi: 10.1111/j.1547-5069.2012.01443.x

Practice Makes Perfect Answers

Primary Healthcare Provider Prescription: Propranolol 40 mg by mouth at bedtime. Available: Propranolol 80 mg tablets

80 mg : 1 tab :: 40 mg : X tabs 80 mg x X tabs = 40 mg x 1 tab 80 mg X = 40 mg tab (80 mg X = 40 mg tab)/(80 mg) X = 0.5 tab

Primary Healthcare Provider Prescription: Methylprednisolone sodium succinate 62.5 mg IVP now. Available: Methylprednisolone sodium succinate 125 mg/2 mL.

125 mg : 2 mL :: 62.5 mg : X mL

125 mg x X mL = 62.5 mg x 2 mL

125 mg X = 125 mg mL

X = 1 mL

Primary Healthcare Provider Prescription: Potassium chloride 40 mg by mouth twice a day. Available: Potassium chloride 10 mg per 1 mL.

10 mg : 1 mL :: 40 mg : X mL

10mg x X mL = 40 mg mL

10mg X = 40 mg mL

X = 4 mL

Primary Healthcare Provider Prescription: Furosemide 30 mg IVP now. Available: Furosemide 80 mg in 2 mL.

80 mg : 2 mL :: 30 mg : X mL

80 mg x X mL = 30 mg x 2 mL

80 mg X = 60 mg mL

80 mg X = 60 mg mL

X = 0.75 mL

Primary Healthcare Provider Prescription: Phenytoin 0.2 grams per NG tube twice a day. Available: Phenytoin 40 mg / 5 mL

In order to answer this question, we must convert grams to milligrams. We must have like measures in order to obtain the correct answer. So let’s say you do not know how many milligrams are in a gram. Well, ratio and proportion can help you with this. If you know that there are 1000 milligrams in 1 gram then you can do ratio and proportion to determine how many milligrams are in 0.2 grams.

1 g : 1000 mg :: 0.2 g : X mg 1 g X mg = 1000 mg x 0.2 g X = 200 mg Now we can move on to the problem. 40 mg : 5 mL :: 200 mg : x mL 40 mg X mL = 1000 mg mL X = 25 mL

September 05

Debra S. McDonough, RN, MSN, EdD