Conquering Nursing Math on the NCLEX®: Part 2

October 1

Debra S. McDonough

Part one of this series demonstrated how using ratio and proportion could help you master dose calculations. Remember, if nurses make an error when calculating dosages, then a medication error will be made when that wrong dose is administered to a client. That is why faculty want students to master dose calculations with 100%. Anything less would result in a medication error, and no one wants that!

Ratio and Proportion

Let’s do a quick review before moving on to some harder dose calculation problems. Here is the basic formula:

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

Primary healthcare provider’s prescription: Furosemide 80 mg by mouth once a day.

What is available: Furosemide 40 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:

40 mg : 1 tablet :: 80 mg : x tablets (Read this formula as: 40 mg is to 1 tablet as 80 mg is to x tablets).

The next step is to multiple the extremes by extremes and means by means. So now we have:

40 mg x X tablets = 80 mg x 1 tablet

When we multiply this out we have:

40 mg X = 80 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 — in this case, 40 mg.

X = 2 tabs

Using Ratio and Proportion for Complex Dose Calculations

Primary Healthcare Provider Prescription – Dopamine 400 mg in 250 mL D5W to infuse at 3 mcg/kg/min. The client’s weight is 190 pounds. How many mL/hour should the infusion pump be set at? Round to the whole number.

This problem requires several steps.

Step one – We need to convert the client’s weight from pounds to kg and we need to convert micrograms to milligrams. What do we know? There are 2.2 pounds to 1 kg. So, set up the formula:

2.2 pounds : 1 kg :: 190 pounds : X kg

2.2 lbs x X kg = 190 lbs x 1 kg

2.2 lbs X = 190 lbs kg

(~~2.2 lbs~~ X)/~~2.2 lbs~~ = (190 lbs kg)/2.2lbs

X = 86.3636364 kg (NCLEX RULE: Do NOT round until the end!)

If we know that there are 1000 mcg in 1 mg, then we can use ratio and proportion to convert mcg to mg.

1000 mcg : 1 mg :: 3 mcg : X mg

1000 mcg x X mg = 3 mcg x 1 mg

(~~1000 mcg~~ X)/~~1000 mcg~~ = (3 mcg mg)/1000 mcg

X = 0.003 mg

Step two – Plug in the client’s kg weight into the formula:

0.003 mg/kg/min = 0.003 mg x 86.3636364 kg = 0.25909091 mg / minute.

But the problem asks how many mL/hour should the infusion pump be set at? So we need to multiple the mg / min by 60 minutes:

0.25909091 mg/min x 60 min = 15.5454546 mg / hour

Step three - The last step is to determine the IV pump rate that will deliver the prescribed mcg/ hr. So we need to take what we know and what we do not know and plug the numbers into our formula:

400 mg : 250 mL :: 15.5454546 mg : X mL

400 mg x X mL = 15.5454546 mg x 250 mL

(~~400 mg~~ X)/~~400 mg~~ = (3886.36364 mg mL)/400 mg

X = 9.7159091 or 10 mL / hour

Practice Makes Perfect!

Work these problems out using ratio and proportion, then check your answers against the answers found at the end of the problems.

Primary Healthcare Provider Prescription: Dopamine 200 mg in 250 mL D5W to infuse at 4 mcg/kg/min. The client’s weight is 175 pounds. How many mL/hour should the infusion pump be set at? Round to the whole number.

Primary Healthcare Provider Prescription: Dopamine 400 mg in 250 mL of NS is infusing at 15 mL/hour on a client weighing 75 kg. How many mcg/kg/min are infusing for this client?

Primary Healthcare Provider Prescription: Procainamide 2 gms in 250 mL D5W to infuse at 3 mg/min. The client weighs 158 pounds. How many mL/hour should the infusion pump be set at? Round to the whole number.

Primary Healthcare Provider Prescription: Nitroglycerin 100 mg in 250 mL NS to infuse at 18 mcg/min. How many mL/hour should the infusion pump be set at? Round to the whole number.

Primary Healthcare Provider Prescription: Heparin 10,000 units in 500 mL NS to infuse at 900 units/hour. How many mL/hour should the infusion pump be set at? Round to the whole number.

Practice Makes Perfect Answers

Step one – Convert pounds to kilograms and micrograms to milligrams. X = 79.5454545 kg

Step two – Calculate how many mg/minute should be infused. 0.004 mg/kg/min = 0.004 mg x 79.5454545 kg = 0.31818182 mg / minute.

Calcuate how many mg/hour should be infused: 0.31818182 mg/min x 60 min = 19.0909091 mg / hour

Step three –

200 mg : 250 mL :: 19.0909091 mg : X mL

400 mg x X mL = 19.0909091 mg x 250 mL

(~~400 mg~~ X)/(~~400 mg~~) = (4772.72727 mg mL)/400 mg

X = 11.9318182or 12 mL / hour

Primary Healthcare Provider Prescription: Dopamine 400 mg in 250 mL of NS is infusing at 15 mL/hour on a client weighing 75 kg. How many mcg/kg/min are infusing for this client?

Step one – Determine how many mg are in 15 mL. 24 mg = X (Dopamine 24 mg are infusing in 15 mL/hour)

Step two – Convert the 24 mg to micrograms. X = 24,000 mcg (Dopamine 24,000 mcg are infusing in 15 mL/hour)

Step three – Determine how many mcg are infusing per minute. 400 mcg = X (There are 400 mcg infusing per minute).

Step four: Determine how many micrograms per kg are infusing every minute. 400 mcg / 75 kg = 5.33333333 mcg/kg/minute

Step one – Convert grams to milligrams. Convert 3 mg/min to mg/hour Note: We do not need the weight in order to answer this problem.

1000 mg : 1 gm :: X mg : 2 gms 3 mg : 1 min :: X mg : 60 min 2000 mg = x 180 mg = X

Step two – Determine how many mg there are in 1 mL. X = 8 mg are in 1 mL

Step three – Determine how many mL per hour the infusion pump should be set at. X = 22.5 or 23 mL/ hour

Primary Healthcare Provider Prescription: Nitroglycerin 100 mg in 250 mL NS to infuse at 18 mcg/min. How many mL/hour should the infusion pump be set at? Round to the whole number.

Step one – Convert micrograms to milligrams. 1000 mcg : 1 mg :: 18 mcg : X mg X = 0.018 mg to infuse / minute

Step two – Determine how many mg per hour need to infuse. 0.018 mg : 1 minute :: X mg : 60 min X = 1.08 mg to infuse / hour

Step three - Determine how many mL / hour the infusion pump should be set at. 100 mg : 250 mL :: 1.08 mg : X mL X = 2.7 or 3 mL/hour

Primary Healthcare Provider Prescription: Heparin 10,000 units in 500 mL NS to infuse at 900 units/hour. How many mL/hour should the infusion pump be set at? Round to the whole number.

Step one – This problem can be done in one step. Determine how many mL of NS contain 900 units of heparin.

10,000 units : 500 mL :: 900 units : X mL

10,000 units x X mL = 500 mL x 900 units

(~~10,000 units~~ X)/(~~10,000 units~~) = (450,000 units mL)/(10,000 units)

X = 45 mL contains 900 units of heparin, so the infusion pump should be set at 45 mL /hr.

September 13

Debra S. McDonough, RN, MSN, EdD