Math Study Guide

Nursing Math Study Guide

Five “Rights” of Medication Administration

The right patient

The right drug

The right dose

The right route

The right time

Tips and Common Errors

- The metric system is used in hospitals, and common mistakes include using the weight

in pounds instead of kilograms, completing conversions incorrectly, or making a

calculation error.

- Complete any conversions first (pounds into kilograms, ounces into milliliters, etc.)

before solving the problem.

Common Conversions

1g = 1000 mg

1L = 1000 ml

1 kg = 2.2 lbs

1 oz = 30 ml

1 teaspoon= 5 ml

1 tablespoon = 15 ml

Mathematical Techniques

Let’s imagine that the dosing for medication A is 30 mg/kg. Our patient weighs 7 kg. How would we find the correct dose? This is where cross multiplication comes in:

30 mg   x   30 mg  x 7 kg = 210 /1 kg = 210 mg of medication

______     =  ______

1kg                7kg 

The other option is to multiply as shown in the second example.

Practice Problems 

Problem 1:

A 3-year-old male comes into clinic with a temperature of 103F. He weighs 25 lbs and the

provider orders acetaminophen at 15 mg/kg. The concentration of the medication is listed on

the bottle as 160 mg/ 5 mg. How many milliliters of acetaminophen should the nurse


Problem 2:

Your two-year-old patient with vesicoureteral reflux is admitted with pyelonephritis. The

physician orders cefepime 100 mg/kg/day in two divided doses. Your patient weighs 10.8 kg.

The concentration of the cefepime is 2 g/100 ml. How many milliliters of cefepime will you

administer to your patient for each dose?

Problem 3:

Your three-year-old patient is prescribed amoxicillin 25 mg/kg/day in two divided doses for otitis media. She weighs 30.6 lbs.  The concentration of the amoxicillin suspension is 250mg per teaspoon. How many ml of amoxicillin should the parents give to the patient for each dose?

For answers to these problems, click on the contact page to send me a message!