# How Is Algebra Used in Nursing?

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## Why Math Knowledge Is Required

Nurses need a solid understanding of basic math concepts in order to safely calculate medication dosages before administering medicine to their patients. In many cases, nurses are also responsible for instructing patients and their families on how to measure medications that will be taken at home. Whether calculating medication dosages and IV infusion drip rates, measuring intake and output of fluids or converting weights to metric units, a nurse must demonstrate the ability to use algebraic concepts. These concepts include knowledge of ratios, proportions and percents. A broad comprehension of the metric system is also needed to calculate the correct amount of medicine to give a patient.

## Factors to Consider

To calculate the correct dose of medication, a nurse must consider both the prescribed dosage and drug label information. Correctly calculating dosage strengths is necessary when orally administering tablets, capsules or liquid medications. It's also needed when administering medications by subcutaneous injection. Giving a patient too little medication usually proves to be ineffective. Administering too much medication can make the patient suffer an overdose. When it comes to administering intravenous medications, flow rates, infusion times and infusion volumes must all be considered. Calculation of intravenous infusion rates is based on the concentration of a specific drug and volume per unit of time or body weight per unit of time.

## Formulas Used for Calculating Medication Dosages

A nurse may choose to use the ratio and proportion method of calculation or the formula method when calculating the proper dose of a drug to be administered at one time. Dimensional analysis is another calculation method that some nurses find easier to use. The equation is set up beginning with the known factor–the dosage of medication to be administered--written as a fraction. Multiply this number by the conversion factor, the number of milligrams contained in each tablet, capsule or milliliter of liquid medicine. This number, too, must be expressed in the form of a fraction (such as 1 tablet/0.025 mg). Once the formula is set up, cancel out and reduce any numerators and denominators that can be canceled out and reduced. Multiply any remaining fractions. Divide to arrive at the final answer. The answer equals the number of tablets, capsules or milliliters of liquid medication that should be given to the patient. While the equations may be more complex, this same formula format can be used to calculate correct dosages for intramuscular and subcutaneous injections. It's also helpful for intravenous flow rates. When using the dimensional analysis method, all problems are set up and solved in the same way.

## Other Mathematical Conversions

Safety concerns, including a nurse’s proven competency in administering the proper dosages of medication, remain a key issue in preventing medication errors. For this reason, it is important for a nurse to have strong math skills in multiple areas. A patient’s weight must be converted to kilograms. Drug doses are often measured in milligrams of medicine to be given per kilogram of body weight. When converted, 1 lb. = 0.454 kilograms. Basing drug dosages on body weight is usually a special concern for pediatric and geriatric patients. Adult dosages are rounded to the nearest tenth, but pediatric dosages are rounded to the nearest hundredth. Other common conversions involve the concentration--or strength--of a medication. This is based on the number of milligrams per milliliter of the drug.

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Amber Keefer has more than 25 years of experience working in the fields of human services and health care administration. Writing professionally since 1997, she has written articles covering business and finance, health, fitness, parenting and senior living issues for both print and online publications. Keefer holds a B.A. from Bloomsburg University of Pennsylvania and an M.B.A. in health care management from Baker College.

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