**Objectives**

*After completing this chapter, you will be able to:*

1. **Calculate three-factor–given quantity to one-factor–, two-factor–, or three-factor–wanted quantity medication problems involving a specific amount of medication or intravenous (IV) fluid based on the weight of the patient and the time required for safe administration.**

2. **Calculate problems requiring reconstitution or preparation of medications using information from a nursing drug reference, label, or package insert.**

Three-factor–given quantity medication problems can be solved implementing the sequential method or the random method of dimensional analysis. The *given quantity* or the physician's order now contains three parts, including a **numerator** (the *dosage* of medication ordered) and two **denominators** (the *weight* of the patient and the *time* required for safe administration).

Below is an example of this problem-solving method showing placement of basic dimensional analysis terms applied to a three-factor medication problem.

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**THINKING IT THROUGH**

The three-factor–given quantity has been set up with a numerator (30 mg) and two denominators (kg/day) leading across the unit path to a two-factor–wanted quantity, with a numerator (mL) and a denominator (day). The conversion factors can now be factored into the unit path to allow cancellation of unwanted units.

The *dose on hand* (300 mg/5 mL) has been factored in and placed so that the wanted unit (mL) correlates with the *wanted quantity* (mL) and the unwanted unit (mg) is canceled.

The child's weight (22 kg) has been factored in and set up to allow the unwanted unit (kg) to be canceled.

All the unwanted units have been canceled, and the wanted units are placed to correlate with the two-factor–wanted quantity (mL/day). Multiply numerators, multiply denominators, and divide the product of the numerators by the product of the denominators to provide the numerical answer. The wanted quantity is 11 mL/day.

The child is to receive 11 mL/day in four divided doses; therefore, the *conversion factor* involves how many doses are in a day (4 divided doses = day).

**EXAMPLE 6.1**

**PREVENTING MEDICATION ERRORS**

Every new medication order for a child should be carefully reviewed for errors related to **dosage, route**, and **frequency.** Many **medication errors** can be eliminated if a double-check system is in place for all new medication orders.

**THINKING IT THROUGH**

The *two-factor–given quantity* (2.8 mL/dose) has been factored in with a *numerator* (2.8 mL) and a *denominator* (dose). The *three-factor–wanted quantity* (mg/kg/day) also has been factored in with a *numerator* (mg) and two *denominators* (kg/day).

The *conversion factors* have been added, and all unwanted units have been canceled from the problem. The wanted unit (mg) is placed in the numerator to correlate with the *wanted quantity* (mg) also in the numerator. The wanted units (kg and day) are in the denominator to correlate with the wanted quantity (kg and day) in the denominator.

**PREVENTING MEDICATION ERRORS**

Knowing the **Five Rights** of medication administration can help to eliminate **medication errors** but another important consideration is being aware of the safe dosage range for each medication being administered.

A Nursing Drug Reference lists the safe dosage range for adults, children, and infants. It is the responsibility of the nurse to be familiar with safe dosage ranges to prevent **medication errors**.

**EXAMPLE 6.2**

**EXAMPLE 6.3**

**THINKING IT THROUGH**

The three-factor–given quantity has been set up with a *numerator* (5 mg) and *two denominators* (kg/min) leading across the unit path to a two-factor–wanted quantity with a *numerator* (mL) and a *denominator* (hr). By using the random method of dimensional analysis, the *conversion factors* are factored to cancel out unwanted units.

The unwanted unit (min) has been canceled by factoring the *conversion factor* (1 hr = 60 min), and the wanted unit corresponds with the *wanted quantity denominator* (hr).

The *dose on hand* (250 mg/ 50 mL) has been factored in and placed so that the *wanted unit* (mL) corresponds with the wanted quantity numerator (mL).

The *conversion factor* (1 mg = 1000 mcg) has been factored in to cancel the unwanted units (mg and mcg).

The final *conversion factors* (1 kg = 2.2 lb) and the *weight* of the patient have been factored in to cancel the remaining unwanted units (kg and lb). All the unwanted units have been canceled, and the wanted units (mL and hr) remain in position to correlate with the *two-factor– wanted quantity* (mL/hr). Multiply the numerators, multiply the denominators, and divide the product of the numerators by the product of the denominators to provide the numerical value for the two-factor–wanted quantity.

**THINKING IT THROUGH**

The *two-factor–given quantity* is identified as the information that the nurse obtained from the IV pump, and the *three-factor– wanted quantity* is the information that the physician has requested.

The *dose on hand* (the IV fluid that is presently infusing) has been factored in to cancel the unwanted unit (mL).

The *conversion factor* (1 mg = 1000 mcg) has been factored in to cancel the unwanted unit (mg). The wanted unit (mcg) remains and corresponds with the wanted quantity in the *numerator*.

The *conversion factor* (1 hr = 60 min) has been factored in to cancel the unwanted unit (hr). The wanted unit (min) remains placed in the *denominator*.

The *conversion factor* (1 kg = 2.2 lb) has been factored in to correspond with the *wanted quantity denominator* (kg). The *weight* of the patient also is factored in to cancel the unwanted unit (lb). After all unwanted units have been canceled and the wanted units have been identified, multiply the numerators, multiply the denominators, and divide the product of the numerators by the product of the denominators to provide the numerical value for the *wanted quantity*.

**EXAMPLE 6.4**

**Dimensional analysis** is a problem-solving method that uses critical thinking. When implementing the *sequential method* or the *random method* of dimensional analysis, the medication problem can be set up in a number of different ways, with a focus on the correct placement of *conversion factors* to allow unwanted units to be canceled from the unit path.

Dimensional analysis is a problem-solving method that nurses can use to calculate a variety of medication problems in the hospital, outpatient, or home care environment. The medication problems may involve one-factor–, two-factor–, or three-factor–given quantity medication orders, resulting in one-factor–, two-factor–, or three-factor–wanted quantity answers.

With advanced nursing and home care nursing resulting in increased autonomy, it is more important than ever that nurses be able to accurately calculate medication problems. Dimensional analysis provides the opportunity to use one problem-solving method for any type of medication problem, thereby increasing consistency and decreasing confusion when calculating medication problems.

**PREVENTING MEDICATION ERRORS**

When caring for critically ill patients, the nurse is responsible for titrating medication for the desired effectiveness (decrease in chest pain, increase in urine output, or increase in blood pressure).

The weight of a patient is extremely important when administering medications to a critically ill patient because a change in weight (either increased or decreased) can change the effectiveness of the medication. To prevent **medication errors**, a daily weight is obtained on every critically ill patient.

**Exercise 6.1 Medication Problems Involving Dosage, Weight, and Time (See page 159–160 for answers)**

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**SUMMARY**

This chapter has taught you to calculate three-factor medication problems involving the **dosage** of medication, the **weight** of the patient, and the amount of **time** over which medications or IV fluids can be safely administered. Using the sequential method or the random method of dimensional analysis, demonstrate your ability to calculate medication problems accurately by completing the following practice problems.

**Practice Problems for Chapter 6: Three-Factor Medication Problems (See pages 160–161 for answers)**

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**Chapter 6 Post-Test: Three-Factor Medication Problems**

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**ANSWER KEY FOR CHAPTER 6: THREE-FACTOR MEDICATION PROBLEMS**

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