Question

Calculate the dosages to be given. Round answers to the nearest tenth as indicated (express answers in milliliters). Order: Famotidine \(20 \mathrm{mg}\) p.o. bi.d. Available: Famotidine \(8 \mathrm{mg}\) per mL.

Short answer

2.5 mL of Famotidine is needed per dose.

Step-by-step solution

Identify the Required Dosage

The doctor's order is for Famotidine to be given at a dosage of 20 mg, twice a day (bi.d.). We need to calculate how many milliliters are required to administer 20 mg of the medication.

Determine the Concentration of Medication

The available medication concentration is given as 8 mg per mL. This means that each milliliter contains 8 mg of Famotidine.

Set Up the Proportion

To find out how many milliliters correspond to the ordered 20 mg, set up a proportion: \[ \frac{8 \text{ mg}}{1 \text{ mL}} = \frac{20 \text{ mg}}{x \text{ mL}} \] where \( x \) is the number of milliliters we need to find.

Solve the Proportion

To solve for \( x \), cross-multiply and divide: \[ 8x = 20 \] \[ x = \frac{20}{8} = 2.5 \text{ mL} \]

Round to the Nearest Tenth (if needed)

The calculated volume is already at the nearest tenth as 2.5 mL, so no further rounding is necessary.

Key concepts

Pharmaceutical Mathematics

Pharmaceutical mathematics is a crucial component when it comes to accurately managing medication dosages. This specialty involves several mathematical techniques and the application of certain principles to ensure that patients receive the correct amount of medication prescribed by their doctor. Calculation of dosages must account for factors such as medication concentration, frequency of administration, and patient-specific factors such as weight or age. The primary goal is always to ensure safe and effective treatment for patients.
By using basic mathematical operations such as multiplication, division, addition, and subtraction, pharmaceutical mathematics allows healthcare professionals to calculate the needed dosage, check for potential errors, and adjust prescriptions as necessary. It acts as a bridge between the written prescription and the actual administration of the drug to the patient.

Proportions in Medication

Proportions in medication are used to solve problems involving the relationship between different quantities of medication and the amount needed to administer the correct dose. A proportion is essentially an equation that sets two ratios equal to each other. In the context of medication, it allows healthcare providers to calculate how much of a diluted or concentrated medication is necessary to meet a stated dosage requirement.

To set up a proportion, always start with the known concentration of the medication, such as 8 mg per mL, and compare it with the prescribed dosage, such as 20 mg. This relationship can be written as \[\frac{8 \text{ mg}}{1 \text{ mL}} = \frac{20 \text{ mg}}{x \text{ mL}}\]Solving this equation will tell you how many milliliters are needed to achieve the desired 20 mg dose.

Medication Concentration

Understanding medication concentration is essential for ensuring that patients receive the correct dosage of their prescribed medicines. Medication concentration typically refers to the amount of active ingredient present in a given volume of solution, expressed as milligrams per milliliter (mg/mL). In the example problem, the concentration of Famotidine is 8 mg/mL.

Concentration helps determine the volume of liquid medication required to reach a certain dose. It is crucial to always check the concentration on the medication label and use it to guide dosage calculations. Being aware of the concentration can prevent overdosage or underdosage and promote effective treatment. It’s also important to adjust calculations according to changes in concentration when these adjustments occur in prescribing or compounding the medication.

Rounding in Dosage Calculations

Rounding is an important process in dosage calculations to ensure that medication amounts are practical and safe for administration. In many cases, doses derived from mathematical calculations may not be evenly divisible into the medication's available form. Proper rounding addresses this issue by approximating the dose to a suitable volume that can be accurately measured.

For dosage calculations, it is common practice to round measurements to the nearest tenth for precision and ease of administration. In our example, the calculated dose of 2.5 mL is already at the nearest tenth. Not requiring further rounding ensures that the dose remains exact and aligns with the prescribed order. However, if the calculation resulted in a number like 2.54 mL, it would be rounded to 2.5 mL to maintain the prescribed precision.