Question

Set up the following problems as a proportion and solve. Include labels in the set up and on the answer. The prescriber orders 0.25 milligram (mg) of a medication. The medication is available in \(0.125 \mathrm{mg}\) tablets. How many tablets will you give?

Short answer

Give 2 tablets to provide the prescribed 0.25 mg dose.

Step-by-step solution

Set Up the Proportion

Start by setting up a proportion where one known ratio compares to an unknown ratio. Here, the known ratio is the amount of medication in one tablet: \[ \frac{0.125 \text{ mg}}{1 \text{ tablet}} \]. The unknown ratio is the prescribed dose compared to the number of tablets needed, represented as: \[ \frac{0.25 \text{ mg}}{x \text{ tablets}} \].

Write the Proportion Equation

Write the proportion equation by setting the two ratios equal to each other:\[ \frac{0.125 \text{ mg}}{1 \text{ tablet}} = \frac{0.25 \text{ mg}}{x \text{ tablets}} \].

Solve for x (Tablets)

To find the value of \(x\), cross-multiply to solve the equation:\[ 0.125 \text{ mg} \times x = 0.25 \text{ mg} \times 1 \text{ tablet} \]\[ 0.125x = 0.25 \]Now, divide both sides by 0.125 to solve for \(x\):\[ x = \frac{0.25}{0.125} \]\[ x = 2 \].

Provide the Final Answer

Since \(x = 2\), the final answer is 2 tablets. This means you need to give 2 tablets to provide the prescribed dose of 0.25 mg of medication.

Key concepts

Medication Dosage Calculation

One of the essential skills in healthcare is calculating medication dosages accurately. Medications often come in different forms, like tablets, capsules, or liquids, and may have varying concentrations. It's crucial for health professionals to determine the correct quantity to match the prescribed dose. This involves understanding proportions in math, where you compare quantities in a meaningful way. In this exercise, we need to decide how many tablets to give when a specific dose is ordered.

To set up the medication dosage calculation, identify the known and unknown quantities. Here, you know that each tablet contains 0.125 mg. The prescribed dose is 0.25 mg. We need a logical way to figure out the number of tablets that would make up this dose. This is where proportions become a powerful tool. By setting up the problem using a proportion, you can systematically and accurately determine the correct dosage.

Cross-Multiplication Technique

Cross-multiplication is a simple and effective method to solve proportions, especially in medication dosage calculations. When you set up a proportion, you usually have two ratios that are equal to each other. The unknown part of your problem can often be quickly found by using cross-multiplication.

In our example, the equation \[ \frac{0.125 \text{ mg}}{1 \text{ tablet}} = \frac{0.25 \text{ mg}}{x \text{ tablets}} \]shows the relationship between the amount of medication per tablet and the desired dose. To solve for \( x \), you multiply across the equals sign diagonally. This means multiplying 0.125 mg by \( x \) and 0.25 mg by 1 tablet, giving you the equation \[ 0.125 \times x = 0.25 \times 1 \].

Then, isolate \( x \) by dividing both sides by 0.125, which leads you to find that \( x = 2 \). This means you need 2 tablets to achieve the desired dose. Cross-multiplication is particularly helpful as it simplifies the process of finding unknowns in a proportion, making calculations straightforward and efficient.

Algebraic Equations in Pharmacy

Algebra forms the backbone of solving equations in pharmacy, such as determining medication dosages. When working with equations, pharmacists often use algebraic manipulations to find unknown quantities. This is crucial in ensuring patient safety as incorrect dosages can lead to adverse effects.

The equation derived from our proportion setup is an algebraic equation. It's important to represent the problem accurately using algebra because it allows clear, precise communication of the relationship between quantities. This equation, \[ 0.125x = 0.25 \] represents the relationship we needed to solve to find the correct dosage.

Knowing how to construct and solve algebraic equations enables pharmacists to make informed decisions. They can interpret prescriptions, compare with available dosage forms, and ensure the correct amount is given to the patient. Solving these algebraic equations helps in providing the right treatment, underscoring how essential math is in pharmacy practices.