Question

A client is taking \(1 / 15\) of a liquid medication containing \(0.375 \mathrm{mg}\) of medication every day. How many milligrams will the client take in 4 days? ______

Short answer

The client will take 0.1 mg of medication in 4 days.

Step-by-step solution

Understanding the daily medication intake

The client takes \(\frac{1}{15}\) of the liquid medication every day, which contains 0.375 mg of the medication. We need to find out how many mg are in this \(\frac{1}{15}\) portion.

Calculate the daily intake

To find out how much medication the client takes each day, we multiply the total amount of medication in the liquid by the portion taken: \(\frac{1}{15} \times 0.375 = 0.025 \text{ mg}\). Thus, the client takes 0.025 mg of medication every day.

Determine the total intake over four days

The medication taken per day, 0.025 mg, is multiplied by 4 days to determine the total intake: \(4 \times 0.025 = 0.1 \text{ mg}\). Therefore, the client will take 0.1 mg of medication in 4 days.

Key concepts

Mathematical Reasoning

When approaching a dosage calculation problem, mathematical reasoning is crucial. It involves translating a word problem into a mathematical expression that accurately represents the situation given. In this problem, the client is taking a specific portion of medication daily. We have to determine the actual amount in milligrams he ingests. By analyzing and breaking down the details, we understand that the client ingests \( \frac{1}{15} \) of the liquid medication per day. Doing the math requires multiplying this fraction by the total milligram amount of the medication, which is 0.375 mg. This multiplication is essential to figuring out what \( \frac{1}{15} \) represents in practical terms. Understanding this aspect is the key to accurately determining the daily dosage.

Unit Conversion

Unit conversion is a foundational skill in dosage calculations. It allows you to change numbers into whatever unit makes the best sense contextually. In this particular problem, units stay consistent as we are dealing with milligrams throughout. However, it's worth noting that awareness of units would be critical if different units were involved, for instance converting grams to milligrams. One gram equals 1000 milligrams, so knowing conversion factors like this can be invaluable.
While straightforward in our example, the logic behind unit conversion strengthens your problem-solving skills. Staying consistent with units ensures accuracy when calculating dosages and prevents errors that could arise from unit mismatches.

Problem-Solving Skills

Effective problem-solving skills are all about applying the correct mathematical operations to achieve a desired outcome. From understanding the problem to performing calculations, each step requires careful thought. Let's break this down for clarity:

• First, understanding the problem statement: the client takes a fraction of medication every day.
• Second, performing the mathematical operation: multiplying this fraction with the actual milligrams available.
• Thirdly, repetition of this operation over time (4 days in this context) to find the cumulative milligrams.

To solve effectively, you have to double-check each calculation, ensuring the logic flows from one step to the next without interruption. These skills allow you to navigate through dosage problems, even when they increase in complexity.