Question

A client takes \(11 / 2\) tablets of medication four times per day for 4 days. How many tablets will the client have taken at the end of the 4 days? ______

Short answer

88 tablets.

Step-by-step solution

Calculate Daily Dosage

First, determine how many tablets the client takes in one day. The client takes \( \frac{11}{2} \) tablets per time. Since they take it four times a day, multiply the dosage per time by four:\[\text{Daily dosage} = \frac{11}{2} \times 4\]

Simplify Daily Dosage Calculation

Simplify the multiplication to find the total number of tablets taken each day:\[\frac{11}{2} \times 4 = \frac{11 \times 4}{2} = \frac{44}{2} = 22\]So, the client takes 22 tablets each day.

Calculate Total Dosage Over 4 Days

Now, multiply the daily dosage by the number of days to find the total number of tablets taken:\[\text{Total tablets} = 22 \times 4\]

Simplify Total Dosage Calculation

Perform the multiplication to find the total number of tablets taken over four days:\[22 \times 4 = 88\]Thus, the client takes a total of 88 tablets over the course of 4 days.

Key concepts

Daily Dosage

In dosage calculations, determining the daily dosage is the first crucial step. In this case, the client is prescribed to take medication four times a day. Each time, the client takes \( \frac{11}{2} \) tablets. To find out how many tablets are taken each day, we simply multiply the dosage per administration by the number of times the client takes it in one day. So, the formula looks like this: \[\text{Daily dosage} = \frac{11}{2} \times 4\]. This multiplication will give us the total number of tablets consumed in a single day. Knowing the daily dosage is essential for understanding the medication's effect and for planning its purchase.

Total Dosage

Once we have the daily dosage figured out, we need to look at the bigger picture, which is the total dosage over the prescribed period. This is where we calculate the cumulative amount of medication taken. After determining that the client takes 22 tablets each day, we multiply this number by the total number of days, in this case, 4. The formula can be expressed as \(\text{Total tablets} = 22 \times 4\). This calculation will give us the entire amount of medication the client needs to take over the 4-day period, ensuring they stick to the prescribed routine.

Simplification

Simplification in medicine dosage calculations is a valuable skill that helps avoid errors and make computation easier. When simplifying expressions like \( \frac{11}{2} \times 4 \), it's helpful to first express each component in a more manageable form. We can break it down: \(\frac{11 \times 4}{2}\). By solving this step by step, first multiplying 11 by 4, then dividing by 2, we simplify the expression to 22. In dosage calculation, especially when managing complex dosages or multiple medications, simplification ensures clarity and accuracy. Remember always to check your work to avoid miscalculations.