Problem 15 - Prealgebra

Question

Express each of the following rates as a ratio with the given units. Intravenous (IV) infusions are often ordered in either milliliters per hour or milliliters per minute. What was the infusion rate in milliliters per hour if it took 5 hours to administer \(2,400\) mL?

Step-by-Step Solution

Answer

480 mL/hour.

Step 1: Understand the Units Involved

We are given that it took 5 hours to administer 2,400 mL of a fluid. The task is to find the infusion rate in milliliters per hour, which means we need to express the rate as mL/hour.

Step 2: Write the Ratio for 1 Hour

Since we need the infusion rate in milliliters per hour, we start by expressing the total amount of fluid administered over the total number of hours as a fraction: \[ \frac{2,400 \text{ mL}}{5 \text{ hours}} \].

Step 3: Perform the Division

Calculate the division to find out how many milliliters were administered per hour: \[ \frac{2,400}{5} = 480 \text{ mL/hour} \].

Step 4: State the Infusion Rate

The calculated infusion rate tells us the fluid was administered at a rate of 480 milliliters per hour.

Key Concepts

Understanding Units of Measurement

When it comes to solving problems, understanding the units of measurement is crucial. In this exercise, we're dealing with milliliters (mL) and hours. These units help us understand the amount of fluid administered and the duration over which it occurs.

• Milliliters (mL): This unit measures volume. It is a small amount of liquid commonly used in both medicine and science. Knowing how many milliliters are involved is key to determining the rate of administration.
• Hours: This unit measures time. We are looking at how many hours it takes to administer a certain volume of fluid.

Grasping these units helps us establish a clear picture of the problem. It allows us to connect the amount of fluid administered with the time taken, a fundamental aspect of rate calculations.

Division in Ratios

After understanding what the units of measurement are, the next essential step is performing division to calculate ratios. Division helps break down complex problems into simpler terms by determining how many times one quantity is contained within another. In this problem, we find the infusion rate ( ext{mL/hour}) by dividing the total milliliters by the total hours. This division gives us the rate of infusion per hour, making the concept clearer and manageable: \[\frac{2,400 \, \text{mL}}{5 \, \text{hours}} = 480 \, \text{mL/hour}\]

• Break it down: Imagine you are distributing 2,400 mL evenly over 5 hours. Division helps us find that amount distributed each hour.
• Simplifying ratios: Calculating step-by-step as shown reduces the complexity, yielding the infusion rate plainly.

By performing division, we get a concise view of how rates transform bulk data into simple, digestible figures.

Effective Problem Solving Steps

Understanding the importance of structured steps in problem-solving can greatly improve learning and application in mathematics. Let’s walk through how recognizing these steps aids in solving the given problem.

• Step 1: Recognizing Units
  Recognize and understand the importance of the units provided. This establishes the groundwork for building the ratio.
• Step 2: Constructing the Ratio
  Combine your knowledge of units to write out the ratio or fraction representing the problem. Example: \(\frac{2,400 \, \text{mL}}{5 \, \text{hours}}\)
• Step 3: Calculation through Division
  Use division to simplify the ratio, revealing the required infusion rate.
• Step 4: Conclusion
  State the final answer clearly, "480 milliliters per hour," ensuring everyone understands the outcome.

These structured steps are not just for this problem but can be adapted for various mathematical challenges. Developing such systematic thinking enhances both accuracy and efficiency in problem-solving.