Problem 22 - Calculate With Confidence

Question

A client consumes 55% of a bowl of chicken broth at lunch. The bowl holds 180 mL. How many milliliters did the client consume? ___________

Step-by-Step Solution

Answer

The client consumed 99 mL of the broth.

Step 1: Understand the Problem

The problem involves finding out how much liquid was consumed given a percentage. The bowl has a total capacity of 180 mL, and the client consumes 55% of it.

Step 2: Convert Percentage to Decimal

To calculate a percentage of a given amount, convert the percentage into a decimal. 55% is equivalent to \(0.55\) in decimal form.

Step 3: Calculate the Consumed Amount

Multiply the total amount in the bowl by the decimal to find out how much was consumed. Using the formula: \[ ext{Consumed Amount} = ext{Total Amount} \times ext{Percentage in Decimal} \]Substitute the values:\[ 180 imes 0.55 \]

Step 4: Perform the Multiplication

Calculate the product of 180 and 0.55:\[ 180 imes 0.55 = 99 \]

Step 5: Conclude

The client consumed 99 mL of the chicken broth.

Key Concepts

Percentages

Percentages are a way to express numbers as parts of a whole, specifically out of 100. When someone says 50%, it means 50 out of 100, or one half of a whole. Using percentages helps us understand proportions and comparisons more easily. In this context, 55% is the portion of the chicken broth that the client consumed. To use percentages in calculations, you usually convert them into decimals for easier multiplication. For instance, 55% is converted to 0.55. This conversion directly translates the part of the whole that we're focusing on.

Mathematical Calculations

Mathematical calculations often involve operations like addition, subtraction, multiplication, and division. Sometimes, these operations are combined with concepts like percentages, as seen in our exercise. Here, the main calculation is multiplication. The operation involved is multiplying a total amount by a percentage (in its decimal form) to find the part of that total amount.

• Take the total amount: 180 mL
• Convert the percentage to a decimal: 55% becomes 0.55
• Multiply them together: \[ 180 \times 0.55 = 99 \]

This multiplication gives us the consumed amount.

Fluid Measurement

Fluid measurement typically involves the use of units such as milliliters (mL), liters (L), gallons, etc. In the exercise, we're working with milliliters, a common unit for measuring small quantities of liquids. In medical and culinary fields, fluid measurement is crucial for precision. Here, the bowl of broth is 180 mL in capacity, which dictates the total amount you start with before performing calculations. Understanding fluid measurement is essential, especially when common everyday activities, like consuming soup, involve it. Accurate measurements are pivotal for correct outcomes, especially when calculating portions using percentages.

Problem Solving Methods

Problem-solving methods often involve breaking a problem into manageable steps. This allows for a systematic approach to finding the solution. In this exercise, we followed a methodical process:

• Start by understanding the problem and identifying what is being asked.
• Convert any percentages into decimals for calculation purposes.
• Use simple mathematical operations to find the solution.
• Conclude by verifying that the solution makes sense in context.

This structured approach can be applied to a wide range of mathematical problems, emphasizing clarity and systematic thinking. Using clear steps prevents errors and ensures you address all aspects of the problem efficiently.