Question

A client consumes \(55 \%\) of a bowl of chicken broth at lunch. The bowl holds \(180 \mathrm{~mL}\). How many milliliters did the client consume?

Short answer

The client consumed 99 mL of broth.

Step-by-step solution

Understand Percentage Consumption

The problem states that the client consumes 55% of the chicken broth. This means that out of the total quantity in the bowl, the client drinks 55 out of every 100 parts. We need to find the actual volume that this percentage corresponds to.

Convert Percentage to Decimal

To perform the calculation, convert the percentage into a decimal by dividing by 100. So, 55% becomes \(0.55\).

Calculate the Consumed Quantity

Multiply the total volume of the broth by the decimal value derived from the percentage. That is, \(180 \, \text{mL} \times 0.55 = 99 \, \text{mL}\).

Conclude the Calculation

Thus, multiplying these values gives us the amount of broth actually consumed by the client.

Key concepts

Measurement Conversion

Measurement conversion is an essential skill, especially when dealing with quantities like volume, weight, and length. In this exercise, we are working with milliliters (mL), which is a common unit for measuring liquid volume. Understanding conversion between different units is important in many scientific and culinary fields.

When performing calculations involving percentages and volumes like we have in this problem, it's crucial that all measurements are in the same unit to avoid confusion and errors. For example, if part of the problem were given in liters, you'd need to convert these to milliliters before proceeding. To convert liters to milliliters, remember that:

• 1 liter = 1000 milliliters

So, always ensure unit consistency when performing measurements and calculations.

Basic Multiplication

Basic multiplication is the foundation of many mathematical operations and plays a central role in solving our problem. By multiplying, we are able to find part of a quantity given a specific percentage. In the context of our exercise, multiplication helps us determine how much broth was consumed.

The calculation involves taking 55% of 180 mL. After converting the percentage to a decimal (0.55), you simply multiply this by the total volume:

• 180 mL imes 0.55 = 99 mL

This step shows how multiplication can be used to apply a percentage to a given quantity to find an exact numerical amount.

Problem Solving Steps

Problem solving is about systematically approaching a question to find a solution. Let's break down the problem-solving steps as seen in this exercise:

1. **Understand the Problem**: Read the question carefully. Here, we identify the percentage of broth consumed and the total bowl volume.
2. **Convert Units if Necessary**: Make sure all measurements are in consistent units (though in this exercise, they were already consistent at 180 mL).
3. **Convert Percentage to Decimal**: Change the percent into a decimal to facilitate multiplication. 55% becomes 0.55.
4. **Perform the Calculation**: Use multiplication to apply the percentage to the total volume: 180 mL imes 0.55 = 99 mL.
5. **Review the Solution**: Check your work to ensure accuracy and that each step logically follows the previous one. This reinforces understanding of the process.

Fractions to Decimals

Converting fractions to decimals or percentages to decimals is a crucial skill in mathematics. It helps simplify calculations and makes it easier to perform multiplications and divisions. In problems involving percentages, this step is often necessary.

To convert a percentage into a decimal, divide by 100. For our exercise, converting 55% involves:

• 55/100 = 0.55

This simple division allows us to multiply using the decimal form, leading to more straightforward calculations. Understanding this conversion is vital, as it frequently appears in a variety of mathematical and real-world problems.