Problem 21 - Calculate With Confidence

Question

A client drank 75% of a 12 ounce can of ginger ale. How many ounces did the client drink? _________________

Step-by-Step Solution

Answer

The client drank 9 ounces.

Step 1: Determine Fraction Drank

First, understand that the client drank 75% of the ginger ale. In decimal form, 75% is equivalent to 0.75.

Step 2: Calculate Ounces Drank

Now, calculate the actual amount the client drank by multiplying the total number of ounces in the can, 12 ounces, by the fraction drank, 0.75. Use the formula: \[ ext{Ounces Drank} = ext{Total Ounces} imes ext{Fraction Drank} = 12 imes 0.75 \]

Step 3: Perform Multiplication

Carry out the multiplication: \[ 12 imes 0.75 = 9 \]Thus, the client drank 9 ounces of the ginger ale.

Key Concepts

Understanding Percentages

Percentages are a way to express numbers as a fraction of 100. In other words, a percentage tells us how many parts there are out of 100. For example, 75% means 75 parts out of 100. Percentages are really useful when comparing different quantities and making sense of ratios.
To convert a percentage to a decimal, you simply divide by 100. So to convert 75% into a decimal, you do the following calculation:

• 75% divided by 100 equals 0.75

This step is essential when you want to perform calculations involving percentages. Once you have the percentage as a decimal, you can easily use it in other math operations, such as multiplication.

Grasping Fractions

Fractions are another form of representing parts of a whole. They consist of a numerator and a denominator. The numerator, at the top, shows how many parts are being considered, while the denominator, at the bottom, shows the total number of parts. For example, \( \frac{3}{4} \) is a fraction where 3 parts are out of a total of 4 parts.
Fractions are very similar to decimals and percentages and can often be converted from one form to another. Understanding fractions allows you to easily switch between these representations depending on what is most suitable or easiest for a given context.
In the exercise, the percentage was converted into a decimal. This decimal (0.75) can be thought of as a fraction of the can that was consumed. Recognizing that 0.75 is also \( \frac{75}{100} \) can help in understanding how much of the whole is involved.

Basics of Multiplication

Multiplication is a mathematical operation that involves adding a number to itself a certain number of times. In simple terms, multiplying two numbers tells us how much we have in total if one number is taken a specific number of times. For instance, multiplying 3 by 4 means adding 3 together 4 times, which equals 12.
When dealing with percentages, fractions, or decimals, multiplication becomes an essential tool. In the exercise, we used multiplication to find out how much of the ginger ale the client drank:

• Total number of ounces in the can: 12
• Fraction of the can that was drunk: 0.75

By multiplying these two numbers \( 12 \times 0.75 \), we discovered that the client drank 9 ounces. This shows how multiplication helps in scaling down the total quantity to a manageable part, as indicated by the fraction or percentage.