Question

A client drank $75\mathrm{\%}$ of a 12 ounce can of ginger ale. How many ounces did the client drink?

Short answer

The client drank 9 ounces of ginger ale.

Step-by-step solution

Understand the Problem

The task is to find out how many ounces out of 12 the client drank if they consumed 75% of the can.

Convert Percentage to Decimal

To use the percentage in calculations, first convert 75% to its decimal form by dividing by 100. So, 75% becomes 0.75.

Multiply the Decimal by the Total Quantity

Multiply the decimal form of the percentage (0.75) by the total ounces in the can (12) to find the number of ounces the client drank: $$0.75\times 12=9$$

Conclusion

The client drank 9 ounces of ginger ale.

Key concepts

Understanding Percentages

Percentages are a way of expressing numbers as a fraction of 100. The word "percent" literally means "per hundred." They make it easy to understand proportions and compare values across different contexts. For example, if you have 75%, this means you have 75 parts out of 100. Percentages are widely used in everyday life, from shopping discounts to understanding statistics in news articles. Knowing how to work with percentages is a fundamental math skill that helps us in various problem-solving situations.

Converting Percentages to Decimals

Converting percentages into decimals is essential for performing many math operations. When a percentage is divided by 100, it changes to its decimal form. This conversion simplifies calculations because decimals can easily be used in arithmetic operations such as addition, subtraction, and multiplication. For instance, converting 75% to a decimal means dividing 75 by 100, resulting in 0.75. This step is crucial before performing any further calculations with percentages, as mathematical operations on decimals are straightforward.

Multiplication in Math

Multiplication is one of the basic operations in mathematics. It involves taking one number and adding it to itself a certain number of times. When you multiply two numbers, you calculate their product. The operation is often represented by the symbol $\times$ or by simply placing numbers together, like $0.75\times 12$. In our exercise, multiplication helps to find out how much of something was consumed based on a percentage. For example, multiplying the decimal form of the percentage of a consumed beverage (0.75) by the total volume of the can (12 ounces) gives us $0.75\times 12=9$ ounces. This operation provides the exact amount consumed.

Problem Solving in Mathematics

Problem solving in mathematics involves a systematic approach to finding solutions. It typically starts with understanding what the problem is asking. In our scenario, the problem requires calculating how much of a drink was consumed. Once the problem is understood, the next step is to strategize and apply the necessary math operations. This involves converting percentages to decimals, performing multiplication, and finally drawing a conclusion. Problem solving is a skill that is not only useful in math but in everyday life, helping us to make decisions, assess situations, and find solutions efficiently. By practicing these steps, students become better prepared to tackle new problems with confidence.