Question

Perform the indicated operations. A client reports that he drank \(40 \%\) of his 12 -ounce can of ginger ale. How many ounces did the client drink?

Short answer

The client drank 4.8 ounces of ginger ale.

Step-by-step solution

Identify the Known Values

The problem states that the client drank 40% of a quantity, and this quantity is 12 ounces of ginger ale.

Convert Percentage to Decimal

To calculate how many ounces 40% represents, first convert the percentage to a decimal. This is done by dividing the percentage by 100: \( \frac{40}{100} = 0.40 \).

Calculate the Amount Drank

Multiply the decimal form of the percentage by the total amount of ginger ale. The calculation is as follows: \( 0.40 \times 12 \text{ ounces} = 4.8 \text{ ounces} \).

State the Answer

The client drank 4.8 ounces of ginger ale, as calculated by multiplying the total amount (12 ounces) by the decimal form of the percentage (0.40).

Key concepts

Percentage Calculations

Understanding percentages is crucial because it allows you to see how parts of a whole can be represented as a fraction of 100. In real-life scenarios, percentages help express various quantities like discounts, scores, and even measurements like the amount of ginger ale consumed. In this context, 40% is used to describe a portion of the full 12-ounce can.

To convert a specific percentage into useful data, you often begin by transforming the percentage into a decimal form. This transformation sets the stage for calculations that provide actionable insights into the quantity being discussed. By memorizing that "per cent" means "out of 100," you equip yourself with the understanding necessary to undertake many practical percentage computations.

For example, understanding that 40% means 40 out of every 100 parts recalls that if the can was hypothetically 100 ounces instead of 12 ounces, the client would have consumed 40 ounces. This intuitive grasp involves the consistency of how percentages scale with quantities.

Decimal Conversion

Decimal conversion is transforming a percentage into a decimal, a vital step in many mathematical operations. This conversion simplifies calculations, especially when multiplying percentages by other numbers. Recognizing that a decimal is another way to express a fraction helps clarify why this step is necessary.

The process involves dividing the percentage figure by 100. For instance, converting 40% into a decimal involves the operation: \( \frac{40}{100} = 0.40 \). This step prepares the number for subsequent calculations by switching it into a format that complements operations such as multiplication.

Understanding decimal placement can also be beneficial. By moving the decimal two places to the left, you swiftly convert any percentage to a decimal. This technique proves helpful in practice, as it minimizes errors and speeds up the calculation process. It’s a simple yet effective strategy that enhances your efficiency and accuracy in problem-solving.

Multiplication

Multiplication builds on the decimal conversion, allowing you to calculate the exact portion of a whole in scenarios like this problem. This operation becomes especially powerful when applied to percentages in their decimal forms, as it neatly calculates fractions of quantities such as the 12-ounce ginger ale can.

To find out how much ginger ale corresponds to 40% consumption, you multiply the decimal (0.40) by the total amount (12 ounces). The formula \( 0.40 \times 12 = 4.8 \) ounces is direct yet highlights the potency of multiplication in breaking down complex problems into simple steps.

Multiplication reveals itself as an essential mathematical operation not only for calculating percentages but for numerous everyday tasks. Ultimately, it turns abstract percentages into concrete values, providing clear answers in contexts like determining exact quantities consumed or needed. Emphasizing the role of multiplication in these contexts empowers students to approach the math with confidence and clarity.