Problem 11 - Calculate With Confidence

Question

A client reports drinking 40% of a 12-ounce can of ginger ale. How many ounces did the client drink? ___________________________

Step-by-Step Solution

Answer

The client drank 4.8 ounces.

Step 1: Identify Total Ounces in a Can

The problem states that the can of ginger ale contains a total of 12 ounces. Therefore, the total quantity we are working with is 12 ounces.

Step 2: Understand the Fraction Consumed

The client drank 40% of the can. To better understand what this means, recognize that 40% is the same as the fraction \( \frac{40}{100} \), which simplifies to \( \frac{2}{5} \).

Step 3: Calculate Ounces Drunk

To find out how many ounces the client consumed, multiply the total ounces in the can by the fraction that was consumed. This is calculated as follows:\[ 12 ext{ ounces} imes \frac{2}{5} = \frac{24}{5} = 4.8 ext{ ounces} \]

Step 4: Verify the Calculation

Double-check the math to verify accuracy. Multiplying \( 12 \times \frac{2}{5} \) indeed results in \( 4.8 \), confirming that the calculations are correct.

Key Concepts

Percentage Calculation

Percentage calculation is an essential aspect of basic arithmetic that you'll often encounter. It simply involves determining what fraction of a total something represents and converting this into a percentage.This can be useful in a variety of real-world situations, such as determining discounts or consuming parts of a whole, like our example with the ginger ale can.
In our exercise, we were told that the client drank 40% of a 12-ounce can of ginger ale. Let's break down how to convert this percentage into practical information:

• First, understand that a percentage is simply a part of 100.
• So when you have 40%, it means 40 out of every 100 units.

To find out what this means in the context of 12 ounces, we need to determine what fraction 40% represents. In this case, we found that 40% is equivalent to \( \frac{40}{100} \).We then simplify this fraction to \( \frac{2}{5} \), which directly indicates what part of the 12 ounces you are dealing with. This makes percentage calculations very useful for translating comparisons into tangible numbers.

Fractions

Fractions are another key concept that you'll often use in arithmetic problems.A fraction represents a part of a whole and is made up of a numerator and a denominator.
In our example, the client drank 40% of a can of ginger ale.We expressed this percentage as the fraction \( \frac{40}{100} \).Understanding how to simplify fractions is crucial:

• The fraction \( \frac{40}{100} \) can be reduced by finding the greatest common divisor of both numbers.
• Here, both 40 and 100 are divisible by 20, which simplifies the fraction to \( \frac{2}{5} \).

This simplification makes calculation easier, as we are now working with smaller numbers.When dealing with real-life scenarios, breaking down percentages into fractions can simplify complex problems and make calculations more intuitive.

Unit Conversion

Unit conversion is a vital skill, especially when dealing with different measurements and quantities.It enables us to translate the calculated fractions into meaningful measurements.
In the original exercise, the purpose was to find out how many ounces were actually consumed out of the total of 12 ounces.Given that 40% equates to \( \frac{2}{5} \) in fraction form, we multiply this fraction by the total quantity:The multiplication looks like this:

• Take the total ounces: 12 ounces.
• Multiply by the fraction consumed: \( 12 \times \frac{2}{5} \).
• This equals \( \frac{24}{5} \), which we convert to the decimal 4.8 ounces.

This type of conversion ensures that the measurement units remain consistent, ensuring accuracy in your results.Knowing how to convert between units using fractions and percentages is useful in fields such as cooking, chemistry, and everyday problem-solving scenarios.