Problem 12 - Prealgebra

Question

Solve each problem using the percent equation. What is \(24.2 \%\) of \(60 ?\)

Step-by-Step Solution

Answer

24.2% of 60 is 14.52.

Step 1: Understand the Percent Equation

The percent equation is used to find the amount, base, or percent. It is expressed as: \( \, amount = (percent \times base) \, \)To solve for 'what is 24.2% of 60?', 'amount' is the unknown, 'percent' is 24.2% which is equal to 0.242 as a decimal, and 'base' is 60.

Step 2: Convert the Percent to Decimal

To use the percent in a calculation, convert the percentage into a decimal by dividing by 100. So, \( 24.2\% \) becomes \( 0.242. \)

Step 3: Substitute Values into the Percent Equation

Substitute the known values into the percent equation: \[ amount = percent \times base \]This becomes:\[ amount = 0.242 \times 60 \]

Step 4: Perform the Multiplication

Calculate the amount by multiplying the decimal equivalent of the percent by the base:\[ amount = 0.242 \times 60 = 14.52 \]

Step 5: State the Result

Therefore, 24.2% of 60 is 14.52.

Key Concepts

Percent to Decimal Conversion

When you're dealing with percentages in math problems, it's important to understand that percentages are a way of expressing fractions out of 100. To convert a percentage to a decimal, you need to divide the percentage value by 100. This is an essential step because most mathematical calculations are performed with decimals rather than percentages. For example, to convert 24.2% to a decimal, we divide 24.2 by 100. This gives us 0.242. The division by 100 effectively shifts the decimal point two places to the left.

Here's the step-by-step process:

• Take the percent value (e.g., 24.2).
• Divide it by 100 (i.e., 24.2 ÷ 100).
• This results in 0.242.

Now, you have the percentage in a form that can be easily used in calculations. Converting between these forms is a simple yet fundamental skill that helps to solve a wide array of mathematical problems.

Multiplication

Multiplication is a basic mathematical operation used in a wide range of calculations, including those involving percentages. Once you've converted a percent into a decimal, the next step is often to multiply that decimal by another number, referred to as the base.

In our example problem, the base is 60. To find 24.2% of 60, we take the decimal form of the percent (0.242) and multiply it by the base (60). The multiplication process is straightforward:

• Write the numbers aligned by their decimal points: 0.242 and 60.
• Multiply them as you would with whole numbers, paying attention to the placement of the decimal point in the final product.

Performing the multiplication:

• Start with the rightmost digits and work your way left.
• The final product is 14.52, which is the result of multiplying 0.242 by 60.

This operation finds the part of the base (60) that corresponds to the given percentage.

Finding a Percentage

Finding a percentage of a given number is a practical math skill that is widely applied in everyday life, from calculating discounts to understanding statistics. It involves applying the percent equation, which is essentially finding a part of a whole. The equation used for finding the percentage is:

\[ \text{amount} = (\text{percent} \times \text{base}) \]This equation breaks down into simple steps that we can use to find what 24.2% of 60 is.

• The 'base' is the whole amount, in this case, 60.
• The 'percent' is how much of the base you are trying to find, here it is 24.2%.

By converting the percentage into a decimal and multiplying it by the base, you discover the 'amount', or 24.2% of 60, which is 14.52 in this example.

Finding percentages is an invaluable tool for assessing changes, comparing values, and making decisions based on numerical data. By mastering this skill, you become capable of interpreting a wide range of mathematical problems and real-life situations that require percentage calculations.