Problem 30 - Introductory Algebra for College Students

Question

Use the percent formula, \(A=P B: A\) is \(P\) percent of \(B,\) to solve. What is \(16 \%\) of \(90 ?\)

Step-by-Step Solution

Answer

16% of 90 is 14.4.

Step 1: Convert Percentage to Decimal

To work with percentages in mathematical operations, first convert the percentage to a decimal form. A percentage can be converted to a decimal by dividing it by 100. Therefore, convert 16% to a decimal by dividing 16 by 100 which equals 0.16.

Step 2: Apply the Percent Formula

Using the formula \(A = P * B\), and substituting \(P\) with 0.16 (the decimal equivalent of 16%) and \(B\) with 90 (the given base number), calculate \(A\). Thus, \(A = 0.16 * 90\).

Step 3: Perform the Calculation

Now, perform the multiplication operation in the previous step to find the value of \(A\). Hence, \(A = 0.16 * 90 = 14.4\).

Key Concepts

Percent Formula

Percentages are a way to express a number as a fraction of 100. To calculate a percentage of a number, we use the percent formula. This formula is helpful in many daily life applications like calculating discounts, interest rates, and more. The formula is structured as:

• A represents the final amount that results from the percentage calculation.
• P is the percentage expressed as a decimal.
• B is the original number or total amount from which the percentage is calculated.

The formula itself is written as: \(A = P \times B\).
Here, the task is to find what 16% of 90 is. First, you'll need to convert the percentage into a decimal, which leads us to the next section.

Decimal Conversion

Understanding how to convert percentages into decimals is crucial for solving percentage calculations effectively. Since percentages are parts out of 100, converting them into decimals simply involves dividing the percentage by 100. This conversion can be visualized as shifting the decimal point two places to the left.

Example: Converting 16% to a Decimal

To convert 16% into a decimal, divide 16 by 100:

• 16 ÷ 100 = 0.16

The result, 0.16, is the decimal form.
This decimal is now ready to be used in further calculations involving the original number from which the percentage is taken.

Multiplication Operation

After converting the percentage to decimal, multiplication is the operation we use to find a specific part or portion of a number. Multiplying the decimal by the original number gives us the desired percentage of that number.

Executing the Multiplication

Using the example from our exercise, we calculated the decimal form as 0.16 and were asked to find 16% of 90. Therefore, perform the multiplication operation:

• Multiply the decimal: \(0.16\)
• By the number 90: \(0.16 \times 90\)

Carry out this calculation to find that the percentage of the number 90 given by the decimal is:

• \(A = 0.16 \times 90 = 14.4\)

This means 16% of 90 equals 14.4, completing the percentage calculation.