Problem 29 - Introductory and Intermediate Algebra for College Students 4th

Question

Use the percent formula, \(A=P B: A\) is \(P\) percent of \(B,\) to solve Exercises \(27-42\) What is \(18 \%\) of \(40 ?\)

Step-by-Step Solution

Answer

The result is 7.2. Thus, \(18\%\) of \(40\) is \(7.2\).

Step 1: Understand the Variables in the Formula

In the formula \(A = PB\), each variable represents something specific. \(A\) represents the final amount, \(P\) represents the percentage (expressed as a decimal), and \(B\) represents the base number. Here, we are given \(P = 18\% = 0.18\) (since percentages are converted to decimals by dividing by \(100\)) and \(B = 40\). Our task is to find \(A\).

Step 2: Apply the Formula

We substitute \(P = 0.18\) and \(B = 40\) into the formula \(A = PB \). This gives us \(A = 0.18 \times 40\).

Step 3: Compute the Result

By calculating \(0.18 \times 40\), we find that \(A = 7.2\).

Key Concepts

Percentage Calculations

Calculating percentages is a common task in mathematics, finance, and many everyday situations. To understand percentage calculations, start by recognizing what a percentage actually is. A percentage represents a part per hundred. For example, 18% means 18 out of every 100 units. When asking "What is 18% of 40?", you're essentially asking for 18 out of every 100 parts of the number 40.

To calculate this using the percent formula, you use the equation \(A = P \times B\), where \(P\) is the percentage in decimal form. This is because working with decimals simplifies arithmetic operations more than dealing with raw percentages. Always remember: transform the percentage to a decimal first, then proceed with the multiplication to find your answer.

• Percentages are useful for understanding proportions.
• Always convert a percentage to a decimal before performing arithmetic operations.
• The formula \(A = P \times B\) is instrumental for such calculations.

Decimal Conversion

Understanding how to convert percentages to decimals is crucial in performing accurate calculations. A percentage format can be cumbersome for calculations, so turning it into a decimal simplifies the process. To convert a percentage to a decimal, divide it by 100. This shift is because percentages are based on a full set of 100 units.

For instance, to convert 18% to a decimal, you divide 18 by 100, resulting in 0.18. Always double-check your conversion to eliminate mistakes as working with correct decimal values is central to accurate outcomes.

• Divide the percentage by 100 to find its decimal equivalent.
• Ensure the decimal is correct to maintain calculation accuracy.
• Use decimals for easier multiplication and other arithmetic operations.

Arithmetic Multiplication

Multiplication is a basic arithmetic operation that allows us to determine the overall result when repeating a number a given number of times. In percentage problems, after converting the percentage to a decimal, you'll usually multiply it by the base or total number. This multiplication gives you the portion that represents the percentage part of the base number.

With 18% of 40, once 18% is converted to the decimal 0.18, you multiply: \(0.18 \times 40\). Executing this calculation results in 7.2, which means 18% of 40 is 7.2.

• Mastering multiplication helps in quick and accurate percentage calculations.
• Remember, multiplication distributes a total into proportional parts.
• Use calculators to ensure accuracy, especially with decimals.