Problem 5 - Prealgebra

Question

Solve each of the following problems. What number is \(54 \%\) of \(38 ?\)

Step-by-Step Solution

Answer

54% of 38 is 20.52.

Step 1: Convert Percentage to Decimal

To find a percentage of a number, first convert the percentage to a decimal. To do this, divide the percentage by 100. Thus, convert \(54\%\) to a decimal: \(0.54\).

Step 2: Multiply by the Base Number

Now multiply the decimal by the base number to find the percentage value. Multiply \(0.54\) by \(38\): \[ 0.54 \times 38 = 20.52 \].

Step 3: Final Result

The result from the multiplication in Step 2 gives you the answer. Therefore, \(54\%\) of \(38\) is \(20.52\).

Key Concepts

Percentage Calculations

Percentage calculations are a basic but essential concept in prealgebra. A percentage expresses a number as a fraction of 100, denoted with the symbol `%`. Understanding this concept enables us to determine how one quantity relates to another in terms of hundreds.
To find a certain percentage of a number:

• First identify the percentage you need to convert.
• Divide that percentage by 100 to convert it to a decimal.
• Once in decimal form, you can use this to find the portion of the total amount.

Let's take an example: If you are asked to find **54%** of **38**, you start by changing the percentage into a more workable number, which is the decimal.

Decimal Conversion

Decimal conversion is the process of turning a percentage into a decimal. This is a crucial step in percentage calculations.
By shifting the decimal point two places to the left or dividing by 100, you can convert any percentage to a decimal:

• A percentage of **54%** becomes **0.54**.

Once the percentage is in decimal form, it becomes easier to perform additional arithmetic operations. Decimal conversion is often the first step before proceeding to multiplication or further calculations. Additionally, understanding decimal places and how movement of the decimal point signifies size can strengthen your math skills in various areas beyond just percentage calculations.

Multiplication

Multiplication is a mathematical operation used when one number needs to be scaled by another. Once you have converted a percentage to a decimal, you then use multiplication to find its value in terms of another number.
So, when you have the decimal, you multiply it with the number you want to find the percentage for.

• For example, **0.54** (representing 54%) multiplied by **38** equals **20.52**.

This step is often the climax of percentage calculations as it provides the specific result you are looking for. Understanding how multiplication of decimals works, especially keeping track of decimal places, ensures accuracy in your calculations.