Problem 26 - Prealgebra

Question

The following problems are similar to Problems \(1-22\). Set them up in the same way, but use a calculator for the calculations. Commission If the commission rate for a mobile home salesperson is \(11 \%,\) what is the commission on the sale of a $$ 15,794$ mobile home?

Step-by-Step Solution

Answer

The commission on the sale is $1,737.34.

Step 1: Determine Commission Rate

Identify the commission rate given in the problem, which is \( 11 \% \). This percentage represents how much of the sale price will be earned as commission.

Step 2: Convert Percentage to Decimal

Convert the commission rate from a percentage to a decimal for calculation purposes. This is done by dividing the percentage by 100. So, \( 11 \% \) becomes \( 0.11 \).

Step 3: Identify Sale Price

Identify the sale price of the mobile home, which is given as \( 15,794 \) dollars.

Step 4: Calculate Commission

Calculate the commission by multiplying the sale price by the commission rate in decimal form. This is calculated as \( 15,794 \times 0.11 \).

Step 5: Use a Calculator

Perform the multiplication using a calculator to find the commission. \( 15,794 \times 0.11 = 1,737.34 \).

Key Concepts

Commission Calculation

Commission calculation is a common task, especially in sales-related professions. It refers to the process of determining the earnings a salesperson receives based on a percentage of sales they made. In our example, we are calculating a commission for a mobile home salesperson. The commission rate specified is 11%. This percentage indicates the portion of the sale price the salesperson will earn as their commission.

• First, make sure to clearly identify both the sale price and the commission rate from the problem statement.
• The sale price in our example is $15,794.
• Once you have these figures, you can easily compute the commission by converting the percentage (11%) into a decimal.

By multiplying the decimal form of the commission rate by the sale price, we find the amount of commission. This step can be greatly simplified using a calculator, ensuring precision in the final answer.

Percentage Conversion

Turning percentages into decimals is a fundamental skill in mathematics that helps simplify various calculations, including commission calculations. To convert percentages to decimals, you divide the percentage by 100. This method shifts the decimal point two places to the left.

• For example, to convert 11% into a decimal, you calculate \( \frac{11}{100} = 0.11 \).
• This step is crucial because it creates a decimal form that can seamlessly fit into further mathematical computations involving multiplication or division with whole numbers.

Once converted, you can use this decimal in problems like commission calculations. This conversion is easy and important, allowing for more straightforward operations with your calculator. Remember to perform this conversion meticulously to avoid calculation errors.

Step-by-Step Math Solutions

Understanding complex math problems often becomes easier with a step-by-step approach. Breaking down a problem into smaller, manageable steps clarifies each part of the process. This approach can be directly applied when dealing with percentage-based problems like commission calculations.

• The first step generally involves identifying key figures in the problem, such as the percentage rate and the base amount.
• Next, transition the percentage into a useable decimal form.
• After that, use this decimal to perform straightforward multiplication with the base amount — in this context, the sale price.
• Finally, a calculator can assist in performing precise arithmetic, ensuring all steps yield accurate results.

This systematic method not only aids in understanding but also boosts confidence when tackling similar problems. It ensures a clear path from problem to solution, which is particularly useful in learning environments. Remember, taking your time with each step will help cement these concepts in your mind.