Problem 12 - Prealgebra

Question

Commission A tire salesperson has a \(12 \%\) commission rate. If he sells a set of radial tires for $$ 400,$ what is his commission?

Step-by-Step Solution

Answer

The commission is \$48 for selling the tires.

Step 1: Identify the Given Information

The commission rate is given as \(12\%\), and the selling price of the set of radial tires is \$400.

Step 2: Convert Percentage to Decimal

To calculate the commission, convert the percentage rate to a decimal. \(12\%\) as a decimal is \(0.12\).

Step 3: Calculate the Commission

Multiply the selling price by the decimal commission rate to find the commission: \(400 \times 0.12\).

Step 4: Compute the Result

Calculate \(400 \times 0.12 = 48\). The commission is \$48.

Key Concepts

Percentage Conversion

Understanding percentage conversion is vital when dealing with commission calculations, as it helps to make calculations straightforward. A percentage represents a part of a hundred and converting it to a decimal simply involves shifting the decimal point two places to the left. This is because percentages are essentially fractions of 100.

• For example, to convert 12% to a decimal, you move the decimal two places left, resulting in 0.12.
• This can be thought of as dividing the percentage by 100: \(12\% = \frac{12}{100} = 0.12\).

This conversion is crucial because mathematical operations, such as multiplication, are more straightforward to perform with decimals than with percentages. Once the conversion is done, you can easily carry out further calculations, such as determining commissions.

Decimal Multiplication

Decimal multiplication is the next crucial step in calculating commissions once the percentage has been converted. In this specific case, you multiply the selling price of the tires by the decimal form of the commission rate.

• The formula for this calculation is: \[\text{Commission} = \text{Selling Price} \times \text{Decimal Commission Rate}\]
• For example, \(400 \times 0.12 = 48\) is the operation to find the commission on a $400 sale at a 12% rate.

When multiplying decimals, align the numbers vertically without paying attention to the decimal. Once the multiplication is completed, count the total number of decimal places in both numbers to position the decimal correctly in the product. In this problem, since 0.12 has two decimal places, the product (48) does not because it is already a whole number.

Mathematical Problem-Solving

Mathematical problem-solving skills are essential for tackling real-life situations like calculating commissions. Breaking down the problem into smaller, more manageable steps aids significantly in understanding and carrying out the solution. The steps we discussed can be used as a blueprint for solving similar problems:

• First, clearly identify all necessary information given in the problem, such as percentages and amounts.
• Then, convert percentages to decimals to ease calculation.
• After conversion, use multiplication to solve for the desired value.
• Finally, double-check your calculations to ensure accuracy.

With these steps, problems that initially seem complex become accessible and easy to solve. Practice these techniques in different scenarios to sharpen your skills and build confidence in your mathematical abilities.