A real estate agent earns an 8% commission on the sale of a house. If the house sells for $300,000,...

1. TRANSLATE the problem information

• Given information:
  • Commission rate: \(8\%\)
  • House selling price: \(\$300,000\)
  • Need to find: Commission amount

• This tells us we need to calculate \(8\%\) of \(\$300,000\)

2. TRANSLATE the percentage to decimal form

• Convert \(8\%\) to decimal: \(8\% = \frac{8}{100} = 0.08\)

• Set up the calculation: \(\mathrm{Commission} = 0.08 \times \$300,000\)

3. SIMPLIFY the multiplication

• Calculate: \(0.08 \times \$300,000 = \$24,000\) (use calculator)

Answer: C - \(\$24,000\)

Why Students Usually Falter on This Problem

Most Common Error Path:

Weak TRANSLATE skill: Students convert \(8\%\) incorrectly to \(0.8\) instead of \(0.08\)

They think "\(8\%\) means 8 tenths" rather than "8 hundredths," so they calculate:
\(0.8 \times \$300,000 = \$240,000\)

Since this isn't among the choices, this leads to confusion and guessing.

Second Most Common Error:

Poor TRANSLATE reasoning: Students calculate a different percentage by mistake

Looking at choice (D) \(\$30,000\), they might think "that looks like \(10\%\) of \(\$300,000\)" and select it, having mixed up \(8\%\) with \(10\%\) in their mental calculation.

This may lead them to select Choice D (\(\$30,000\)).

The Bottom Line:

The key challenge is accurately converting the percentage to decimal form. Students who rush through the percentage-to-decimal conversion or who haven't solidified this foundational skill will struggle with this otherwise straightforward problem.