There are a total of 840 seats in a school auditorium. During an assembly, students occupied 50% of the seats...

1. TRANSLATE the problem information

• Given information:
  • Total seats in auditorium: 840 seats
  • Students occupied 50% of these seats

• What this tells us: We need to find 50% of 840

2. TRANSLATE the percentage into a calculation

• "50% of 840" means: \(840 \times \frac{50}{100}\)
• We can also write this as: \(840 \times 0.5\)

3. SIMPLIFY to find the answer

• \(840 \times \frac{50}{100}\)
  \(= 840 \times 0.5\)
  \(= 420\)

Answer: C. 420

Why Students Usually Falter on This Problem

Most Common Error Path:

Weak TRANSLATE skill: Students may confuse what "50% of 840" actually means. Some students might think they need to find what percentage 50 is of 840, leading them to calculate \(\frac{50}{840}\) or similar incorrect operations.

This type of confusion typically leads to abandoning systematic solution and guessing among the answer choices.

Second Most Common Error:

Conceptual confusion about percentages: Students might remember that 50% = 1/2, but then incorrectly think they should divide 840 by 50 instead of multiplying by 0.5.

This may lead them to calculate \(840 \div 50 = 16.8\), which doesn't match any answer choice, causing them to get stuck and guess.

The Bottom Line:

This problem tests whether students can correctly TRANSLATE percentage language into the right mathematical operation. The key insight is recognizing that "50% of a number" always means "multiply that number by 0.5 (or 50/100)."