A fitness club has 635 members. 12% of them are premium members. How many members are premium members?

1. TRANSLATE the problem information

• Given information:
  • Total members: 635
  • Premium members: 12% of total
  • Need to find: Number of premium members

• This translates to: Find \(12\% \text{ of } 635\)

2. INFER the calculation approach

• Since we need "12% of 635," this is a percentage calculation problem
• We can solve this by converting the percentage to either a decimal or fraction, then multiply

3. SIMPLIFY using percentage calculation

Choose your preferred method:

Method A (decimal conversion):

• \(12\% = 12 \div 100 = 0.12\)
• \(635 \times 0.12 = 76.2\) (use calculator)

Method B (fraction method):

• \(12\% = \frac{12}{100}\)
• \(635 \times \frac{12}{100} = 635 \times 12 \div 100 = 7620 \div 100 = 76.2\)

4. APPLY CONSTRAINTS for real-world context

• Since we're counting people, round 76.2 to the nearest whole number
• 76.2 rounds to 76 people

Answer: B. 76

Why Students Usually Falter on This Problem

Most Common Error Path:

Weak TRANSLATE skill: Misunderstanding what "12% of" means mathematically

Students might think "12% of 635" means adding 12 to 635, or they might confuse the operation entirely. Some students struggle with the concept that "of" means multiplication in percentage problems.

This leads to confusion and random guessing among the answer choices.

Second Most Common Error:

Poor SIMPLIFY execution: Making arithmetic errors in the calculation

Students correctly set up \(635 \times 0.12\) but make mistakes in multiplication, or they forget to convert the percentage properly (using 12 instead of 0.12). Calculator entry errors are also common here.

This may lead them to select Choice A (66) or Choice D (86) depending on their specific calculation error.

The Bottom Line:

This problem tests whether students truly understand that percentage calculations involve multiplication, not addition, and whether they can execute the arithmetic accurately. The key insight is recognizing that "12% of" always means "multiply by 0.12."