Of 900,000 beads, 828,000 are silver. What percentage of the beads are silver?

1. TRANSLATE the problem information

• Given information:
  • \(\mathrm{Total\,beads = 900,000}\)
  • \(\mathrm{Silver\,beads = 828,000}\)
• What we need: Percentage of beads that are silver

2. INFER the approach

• To find what percentage silver beads represent, we need the part-to-whole ratio
• Silver beads are the "part," total beads are the "whole"
• Use the percentage formula: \(\mathrm{Percentage = \frac{Part}{Whole} \times 100\%}\)

3. SIMPLIFY the calculation

• Set up the fraction: \(\mathrm{\frac{828,000}{900,000}}\)
• Divide: \(\mathrm{828,000 \div 900,000 = 0.92}\)
• Convert to percentage: \(\mathrm{0.92 \times 100\% = 92\%}\)

Answer: D. 92%

Why Students Usually Falter on This Problem

Most Common Error Path:

Weak TRANSLATE skill: Finding the percentage of NON-silver beads instead of silver beads

Students sometimes get confused about what the question is asking for. They might calculate:

• Non-silver beads \(\mathrm{= 900,000 - 828,000 = 72,000}\)
• Then find: \(\mathrm{\frac{72,000}{900,000} = 0.08 = 8\%}\)

This may lead them to select Choice A (8%)

The Bottom Line:

This problem tests whether students can correctly identify what represents the "part" in a part-to-whole percentage calculation. The key is carefully reading what the question asks for - percentage of silver beads, not non-silver beads.