Of 300,000 paper clips, 234,000 are size large. What percentage of the paper clips are size large?

1. TRANSLATE the problem information

• Given information:
  • Total paper clips: 300,000
  • Large paper clips: 234,000
  • Find: What percentage are large?
• This asks us to find what portion of the total the large clips represent, expressed as a percentage.

2. TRANSLATE what "percentage" means

• Percentage = (Part ÷ Whole) × 100%
• Here: Part = 234,000 (large clips), Whole = 300,000 (total clips)

3. SIMPLIFY by calculating the division

• Calculate: \(\mathrm{234{,}000 ÷ 300{,}000 = 0.78}\) (use calculator)

4. SIMPLIFY by converting to percentage

• Convert decimal to percentage: \(\mathrm{0.78 × 100\% = 78\%}\)

Answer: D. 78%

Why Students Usually Falter on This Problem

Most Common Error Path:

Weak TRANSLATE skill: Students misunderstand what they're calculating and find the percentage of non-large clips instead.

They calculate: \(\mathrm{(300{,}000 - 234{,}000) ÷ 300{,}000 = 66{,}000 ÷ 300{,}000 = 0.22 = 22\%}\)

This may lead them to select Choice A (22%)

Second Most Common Error:

Incomplete SIMPLIFY execution: Students correctly calculate \(\mathrm{234{,}000 ÷ 300{,}000 = 0.78}\) but forget the final step of converting to percentage.

They might see 0.78 and get confused about how to match it to the answer choices, leading to confusion and guessing.

The Bottom Line:

The key challenge is carefully reading what the problem asks for. Students must distinguish between "percentage that are large" versus "percentage that are not large" - a common source of careless errors in percentage problems.