Of the 840,000 registered voters in a congressional district, 756,000 actually voted in the recent election. What percentage of the...

1. TRANSLATE the problem information

• Given information:
  • Total registered voters: \(\mathrm{840,000}\)
  • Actual voters: \(\mathrm{756,000}\)
  • Find: Percentage who did NOT vote

• This tells us we need to find what fraction of the total chose not to participate, then convert to a percentage.

2. INFER the solution approach

• Since we want non-voters, we first need to find how many people didn't vote
• Then we'll calculate what percentage this represents of the total registered voters
• Strategy: Subtraction first, then percentage calculation

3. Calculate the number of non-voters

• Non-voters = Total registered - Actual voters
• Non-voters = \(\mathrm{840,000 - 756,000 = 84,000}\)

4. TRANSLATE this into a percentage calculation

• We need: \(\mathrm{(non\text{-}voters ÷ total\ registered) × 100\%}\)
• Percentage = \(\mathrm{(84,000 ÷ 840,000) × 100\%}\)

5. SIMPLIFY the fraction

• \(\mathrm{84,000 ÷ 840,000 = 84 ÷ 840 = 1 ÷ 10 = 0.1}\)
• \(\mathrm{0.1 × 100\% = 10\%}\)

Answer: A (10%)

Why Students Usually Falter on This Problem

Most Common Error Path:

Weak TRANSLATE skill: Students calculate the percentage of people who DID vote instead of those who did NOT vote.

They correctly find that \(\mathrm{756,000 ÷ 840,000 = 0.9 = 90\%}\), but they answer the wrong question. They're finding the participation rate rather than the non-participation rate.

This leads them to select Choice C (90%).

Second Most Common Error:

Poor INFER reasoning: Students attempt to work directly with the given numbers without recognizing they need to find the non-voters first.

They might try complex calculations or get confused about which numbers to use in their percentage formula, leading to computational errors or abandoning the systematic approach.

This causes them to get stuck and guess among the remaining choices.

The Bottom Line:

This problem requires careful attention to what exactly is being asked. The key challenge isn't the math—it's making sure you're calculating the percentage of the RIGHT group (non-voters, not voters).