Of 1{,}250{,}000 marbles, 100{,}000 are red. What percentage of the marbles are not red?8%36%72%92%

1. TRANSLATE the problem information

• Given information:
  • Total marbles: \(1,250,000\)
  • Red marbles: \(100,000\)
  • Find: percentage that are NOT red
• What this tells us: We need the percentage of all marbles except the red ones

2. INFER the solution approach

• To find percentage of "not red" marbles, we first need to find how many marbles are "not red"
• "Not red" means all the marbles minus the red ones
• Then we'll convert that quantity to a percentage of the total

3. Calculate the number of non-red marbles

\(\mathrm{Not\;red\;marbles} = \mathrm{Total\;marbles} - \mathrm{Red\;marbles}\)

\(\mathrm{Not\;red\;marbles} = 1,250,000 - 100,000 = 1,150,000\)

4. SIMPLIFY to convert to percentage

\(\mathrm{Percentage} = (1,150,000 \div 1,250,000) \times 100\%\)

Simplify the fraction: \(1,150,000 \div 1,250,000 = 1,150 \div 1,250 = 23 \div 25 = 0.92\)

Convert to percentage: \(0.92 \times 100\% = 92\%\)

Answer: D (92%)

Why Students Usually Falter on This Problem

Most Common Error Path:

Weak TRANSLATE skill: Students misread the question and find the percentage of RED marbles instead of NOT red marbles.

They correctly calculate: \(100,000 \div 1,250,000 = 0.08 = 8\%\), but this answers the wrong question. They miss the critical word "not" in "What percentage of the marbles are not red?"

This leads them to select Choice A (8%).

Second Most Common Error:

Poor SIMPLIFY execution: Students set up the problem correctly but make arithmetic errors when converting the fraction \(1,150,000 \div 1,250,000\) to a percentage.

Division errors or percentage conversion mistakes can lead to confusion and potentially selecting wrong answer choices based on their incorrect calculations.

The Bottom Line:

This problem tests careful reading comprehension as much as mathematical calculation. The word "not" completely changes what quantity needs to be found, making precise TRANSLATE skills essential for success.