432 is 96% of what number?

1. TRANSLATE the problem information

• Given information:
  • 432 is 96% of some unknown number
• What this tells us: We need to find the number that, when we take 96% of it, gives us 432

2. TRANSLATE into mathematical notation

• Let x = the unknown number
• "432 is 96% of x" becomes: \(432 = 96\% \times \mathrm{x}\)
• Convert percentage to decimal: \(432 = 0.96\mathrm{x}\)

3. SIMPLIFY to solve for x

• We have the equation: \(432 = 0.96\mathrm{x}\)
• Divide both sides by 0.96: \(\mathrm{x} = 432 \div 0.96\)
• Calculate (use calculator): \(\mathrm{x} = 450\)

4. Check your answer

• Does 96% of 450 equal 432?
• \(0.96 \times 450 = 432\) ✓

Answer: 450

Why Students Usually Falter on This Problem

Most Common Error Path:

Weak TRANSLATE reasoning: Students misinterpret the problem structure and think they need to find 96% of 432 instead of finding what number 432 is 96% of.

They calculate: \(432 \times 0.96 = 414.72\)

This leads to confusion since 414.72 doesn't make sense as an answer, causing them to abandon systematic solution and guess.

Second Most Common Error:

Poor SIMPLIFY execution: Students set up the equation correctly but make arithmetic errors when dividing 432 by 0.96, especially if attempting the division without a calculator.

Common mistakes include misplacing decimal points or incorrect long division, leading to answers like 45, 4500, or other incorrect values.

The Bottom Line:

The key challenge is recognizing that "A is B% of what number?" requires setting up A = B% × x and solving for x, not calculating B% × A. The language structure can be confusing, making proper translation the critical first step.