What percent of 360 is 90?25%30%270%324%

1. TRANSLATE the problem information

• TRANSLATE "What percent of 360 is 90?" into mathematical language:
  • Let \(\mathrm{x}\) = the unknown percentage
  • "x percent of 360 equals 90" becomes: \(\frac{\mathrm{x}}{100} \times 360 = 90\)

2. SIMPLIFY to solve for the percentage

• Divide both sides by 360:
  \(\frac{\mathrm{x}}{100} = \frac{90}{360}\)

• SIMPLIFY the fraction:
  \(\frac{\mathrm{x}}{100} = \frac{1}{4}\)

• Multiply both sides by 100:
  \(\mathrm{x} = 25\)

• This means 90 is 25% of 360

3. Verify using the alternative method

• SIMPLIFY: \(90 \div 360 = 0.25 = 25\%\) ✓

Answer: A

Why Students Usually Falter on This Problem

Most Common Error Path:

Weak TRANSLATE skill: Students confuse "what percent of 360 is 90" with "90 is what percent more than 360" or mix up which number should be in the numerator vs denominator.

Instead of setting up \(\frac{\mathrm{x}}{100} \times 360 = 90\), they might set up \(\frac{\mathrm{x}}{100} \times 90 = 360\), leading to \(\mathrm{x} = 400\%\). Since 400% isn't among the choices, this leads to confusion and guessing.

Second Most Common Error:

Poor SIMPLIFY execution: Students correctly set up the equation but make arithmetic errors when reducing \(\frac{90}{360}\).

They might incorrectly simplify \(\frac{90}{360}\) as \(\frac{3}{4}\) instead of \(\frac{1}{4}\), leading to 75% instead of 25%. Since 75% isn't an option, they may select Choice D (324%) thinking they made a calculation error somewhere and picking the largest value.

The Bottom Line:

This problem tests whether students can correctly interpret percentage language and translate it into the right mathematical setup. The key insight is recognizing that "what percent of A is B" means finding x where \(\frac{\mathrm{x}}{100} \times \mathrm{A} = \mathrm{B}\).