What is 20% of 440?

1. TRANSLATE the problem information

• Given: Find \(20\%\) of \(440\)
• What this means mathematically: We need to multiply \(440\) by the decimal equivalent of \(20\%\)

2. TRANSLATE percentage to usable form

• Convert \(20\%\) to decimal: \(20\% = \frac{20}{100} = 0.20\)
• Alternative approach: Keep as fraction \(\frac{20}{100}\)

3. SIMPLIFY by performing the calculation

• Method 1: \(0.20 \times 440 = 88\)
• Method 2:
  \(\frac{20}{100} \times 440 = \frac{20 \times 440}{100}\)
  \(= \frac{8,800}{100}\)
  \(= 88\)

Answer: 88 (Choice B)

Why Students Usually Falter on This Problem

Most Common Error Path:

Weak TRANSLATE skill: Students confuse percentage notation and think "\(20\%\)" means "multiply by 20" instead of "multiply by 0.20."

They calculate: \(20 \times 440 = 8,800\), which isn't even among the answer choices. This leads to confusion and guessing, or they might notice that \(8,800 \div 10 = 880\) and incorrectly select Choice C (880).

Second Most Common Error:

Incomplete TRANSLATE reasoning: Students correctly understand that percentages involve division by 100, but get confused about the order of operations.

They might calculate \(\frac{440}{100}\) first (getting \(4.4\)) then multiply by 20 (getting 88) - which actually gives the right answer by accident. However, some students calculate \(\frac{20}{440}\) instead, leading to a very small decimal that doesn't match any choices. This causes them to get stuck and randomly select an answer.

The Bottom Line:

Success on percentage problems depends entirely on correctly translating "\(\mathrm{X\%~of~Y}\)" into "\(\frac{\mathrm{X}}{100} \times \mathrm{Y}\)" or "\(0.0\mathrm{X} \times \mathrm{Y}\)". Once that translation is solid, the arithmetic is straightforward.