What is 23% text{ of } 100?

1. TRANSLATE the problem information

• Given information:
  • We need to find \(23\%\) of \(100\)
  • This means: \(\frac{23}{100} \times 100\)

2. SIMPLIFY the calculation

• Set up the multiplication: \(\left(\frac{23}{100}\right) \times 100\)
• Notice that 100 in numerator and denominator cancel: \(\left(\frac{23}{100}\right) \times 100 = 23\)
• The calculation becomes straightforward: \(23\)

Answer: 23 (Choice A)

Why Students Usually Falter on This Problem

Most Common Error Path:

Weak TRANSLATE skill: Misunderstanding what "23% of 100" means

Students often confuse "23% of 100" with related but different concepts:

• "23% less than 100" (which would be \(100 - 23 = 77\))
• "23% more than 100" (which would be \(100 + 23 = 123\))

This confusion about the meaning of "of" in percentage problems may lead them to select Choice C (77) or Choice D (123).

Second Most Common Error:

Poor TRANSLATE reasoning: Misapplying percentage concepts

Some students might think that finding a percentage involves doubling or other operations, leading to calculations like \(23 \times 2 = 46\).

This may lead them to select Choice B (46).

The Bottom Line:

The key challenge is correctly interpreting the phrase "X% of Y" as meaning \(\left(\frac{X}{100}\right) \times Y\), not adding or subtracting the percentage from the base number.