There are 450 tiles in a box. Of these tiles, 6% are black. How many black tiles are in the...

1. TRANSLATE the problem information

• Given information:
  • Total tiles: 450
  • Percentage that are black: \(6\%\)
  • Need to find: Number of black tiles

2. INFER the mathematical approach

• To find "\(6\%\) of 450," I need to multiply 450 by \(6\%\)
• First, I must convert the percentage to a usable mathematical form

3. TRANSLATE percentage to mathematical form

• \(6\% = \frac{6}{100} = 0.06\)
• This means 6 out of every 100 tiles are black

4. Calculate the result

• Number of black tiles = \(0.06 \times 450 = 27\)
• Alternative: \(\frac{6}{100} \times 450 = \frac{6 \times 450}{100} = \frac{2700}{100} = 27\)

Answer: 27

Why Students Usually Falter on This Problem

Most Common Error Path:

Weak TRANSLATE skill: Students convert \(6\%\) incorrectly as \(0.6\) instead of \(0.06\)

They think: "\(6\%\) becomes \(0.6\), so \(0.6 \times 450 = 270\)"

This fundamental misunderstanding of how percentages convert to decimals leads to an answer that's 10 times too large. This leads to confusion when none of the answer choices match 270.

Second Most Common Error:

Poor INFER reasoning: Students think they should divide instead of multiply

They reason: "If \(6\%\) are black, maybe I divide 450 by 6 to get 75"

This stems from not understanding that "\(6\%\) of something" always means multiplication, not division. This may lead them to select an incorrect answer of 75 if it appears as a choice.

The Bottom Line:

Success on percentage problems depends entirely on correctly translating the percentage into decimal or fraction form. Once that translation is accurate, the rest is straightforward multiplication.