Question:The sum of a number z and 6, divided by 4, is equal to 9. Which equation represents this situation?z...

1. TRANSLATE the problem information

• Given phrase: 'The sum of a number z and 6, divided by 4, is equal to 9'
• Break this into parts:
  • 'The sum of a number z and 6' → \((z + 6)\)
  • 'divided by 4' → the entire sum ÷ 4 → \(\frac{(z + 6)}{4}\)
  • 'is equal to 9' → \(= 9\)

2. INFER the correct grouping

• The key insight: 'divided by 4' applies to the entire sum, not just part of it
• This means we need parentheses around \((z + 6)\) to show that the addition happens first
• Without parentheses, division would only apply to the last term

3. Combine the parts

• Putting it all together: \(\frac{(z + 6)}{4} = 9\)
• This matches choice (D)

Answer: D

Why Students Usually Falter on This Problem

Most Common Error Path:

Weak TRANSLATE skill: Students don't recognize that 'the sum...divided by 4' means the entire sum needs parentheses.

They might translate it as \(z + \frac{6}{4} = 9\), thinking each term is handled separately. This follows order of operations where division happens before addition, giving them \(z + 1.5 = 9\) instead of the intended meaning.

This leads them to select Choice A (\(z + \frac{6}{4} = 9\)).

Second Most Common Error:

Poor TRANSLATE reasoning: Students see the word 'divided' but misinterpret the structure, thinking about multiplication instead.

They might reason 'if something is divided by 4, then 4 times that something equals the result,' leading to \(4(z + 6) = 9\). This reverses the relationship completely.

This may lead them to select Choice B (\(4(z + 6) = 9\)).

The Bottom Line:

Word problems requiring translation to algebra are all about careful attention to grouping and order of operations. The phrase 'the sum...divided by' is a signal that parentheses are needed to group the sum before applying the division.