Question:The thickness of a book is 3/8 of its width. If the width is 400 millimeters, what is the total...

1. TRANSLATE the problem information

• Given information:
  • Book thickness = \(\frac{3}{8}\) of its width
  • Width = \(400\) millimeters
  • Need total thickness of 6 books stacked vertically

This tells us we need to find one book's thickness first, then calculate the total for 6 books.

2. INFER the solution approach

• Since the books are stacked vertically, their thicknesses will add up
• We need to: (1) find thickness of one book, (2) multiply by 6

3. Calculate the thickness of one book

• Thickness = \(\frac{3}{8} \times 400\) millimeters
• Thickness = \(3 \times 400 \div 8\)
  \(= 1200 \div 8\)
  \(= 150\) millimeters

4. SIMPLIFY to find the total thickness

• Total thickness = \(6 \times 150\)
  \(= 900\) millimeters

Answer: C) 900

Why Students Usually Falter on This Problem

Most Common Error Path:

Incomplete solution process: Students correctly find that one book has thickness of \(150\) millimeters but forget the second step of multiplying by 6 books.

They see \(150\) millimeters as their final answer and don't realize this is only for one book, not the stack of 6 books the problem asks for.

This leads them to select Choice A (150).

Second Most Common Error:

Weak TRANSLATE skill: Students misinterpret "\(\frac{3}{8}\) of its width" and perform incorrect calculations, such as calculating \(\frac{3}{8} + 400\) instead of \(\frac{3}{8} \times 400\), or making arithmetic errors in the fraction multiplication.

This causes them to get an incorrect thickness for one book, which when multiplied by 6 gives them one of the other incorrect answer choices.

The Bottom Line:

This is a two-step problem disguised as a single calculation. Success requires both accurately translating the fractional relationship and remembering to complete the full solution by accounting for all 6 books in the stack.