A factory produces 240 units in each shift. In each shift, 3/4 of the units pass final inspection. If the...

1. TRANSLATE the problem information

• Given information:
  • 240 units produced per shift
  • 3/4 of units pass inspection each shift
  • Factory operates for 8 shifts
  • Need: Total units passing inspection

2. INFER the solution approach

• Key insight: We can solve this two ways:
  • Method A: Find passing units per shift, then multiply by 8 shifts
  • Method B: Find total units produced, then apply the 3/4 rate
• Let's use Method A (it's often easier to work with smaller numbers first)

3. SIMPLIFY to find units passing inspection per shift

• Calculate: \(\frac{3}{4} \times 240\)
• \(\frac{3}{4} \times 240 = \frac{3 \times 240}{4} = \frac{720}{4} = 180\) units per shift

4. SIMPLIFY to find total passing units over 8 shifts

• \(180\) units per shift \(\times 8\) shifts \(= 1,440\) units

Answer: 1440

Why Students Usually Falter on This Problem

Most Common Error Path:

Weak TRANSLATE skill: Students misinterpret what "3/4 of the units pass inspection" means and instead calculate \(\frac{3}{4} \times 8\) shifts \(= 6\) shifts, then multiply \(240 \times 6 = 1,440\). While this accidentally gives the right answer, the reasoning is completely wrong - they're treating 3/4 as a fraction of shifts rather than a fraction of units produced.

Second Most Common Error:

Poor SIMPLIFY execution: Students correctly set up \(\frac{3}{4} \times 240\) but make calculation errors, such as:

• Getting \(3 \times 240 = 720\), but then dividing \(720 \div 4 = 160\) instead of 180
• Or calculating \(240 \div 4 = 60\), then \(60 \times 3 = 180\), but forgetting to multiply by 8 shifts

This leads to answers like \(160 \times 8 = 1,280\) or stopping at 180 without considering all 8 shifts.

The Bottom Line:

This problem requires careful attention to what each number represents (units vs. shifts) and systematic execution of fraction multiplication across multiple steps. Success depends on translating the language correctly and following through with all calculations.

6. Question Type - Student Response

Students can enter their answer as: 1440