A fish swam a distance of 5,104 yards. How far did the fish swim, in miles? (1 mile = 1,760...

1. TRANSLATE the problem information

• Given information:
  • Distance swum: 5,104 yards
  • Conversion factor: \(\mathrm{1\ mile = 1{,}760\ yards}\)
  • Need to find: distance in miles

• What this tells us: We need to convert from a smaller unit (yards) to a larger unit (miles)

2. INFER the approach

• This is a unit conversion problem
• Since we're going from smaller units to larger units, we need to divide by the conversion factor
• Set up: \(\mathrm{5{,}104\ yards ÷ 1{,}760\ yards\ per\ mile}\)

3. SIMPLIFY by performing the calculation

• \(\mathrm{5{,}104 ÷ 1{,}760 = 2.9}\) (use calculator)

Answer: B. 2.9

Why Students Usually Falter on This Problem

Most Common Error Path:

Weak INFER skill: Students confuse the direction of conversion and multiply instead of divide

They think: "I have yards and need miles, so I'll multiply by the conversion factor"
→ \(\mathrm{5{,}104 × 1{,}760 = 8{,}982{,}040\ yards}\) (nonsensical large number)

Since this doesn't match any answer choice, they might try: \(\mathrm{5{,}104 + 1{,}760 = 6{,}864}\)
This may lead them to select Choice D (6,864)

Second Most Common Error:

Poor TRANSLATE reasoning: Students set up the conversion backwards

They calculate: \(\mathrm{1{,}760 ÷ 5{,}104 ≈ 0.34}\), which rounds to 0.3
This may lead them to select Choice A (0.3)

The Bottom Line:

The key challenge is understanding the relationship between unit sizes and operation choice - when converting from smaller to larger units, you always divide by the conversion factor.