An antique recipe requires 19 gills of buttermilk. If 1 gill is equivalent to 4 fluid ounces, what is the...

1. TRANSLATE the problem information

• Given information:
  • Recipe needs 19 gills of buttermilk
  • Conversion factor: \(1 \text{ gill} = 4 \text{ fluid ounces}\)
• What we need to find: Total fluid ounces required

2. INFER the solution approach

• This is a unit conversion problem
• When converting units with a given factor, multiply the original amount by the conversion factor
• Setup: \(19 \text{ gills} \times 4 \text{ fluid ounces per gill}\)

3. Calculate the result

• \(19 \times 4 = 76 \text{ fluid ounces}\)

Answer: C. 76

Why Students Usually Falter on This Problem

Most Common Error Path:

Weak INFER skill: Students confuse unit conversion with simple arithmetic operations and add instead of multiply.

They might think: "I have 19 gills and each gill is 4 fluid ounces, so \(19 + 4 = 23 \text{ fluid ounces}\) total." This fundamental misunderstanding of how unit conversion works leads them to select Choice B (23).

Second Most Common Error:

Arithmetic execution error: Students set up the problem correctly but make a calculation mistake.

A common error is calculating \(20 \times 4 = 80\) when using the mental math approach (19 = 20 - 1) but forgetting to subtract the extra 4, leading them to select Choice D (80).

The Bottom Line:

This problem tests whether students understand the fundamental concept of unit conversion - that you multiply by conversion factors, not add them. The arithmetic is straightforward once the setup is correct.