F = 9/5C + 32 The given equation converts a temperature from degrees Celsius, C, to degrees Fahrenheit, F. Which...

1. TRANSLATE the problem information

• Given equation: \(\mathrm{F = \frac{9}{5}C + 32}\)
• Goal: Solve for C in terms of F

2. INFER the solution strategy

• To isolate C, we need to "undo" what's been done to it
• C is multiplied by 9/5, then 32 is added
• We'll use inverse operations in reverse order: subtract 32 first, then divide by 9/5

3. SIMPLIFY by subtracting 32 from both sides

\(\mathrm{F = \frac{9}{5}C + 32}\)

\(\mathrm{F - 32 = \frac{9}{5}C}\)

4. SIMPLIFY by multiplying both sides by 5/9

• To isolate C, multiply by the reciprocal of 9/5, which is 5/9
• \(\mathrm{\frac{5}{9}(F - 32) = \frac{5}{9} \times \frac{9}{5}C}\)
• \(\mathrm{\frac{5}{9}(F - 32) = C}\)

Answer: B. \(\mathrm{C = \frac{5}{9}(F - 32)}\)

Why Students Usually Falter on This Problem

Most Common Error Path:

Weak SIMPLIFY execution: Students make order of operations errors when dealing with the subtraction and fraction multiplication.

They might subtract 32 from both sides correctly but then distribute the 5/9 incorrectly, getting:

\(\mathrm{C = \frac{5}{9}F - 32}\)

This leads them to select Choice A (\(\mathrm{C = \frac{5}{9}F - 32}\))

Second Most Common Error:

Poor INFER reasoning: Students use the wrong reciprocal or get confused about which fraction to multiply by.

Instead of multiplying by 5/9, they might multiply by 9/5 (thinking they need the same fraction), leading to:

\(\mathrm{C = \frac{9}{5}(F - 32)}\)

This may lead them to select Choice C (\(\mathrm{C = \frac{9}{5}(F - 32)}\))

The Bottom Line:

This problem tests careful execution of inverse operations with fractions. The key insight is recognizing that parentheses matter - you must multiply the entire expression (F - 32) by 5/9, not just F.