A wind vane rotates clockwise through an angle equal to (\frac{7}{15}) of a full revolution.One full revolution measures 360 degrees.What...

1. TRANSLATE the problem information

• Given information:
  • Wind vane rotates \(\frac{7}{15}\) of a full revolution clockwise
  • One full revolution = \(360\) degrees
  • Need the rotation measure in degrees

• What this tells us: We need to find \(\frac{7}{15}\) of \(360\) degrees

2. SIMPLIFY the calculation

• Set up: \(\frac{7}{15} \times 360°\)
• Recognize that \(360 \div 15 = 24\)
• So: \(\frac{7}{15} \times 360 = 7 \times 24 = 168°\)

Answer: 168

Why Students Usually Falter on This Problem

Most Common Error Path:

Weak TRANSLATE skill: Students may not recognize that "\(\frac{7}{15}\) of a full revolution" means they need to multiply \(\frac{7}{15} \times 360\).

Some students might think they need to divide \(360\) by \(\frac{7}{15}\), or they might get confused about whether to multiply or divide. Others might not connect "\(\frac{7}{15}\) of" with multiplication at all.

This leads to confusion and incorrect calculations, potentially resulting in answers like \(77\) \((360 \div 7 \times 15)\) or other incorrect values.

Second Most Common Error:

Poor SIMPLIFY execution: Students correctly set up \(\frac{7}{15} \times 360\) but make calculation errors.

They might calculate this as \((7 \times 360) \div 15 = 2520 \div 15\) and then make division errors, or they might not recognize that \(360 \div 15 = 24\) simplifies the problem significantly.

This leads to arithmetic mistakes that produce incorrect integer answers.

The Bottom Line:

This problem tests whether students understand that "fraction of" means multiplication and can perform the arithmetic efficiently. The key insight is recognizing that fractions of standard measurements (like \(360°\)) often simplify nicely.