To determine how many pieces of rope measuring \( \frac{5}{7} \) of a yard Chad can divide his 15-yard rope into, you can set up the equation:
\[ \text{Number of pieces} = \frac{\text{Total length of rope}}{\text{Length of each piece}} = \frac{15}{\frac{5}{7}} \]
To divide by a fraction, you can multiply by its reciprocal:
\[ \frac{15}{\frac{5}{7}} = 15 \times \frac{7}{5} = \frac{15 \times 7}{5} = \frac{105}{5} = 21 \]
Therefore, Chad can divide his rope into 21 pieces of \( \frac{5}{7} \) of a yard.
The correct answer is A. 21.