To find the quotient of \( \frac{1}{2} \) and \( \frac{12}{7} \), you can divide \( \frac{1}{2} \) by \( \frac{12}{7} \). Dividing by a fraction is the same as multiplying by its reciprocal.
So, we can calculate:
\[ \frac{1}{2} \div \frac{12}{7} = \frac{1}{2} \times \frac{7}{12} \]
Now, multiply the fractions:
\[ \frac{1 \times 7}{2 \times 12} = \frac{7}{24} \]
Therefore, the quotient of \( \frac{1}{2} \) and \( \frac{12}{7} \) is \( \frac{7}{24} \).