To determine the sign of the product \(-\frac{2}{9} \times \frac{1}{7}\), we can analyze the signs of the numbers involved.
- The fraction \(-\frac{2}{9}\) is negative because it has a negative numerator.
- The fraction \(\frac{1}{7}\) is positive because it has a positive numerator.
When multiplying a negative number by a positive number, the result is negative.
Therefore, the sign of the product \(-\frac{2}{9} \times \frac{1}{7}\) is \(-\).
The answer is \(-\).