To determine the sign of the product \(-\frac{2}{9} \times \frac{1}{7}\), we first note the signs of the numbers being multiplied.
- The number \(-\frac{2}{9}\) is negative.
- The number \(\frac{1}{7}\) is positive.
The product of a negative number and a positive number is always negative.
Therefore, the sign of the product \(-\frac{2}{9} \times \frac{1}{7}\) is negative.
Thus, the answer is: \(-\)