To determine the sign of the product of \(-\frac{2}{9} \times \frac{1}{7}\), we look at the signs of the individual numbers being multiplied.
- The first number, \(-\frac{2}{9}\), is negative.
- The second number, \(\frac{1}{7}\), is positive.
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 negative.
So the answer is: -