1. **State the problem:** Calculate the product of $\frac{7}{9}$ and $-\frac{9}{8}$. 2. **Formula used:** When multiplying fractions, multiply the numerators together and the denominators together: $$\frac{a}{b} \times \frac{c}{d} = \frac{a \times c}{b \times d}$$ 3. **Apply the formula:** $$\frac{7}{9} \times \left(-\frac{9}{8}\right) = \frac{7 \times (-9)}{9 \times 8}$$ 4. **Calculate numerator and denominator:** Numerator: $7 \times (-9) = -63$ Denominator: $9 \times 8 = 72$ So, $$\frac{-63}{72}$$ 5. **Simplify the fraction:** Find the greatest common divisor (GCD) of 63 and 72, which is 9. Divide numerator and denominator by 9: $$\frac{-63 \div 9}{72 \div 9} = \frac{-7}{8}$$ 6. **Final answer:** $$\boxed{-\frac{7}{8}}$$