1. The problem is to multiply $9$ by $-\frac{5}{3}$. 2. The formula for multiplication of a whole number and a fraction is: $$a \times \frac{b}{c} = \frac{a \times b}{c}$$ 3. Applying the formula: $$9 \times \left(-\frac{5}{3}\right) = \frac{9 \times (-5)}{3}$$ 4. Multiply the numerators: $$\frac{9 \times (-5)}{3} = \frac{-45}{3}$$ 5. Simplify the fraction by dividing numerator and denominator by their greatest common divisor, which is 3: $$\frac{\cancel{45}}{\cancel{3}} = -15$$ 6. Therefore, the final answer is: $$-15$$