1. **State the problem:** Simplify the expression $$\frac{5w}{3} - \frac{9}{2}$$. 2. **Formula and rules:** To subtract fractions, they must have a common denominator. The common denominator of 3 and 2 is 6. 3. **Rewrite each fraction with denominator 6:** $$\frac{5w}{3} = \frac{5w \times 2}{3 \times 2} = \frac{10w}{6}$$ $$\frac{9}{2} = \frac{9 \times 3}{2 \times 3} = \frac{27}{6}$$ 4. **Subtract the fractions:** $$\frac{10w}{6} - \frac{27}{6} = \frac{10w - 27}{6}$$ 5. **Final answer:** The simplified expression is $$\frac{10w - 27}{6}$$. This means the difference between the two fractions is a single fraction with numerator $10w - 27$ and denominator 6.