1. **State the problem:** Simplify the expression $30 - \frac{5}{15} + 3$. 2. **Recall the order of operations:** Perform division before addition and subtraction. 3. **Calculate the division:** $$\frac{5}{15} = \frac{\cancel{5}}{\cancel{15}} = \frac{1}{3}$$ 4. **Rewrite the expression:** $$30 - \frac{1}{3} + 3$$ 5. **Combine the whole numbers:** $$30 + 3 = 33$$ 6. **Rewrite the expression:** $$33 - \frac{1}{3}$$ 7. **Convert 33 to a fraction with denominator 3:** $$33 = \frac{33 \times 3}{3} = \frac{99}{3}$$ 8. **Subtract the fractions:** $$\frac{99}{3} - \frac{1}{3} = \frac{99 - 1}{3} = \frac{98}{3}$$ 9. **Final answer:** $$\frac{98}{3}$$ or approximately $32.67$. This is the simplified form of the expression.