1. **State the problem:** Add the fractions and mixed number: $\frac{1}{3} + \frac{1}{6} + 2 \frac{1}{4}$. 2. **Convert the mixed number to an improper fraction:** $$2 \frac{1}{4} = \frac{2 \times 4 + 1}{4} = \frac{9}{4}$$ 3. **Find a common denominator for all fractions:** The denominators are 3, 6, and 4. The least common denominator (LCD) is 12. 4. **Convert each fraction to have denominator 12:** $$\frac{1}{3} = \frac{1 \times 4}{3 \times 4} = \frac{4}{12}$$ $$\frac{1}{6} = \frac{1 \times 2}{6 \times 2} = \frac{2}{12}$$ $$\frac{9}{4} = \frac{9 \times 3}{4 \times 3} = \frac{27}{12}$$ 5. **Add the fractions:** $$\frac{4}{12} + \frac{2}{12} + \frac{27}{12} = \frac{4 + 2 + 27}{12} = \frac{33}{12}$$ 6. **Simplify the fraction:** Divide numerator and denominator by 3: $$\frac{33}{12} = \frac{11}{4}$$ 7. **Convert back to a mixed number:** $$\frac{11}{4} = 2 \frac{3}{4}$$ **Final answer:** $2 \frac{3}{4}$