1. **State the problem:** We need to find the total volume of lemonade made by mixing 2 1/2 liters of water, 3/4 liters of lemon juice, and 1/4 liters of sugar syrup. 2. **Convert mixed numbers to improper fractions:** - Water: $2 \frac{1}{2} = \frac{5}{2}$ liters - Lemon juice: $\frac{3}{4}$ liters - Sugar syrup: $\frac{1}{4}$ liters 3. **Add all volumes together:** $$\frac{5}{2} + \frac{3}{4} + \frac{1}{4}$$ 4. **Find a common denominator:** The common denominator for 2 and 4 is 4. $$\frac{5}{2} = \frac{5 \times 2}{2 \times 2} = \frac{10}{4}$$ 5. **Sum the fractions:** $$\frac{10}{4} + \frac{3}{4} + \frac{1}{4} = \frac{10 + 3 + 1}{4} = \frac{14}{4}$$ 6. **Simplify the fraction:** $$\frac{14}{4} = \frac{\cancel{14}^7}{\cancel{4}^2} = \frac{7}{2}$$ 7. **Convert back to mixed number:** $$\frac{7}{2} = 3 \frac{1}{2}$$ liters **Final answer:** The total volume of lemonade made is $3 \frac{1}{2}$ liters.