1. **State the problem:** Samar has a rectangular garden with length $7 \frac{1}{2}$ meters and width $2.5$ meters. Samar already has $12.5$ meters of fencing and wants to know how much more fencing is needed to enclose the garden. 2. **Formula for perimeter of a rectangle:** $$P = 2(\text{length} + \text{width})$$ The perimeter is the total length of fencing needed to enclose the garden. 3. **Calculate the perimeter:** Convert $7 \frac{1}{2}$ to decimal: $7.5$ meters. $$P = 2(7.5 + 2.5) = 2(10) = 20 \text{ meters}$$ 4. **Calculate additional fencing needed:** Samar already has $12.5$ meters, so the extra fencing needed is: $$20 - 12.5 = 7.5 \text{ meters}$$ 5. **Interpretation:** Samar needs to buy $7.5$ meters more fencing to enclose the garden. **Final answer:** $7.5$ meters