To determine how much more fencing needs to be purchased, you need to subtract the amount of fencing already available from the total distance around the property.
- Total fencing needed: \( \frac{112}{1} \) miles (or simply 112 miles for simplicity).
- Fencing already available: \( \frac{34}{1} \) miles (or simply 34 miles for simplicity).
Now, subtract the fencing already available from the total needed:
\[ 112 - 34 = 78 \]
So, the amount of fencing needed to purchase is 78 miles.
However, I need to review the options you provided, as there seems to be a misunderstanding or error in the context:
- \( \frac{3}{4} \) of a mile
- \( \frac{1}{2} \) of a mile
- 1 mile
- \( \frac{2}{4} \) of a mile (which is equivalent to \( \frac{1}{2} \))
Given the options don't reflect this calculation, kindly double-check the total distance around the property and the fencing already available. If there is any discrepancy, we can correct it and provide you the right answer.