To find out how many gallons of vinegar will be used for 69 batches, we need to multiply the amount of vinegar used in each batch by the number of batches.
Each batch uses \( \frac{1}{2} \) gallon of vinegar, so for 69 batches, we calculate:
\[ 69 \times \frac{1}{2} = \frac{69}{1} \times \frac{1}{2} = \frac{69 \times 1}{1 \times 2} = \frac{69}{2} \]
Now, we simplify \( \frac{69}{2} \):
\[ \frac{69}{2} = 34 \frac{1}{2} \]
So, the total amount of vinegar used in 69 batches is:
\[ \frac{69}{2} \text{ gallons} \text{ or } 34 \frac{1}{2} \text{ gallons} \]
Thus, the answer is \( \frac{69}{2} \) gallons or \( 34 \frac{1}{2} \) gallons.
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