To find out how many gallons of vinegar are used in 7 batches, we need to multiply the amount of vinegar used in each batch by the number of batches.
The amount of vinegar used in each batch is \( \frac{3}{5} \) gallons.
So, we calculate:
\[ \text{Total vinegar} = \frac{3}{5} \times 7 \]
To multiply the fraction by a whole number, we can express 7 as a fraction:
\[ 7 = \frac{7}{1} \]
Now, we multiply the fractions:
\[ \text{Total vinegar} = \frac{3}{5} \times \frac{7}{1} = \frac{3 \times 7}{5 \times 1} = \frac{21}{5} \]
Next, we can convert \( \frac{21}{5} \) into a mixed number.
Dividing 21 by 5 gives us 4 with a remainder:
\[ 21 \div 5 = 4 \quad \text{R}1 \]
Thus, we can express \( \frac{21}{5} \) as:
\[ 4 \frac{1}{5} \]
So, the total amount of vinegar used in 7 batches is:
\[ \boxed{\frac{21}{5}} \text{ gallons} \quad \text{or} \quad 4 \frac{1}{5} \text{ gallons} \]