To find out how many gallons of vinegar will be used in 9 batches, we can multiply the amount of vinegar per batch by the number of batches.
The amount of vinegar per batch is \( \frac{4}{5} \) gallons. The number of batches is 9.
We can set up the multiplication as follows:
\[ \text{Total vinegar} = \left(\frac{4}{5}\right) \times 9 \]
To multiply a fraction by a whole number, we can express the whole number as a fraction:
\[ 9 = \frac{9}{1} \]
Now we can multiply:
\[ \text{Total vinegar} = \frac{4}{5} \times \frac{9}{1} = \frac{4 \times 9}{5 \times 1} = \frac{36}{5} \]
Now, we can convert \( \frac{36}{5} \) into a mixed number. To do this, we divide 36 by 5:
\[ 36 \div 5 = 7\quad \text{(with a remainder of 1)} \]
So, that means:
\[ 36 = 5 \times 7 + 1 \]
This tells us that \( \frac{36}{5} \) can be expressed as:
\[ 7 \frac{1}{5} \]
Therefore, the total amount of vinegar used in 9 batches is
\[ \frac{36}{5} \text{ gallons} \text{ or } 7 \frac{1}{5} \text{ gallons}. \]
Final answer: \( \frac{36}{5} \) gallons or \( 7 \frac{1}{5} \) gallons.