To determine how many bottles Kendall can fill with 2 gallons of ketchup when each bottle holds \( \frac{1}{9} \) of a gallon, we can divide the total amount of ketchup by the capacity of one bottle.
First, we convert the 2 gallons into a fraction that is compatible with the bottle size:
\[ 2 \text{ gallons} = \frac{2}{1} \]
Now, we need to divide \( \frac{2}{1} \) by \( \frac{1}{9} \):
\[ \frac{2}{1} \div \frac{1}{9} = \frac{2}{1} \times \frac{9}{1} = \frac{2 \times 9}{1 \times 1} = \frac{18}{1} = 18 \]
Kendall can fill 18 bottles with the 2 gallons of ketchup.