To find out how many days 414 ounces of cat food will last if Conor feeds his cats 9 ounces each day, you can divide the total amount of food by the daily amount.
\[ \text{Number of days} = \frac{\text{Total ounces of food}}{\text{Ounces of food per day}} = \frac{414 \text{ ounces}}{9 \text{ ounces/day}} \]
Now, performing the division:
\[ \frac{414}{9} = 46 \]
Thus, 414 ounces of food will last for 46 days.