The regular price of a large bag of cat food is $\$12$. Ike bought a bonus bag with $20\%$ more than the large bag, and the bonus bag was on sale for $\$9$. Ike then used a "$\$1$ off coupon" when purchasing the bonus bag. What fraction of the regular price per ounce for the large bag did Ike pay for an ounce of food in the bonus bag? Express your answer as a common fraction.