To find out how many ounces your friend ate, we need to calculate \( \frac{1}{4} \) of the bag's total weight, which is \( 13 \frac{1}{3} \) ounces.
First, convert \( 13 \frac{1}{3} \) into an improper fraction:
\[ 13 \frac{1}{3} = \frac{13 \times 3 + 1}{3} = \frac{39 + 1}{3} = \frac{40}{3} \text{ ounces} \]
Now, calculate \( \frac{1}{4} \) of \( \frac{40}{3} \):
\[ \frac{1}{4} \times \frac{40}{3} = \frac{40}{12} \]
Now simplify \( \frac{40}{12} \):
\[ \frac{40 \div 4}{12 \div 4} = \frac{10}{3} \]
Now convert \( \frac{10}{3} \) back to a mixed number:
\[ \frac{10}{3} = 3 \frac{1}{3} \text{ ounces} \]
So, your friend ate \( 3 \frac{1}{3} \) ounces of popcorn.