To find out how many ounces your friend ate from the bag of popcorn, we first need to determine how much of the bag is equivalent to \( \frac{1}{4} \) of the total weight.
The bag of popcorn contains \( 13 \frac{1}{3} \) ounces. We can convert this mixed number to an improper fraction:
\[ 13 \frac{1}{3} = \frac{13 \times 3 + 1}{3} = \frac{39 + 1}{3} = \frac{40}{3} \text{ ounces} \]
Next, we need to find \( \frac{1}{4} \) of this weight:
\[ \frac{1}{4} \times \frac{40}{3} = \frac{40}{12} = \frac{10}{3} \text{ ounces} \]
Now we can convert \( \frac{10}{3} \) ounces 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.