To find out how much cheese Kathleen puts in each bowl, we need to divide the total amount of cheese (1/4 cup) by the number of bowls (3).
So, we calculate:
\[ \text{Amount of cheese per bowl} = \frac{1/4 \text{ cup}}{3} \]
Dividing by 3 is the same as multiplying by the reciprocal of 3, which is \( \frac{1}{3} \):
\[ \text{Amount of cheese per bowl} = \frac{1}{4} \times \frac{1}{3} = \frac{1 \times 1}{4 \times 3} = \frac{1}{12} \]
Therefore, Kathleen puts \( \frac{1}{12} \) of a cup of cheese in each bowl.