To determine how many batches of cupcakes Frosting Mountain can make, we can divide the total amount of vanilla they have by the amount of vanilla needed for each batch.
They have 2 cups of vanilla, and each batch requires \( \frac{1}{4} \) cup.
We can set up the division as follows:
\[ \text{Number of batches} = \frac{\text{Total vanilla}}{\text{Vanilla per batch}} = \frac{2}{\frac{1}{4}} \]
To divide by a fraction, we multiply by its reciprocal:
\[ \frac{2}{\frac{1}{4}} = 2 \times 4 = 8 \]
Thus, Frosting Mountain can make 8 batches of cupcakes before they run out of vanilla.