If the recipe calls for \( \frac{1}{4} \) cup of lime juice for every 4 avocados, we can first determine how many batches of the recipe Desiree can make with 1 cup of lime juice.
To find out how many \( \frac{1}{4} \) cups are in 1 cup, we can divide:
\[ 1 \text{ cup} \div \frac{1}{4} \text{ cup} = 1 \times \frac{4}{1} = 4 \]
So, she can make 4 batches of the recipe with 1 cup of lime juice.
Since each batch requires 4 avocados, we can now multiply the number of batches by the number of avocados per batch:
\[ 4 \text{ batches} \times 4 \text{ avocados per batch} = 16 \text{ avocados} \]
Therefore, Desiree needs 16 avocados for 1 cup of lime juice.