Final answer:
Ariana can bake 1/6 of the batch with the amount of flour she has.
Step-by-step explanation:
To find out what fraction of the batch Ariana can bake, we need to compare the amount of flour she has to the total amount needed. Ariana has half a cup of flour, and she needs 3 cups to bake a batch. So, the fraction of the batch she can bake is:
1/2 cup / 3 cups = 1/6
Therefore, Ariana can bake 1/6 of the batch with the amount of flour she has.