She uses 1/2 cup in each batch.
So, if she has 3 1/4 cups in total, we have to divide this total by 1/2 to know how many batchs she can make:
[tex]\frac{\text{Total}}{\text{Batch}}=\frac{3+\frac{1}{4}}{\frac{1}{2}}=\frac{\frac{3\cdot4}{4}+\frac{1}{4}}{\frac{1}{2}}=\frac{12+1}{4}\cdot2=\frac{13}{2}=\frac{12}{2}+\frac{1}{2}=6+\frac{1}{2}[/tex]She can make 6 1/2 batches.
