Sarah put raisins into 3/4 of the oatmeal cookie dough she was making. she put nuts into 2/5 of the oatmeal cookie dough with the raisins. what fraction of the entire batch has both raisins and nuts.

The LCM (lowest common multiple) of 4 and 5 is 20, so convert them so that the denominator is 20:

3/4 = 15/20
2/5 = 8/20

I didn't quite read the question properly, but regardless. Since only 15/20 of the batch has raisins, of which only 8/20 has nuts, we can formulate this equation to solve:

1x15/20x8/20
=3/10