If Mrs. Smith's oatmeal cookie recipe calls for 2/5 of a cup of sugar to make a full batch of cookies, then to make half a batch of cookies, she will need half the amount of sugar.
So, to find out how much sugar Mrs. Smith needs to make half a batch of cookies, we can use the following calculation:
Sugar needed for half a batch = (2/5 cup sugar) x (1/2 batch)
Simplifying this expression, we get:
Sugar needed for half a batch = 2/10 cup sugar
Which can be further simplified to:
Sugar needed for half a batch = 1/5 cup sugar
Therefore, Mrs. Smith will need 1/5 cup of sugar to make half a batch of oatmeal cookies.