A team of arborists is studying a forest in the Appalachian mountains that has 800 oak trees. They found that 2/5 of the oaks are red oaks, and the rest are white oaks. If 3/8 of the red oaks and 1/6 of the white oaks have oak wilt disease, what fraction of the oak trees in the forest have the disease?
Out of the 800 oak trees, there are 2/5 * 800 = <<2/5*800=320>>320 red oaks.
And there are 800 - 320 = <<800-320=480>>480 white oaks.
There are 3/8 * 320 = <<3/8*320=120>>120 red oaks with oak wilt.
There are 1/6 * 480 = <<1/6*480=80>>80 white oaks with oak wilt.
So there are a total of 120 + 80 = <<120+80=200>>200 oak trees with oak wilt.
Thus, the fraction of oak trees with the disease is 200 / 800 = 1 / <<200/800=4>>4. Answer: \boxed{\frac{1}{4}}.