James uses 1/2 of a cup of sugar in his cookies, and Jade uses 3/4 of a cup of sugar in her cookies. Noel takes the sum of the two amounts of sugar and divides it into two equal portions, planning to use only one portion of it in his cookies. How much sugar does Noel use in his cookies?
The total amount of sugar used is 1/2 + 3/4 = <<1/2+3/4=5/4>>5/4 = 1.25 cups of sugar.
Noel uses 1/2 * 1.25 = <<1/2*1.25=0.625>>0.625 cups of sugar. Answer: \boxed{0.625}.