The Rodriguez family ate one-third of a pan of brownies, which means that two-thirds of the pan of brownies remains (since \(1 - \frac{1}{3} = \frac{2}{3}\)).
They plan to divide the remaining two-thirds into two equal parts. To find out how much each place will get, we divide the remaining brownies:
\[ \frac{2}{3} \div 2 = \frac{2}{3} \times \frac{1}{2} = \frac{2}{6} = \frac{1}{3} \]
So, each place will get one-third of the whole pan of brownies.
The answer is One-third.