Let's break down the problem step-by-step:
1. Initial Amount:
The whole pan of brownies can be considered as 1 whole or represented by the fraction [tex]\( \frac{3}{3} \)[/tex].
2. Amount Eaten:
The Rodriguez family ate [tex]\( \frac{1}{3} \)[/tex] of the pan of brownies.
3. Amount Remaining:
To find the amount of brownies remaining, we subtract the amount eaten from the whole pan:
[tex]\[
1 - \frac{1}{3} = \frac{3}{3} - \frac{1}{3} = \frac{2}{3}
\][/tex]
4. Dividing the Remaining Amount:
The remaining [tex]\( \frac{2}{3} \)[/tex] of the pan needs to be divided into two equal parts. Each part will be:
[tex]\[
\frac{2}{3} \div 2 = \frac{2}{3} \times \frac{1}{2} = \frac{2 \times 1}{3 \times 2} = \frac{2}{6} = \frac{1}{3}
\][/tex]
So, both the block party and the co-workers will each get [tex]\( \frac{1}{3} \)[/tex] of the whole pan of brownies.
Therefore, the correct answer is:
[tex]\[
\boxed{\frac{1}{3}}
\][/tex]
