To find out how many students occupy 2/3 of the seats in the classroom, we first need to determine the total number of seats in the classroom based on the information that 18 students occupy 3/5 of the seats.
Let's denote the total number of seats in the classroom as \( S \). According to the problem:
\[ \frac{3}{5} S = 18 \]
To find \( S \), we can solve the equation:
- Multiply both sides of the equation by \( \frac{5}{3} \):
\[ S = 18 \times \frac{5}{3} \]
- Calculate \( 18 \times \frac{5}{3} \):
\[ S = 18 \times \frac{5}{3} = 6 \times 5 = 30 \]
Now we know that there are 30 seats in total in the classroom.
Next, we need to determine how many students would occupy \( \frac{2}{3} \) of the seats:
\[ \frac{2}{3} S = \frac{2}{3} \times 30 \]
Calculating this gives:
\[ \frac{2}{3} \times 30 = 20 \]
So, the number of students that would occupy \( \frac{2}{3} \) of the seats in the room is:
\[ \boxed{20} \]