To find the number of oranges in the box, we can calculate two-thirds of the total number of pieces of fruit.
The total number of pieces of fruit is 54.
To find two-thirds of 54: \[ \text{Number of oranges} = \frac{2}{3} \times 54 \] Calculating that: \[ \frac{2 \times 54}{3} = \frac{108}{3} = 36 \]
Thus, there are 36 oranges in the box.