To find the height of the basketball player's son, we need to calculate \( \frac{1}{4} \) of the player's height. The player's height is \( 6 \frac{2}{3} \) feet.
First, convert \( 6 \frac{2}{3} \) into an improper fraction:
\[ 6 \frac{2}{3} = 6 + \frac{2}{3} = \frac{18}{3} + \frac{2}{3} = \frac{20}{3} \text{ feet} \]
Next, calculate \( \frac{1}{4} \) of \( \frac{20}{3} \):
\[ \frac{1}{4} \times \frac{20}{3} = \frac{20}{12} = \frac{5}{3} \text{ feet} \]
Convert \( \frac{5}{3} \) into a mixed number:
\[ \frac{5}{3} = 1 \frac{2}{3} \text{ feet} \]
Thus, the height of the son is \( 1 \frac{2}{3} \) feet.
So the correct response is:
1 2/3 ft.