To solve this problem, you need to divide the total amount of apple juice by the number of people sharing it.
- You start with \( \frac{2}{3} \) gallon of apple juice.
- There are 4 people sharing the juice.
To find out how much each person will get, you need to divide \( \frac{2}{3} \) by 4:
\[ \frac{2}{3} \div 4 = \frac{2}{3} \times \frac{1}{4} = \frac{2 \times 1}{3 \times 4} = \frac{2}{12} = \frac{1}{6} \]
Each runner will get \( \frac{1}{6} \) gallon of apple juice.