To find out how much fruit punch each person gets when 6 people share \( \frac{3}{4} \) gallon of fruit punch equally, we divide the total amount of fruit punch by the number of people:
\[ \text{Amount per person} = \frac{\frac{3}{4}}{6} \]
Dividing a fraction by an integer can be done by multiplying the fraction by the reciprocal of that integer:
\[ \text{Amount per person} = \frac{3}{4} \times \frac{1}{6} = \frac{3 \times 1}{4 \times 6} = \frac{3}{24} \]
Now, simplify \( \frac{3}{24} \):
\[ \frac{3}{24} = \frac{1}{8} \]
Thus, each person gets \( \frac{1}{8} \) gallon of fruit punch.
The correct answer is:
A. \( \frac{1}{8} \) gallon