Final answer:
Each person gets 1/8 of a pitcher of juice after dividing 3/4 of a pitcher equally among 6 people by multiplying 3/4 by the reciprocal of 6 (1/6), which equals 3/24, and then simplifying it to 1/8.
Step-by-step explanation:
To determine how much juice each person gets, you need to divide the total amount of juice by the number of people sharing it. There is 3/4 of a pitcher of juice, which needs to be shared equally among 6 people. We must divide 3/4 by 6.
Dividing fractions requires multiplying by the reciprocal of the divisor. So, we take 3/4 and multiply it by 1/6, which is the reciprocal of 6/1.
3/4 × 1/6 = 3/24, which simplifies to 1/8. Therefore, each person receives 1/8 of a pitcher of juice.