Final answer:
Ethan can fill 4 1/2 cups with a 3/4 gallon jug of water by dividing the total gallons by the amount each cup can hold.
Step-by-step explanation:
Ethan has a full jug of water that holds 3/4 gallon of water. He wants to pour this into cups that hold 1/6 gallon each. To determine how many cups Ethan can fill, we divide the total amount of water by the amount each cup can hold:
3/4 gallon ÷ 1/6 gallon/cup = (3×4)/(4×6) cups = 12/4 cups = 4 1/2 cups.
So, Ethan can fill 4 1/2 cups with the 3/4 gallon of water in the jug. The correct answer option is A) 4 1/2 cups.