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A bucket contains 11 2/3 gallons of water and is 5/6 full

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Explanation:

what is the question ?

how much water does the full bucket contain ?

if so, then I understand that

11 2/3 gallons = 5/6 bucket

(11×3 + 2)/3 gallons = 5/6 bucket

35/3 gallons = 5/6 bucket

what do we need to do to get 1 bucket (5/5 or 6/6 or 3/3 or ...) on the right side ?

we multiply everything by 6/5 :

35/3 × 6/5 gallons = 5/6 × 6/5 bucket

(6×35)/(5×3) gallons = 1 bucket

(2×7)/(1×1) gallons = 1 bucket

14 gallons = 1 bucket

the bucket can contain 14 gallons of water.

User Hennes
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