Final answer:
After subtracting 1/6 gallon from the initial 6/7 gallons, Stacy is left with 29/42 gallons of water in the bucket.
Step-by-step explanation:
To calculate how much water is left in the bucket after Stacy poured out 1/6 of a gallon from the initial 6/7 gallons, we perform a subtraction operation in fractions.
First, we need to make sure both fractions have a common denominator before we subtract them. 6/7 gallons need to be presented in terms of 6ths, so we find the equivalent fraction. Multiplying both the numerator and the denominator of 6/7 by 6, we get 36/42 gallons of water initially.
Now, subtracting 1/6 of a gallon from 36/42 gallons, we convert 1/6 to 7/42 to have a common denominator of 42. The calculation will look like this: 36/42 - 7/42 = 29/42 gallons of water left.
Therefore, Stacy has 29/42 gallons of water remaining in the bucket.