Question

Sebastian filled a bucket with 8 1/6 gallons of water. A few minutes later, he realized only 1/2 of a gallon of water remained. How much water had leaked out of the bucket?

Write your answer as a fraction or as a whole or mixed number.

gallons

Answer 1

To determine how much water leaked out of the bucket, we need to subtract the amount of water that remained in the bucket from the original amount that was filled.

1. **Original amount of water**: \(8 \frac{1}{6}\) gallons
2. **Amount of water remaining**: \(\frac{1}{2}\) gallon

Now we will convert \(8 \frac{1}{6}\) into an improper fraction for easier subtraction.

First, convert \(8 \frac{1}{6}\):
\[
8 \frac{1}{6} = 8 + \frac{1}{6} = \frac{8 \times 6}{6} + \frac{1}{6} = \frac{48}{6} + \frac{1}{6} = \frac{49}{6}
\]

Next, we convert \(\frac{1}{2}\) into sixths to match the denominator:
\[
\frac{1}{2} = \frac{1 \times 3}{2 \times 3} = \frac{3}{6}
\]

Now we can perform the subtraction:
\[
\text{Amount leaked} = \text{Original amount} - \text{Remaining amount} = \frac{49}{6} - \frac{3}{6} = \frac{49 - 3}{6} = \frac{46}{6}
\]

Next, simplify \(\frac{46}{6}\):
\[
\frac{46}{6} = \frac{23}{3}
\]

To convert this to a mixed number:
\[
\frac{23}{3} = 7 \frac{2}{3}
\]

Thus, the amount of water that leaked out of the bucket is:
\[
\boxed{7 \frac{2}{3}} \text{ gallons}
\]