Questions: Sandeep filled a bucket with 2 / 3 of a gallon of water. A few minutes later, he realized only 2 / 5 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

$Sandeep filled a bucket with 2 / 3 of a gallon of water. A few minutes later, he realized only 2 / 5 of a gallon of water remained. How much water had leaked out of the bucket? Write your answer as a fraction or as a whole or mixed number. gallons$

Transcript text: Sandeep filled a bucket with $2 / 3$ of a gallon of water. A few minutes later, he realized only $2 / 5$ of a gatton 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. $\square$ gallons

Solution

Solution Steps

To determine how much water leaked out of the bucket, we need to subtract the amount of water remaining from the initial amount of water.

Step 1: Initial Amount of Water

Sandeep initially filled the bucket with $ \frac{2}{3} $ gallons of water.

Step 2: Remaining Amount of Water

After some time, the amount of water remaining in the bucket is $ \frac{2}{5} $ gallons.

Step 3: Calculate the Leaked Water

To find the amount of water that leaked out, we subtract the remaining water from the initial amount: \[ \text{Leaked Water} = \text{Initial Water} - \text{Remaining Water} = \frac{2}{3} - \frac{2}{5} \] To perform this subtraction, we need a common denominator, which is 15: \[ \frac{2}{3} = \frac{10}{15}, \quad \frac{2}{5} = \frac{6}{15} \] Thus, \[ \text{Leaked Water} = \frac{10}{15} - \frac{6}{15} = \frac{4}{15} \]