Answer:
3 3/5 gallons of water leaked out of the bucket.
Explanation:
Creating an equation to represent the situation:
- We know that the original amount of water - the leaking amount = the remaining amount.
Allowing x to represent the amount of water that leaked, we can represent this with the following equation:
9 4/5 gal - x gal = 6 1/5 gal
Converting 9 4/5 and 6 1/5 to improper fractions:
- Before we solve, we can convert 9 4/5 and 6 1/5 to improper fractions for the sake of simplicity when solving.
- When converting a fraction from a mixed number to an improper fraction, we keep the same denominator.
- For the new numerator, we add the old numerator to the product of the whole number and the denominator.
Converting 9 4/5 to an improper fraction:
9 4/5 = ((9 * 5) + 4) / 5
9 4/5 = (45 + 4) / 5
9 4/5 = 49/5
Thus, 9 4/5 as an improper fraction is 49/5.
Converting 6 1/5 to an improper fraction:
6 1/5 = ((6 * 5) + 1) / 5
6 1/5 = (30 + 1) / 5
6 1/5 = 31/5
Thus, 6 1/5 as an improper fraction is 31/5.
Solving the equation for x:
Thus, we substitute 49/5 for 9 4/5 and 31/5 for 6 1/5 in our equation and then we can solve for x (the amount of water that leaked out of the bucket):
(49/5 - x = 31/5) - 49/5
(-x = -18/5) / -1
x = 18/5
Therefore, 18/5 gallons of water leaked out of the bucket.
Converting 18/5 to a mixed number:
- To convert 18/5 to a mixed number manually, we do long division.
- 18 is our dividend and 5 is our divisor.
- We get a quotient of 3 and a remainder of 3.
- For the mixed number, the quotient is the whole number.
- The fraction part is the remainder / divisor.
Thus, 18/5 as a mixed number is 3 3/5, meaning 3 3/5 gallons of water leaked out of the bucket.
I attached a picture showing how we'd convert 18/5 to a mixed number manually with long division.