A bucket containing 2 4/5 gallons of water is 1/3 full. How many gallons of water is in one fully filled bucket?
A.
14/15
B.
2 7/15
C.
8 2/5
D.
6 4/5
The correct answer and Explanation is :
Let’s start by finding out how many gallons of water the bucket holds when it’s fully filled.
We are given that the bucket contains 2 4/5 gallons of water when it is 1/3 full. To find how many gallons the bucket can hold when completely full, we need to multiply the amount of water by 3 (since 1/3 of the bucket is already 2 4/5 gallons, and we want the full capacity).
Step 1: Convert the mixed number to an improper fraction
First, convert 2 4/5 to an improper fraction:
- ( 2 \frac{4}{5} = \frac{2 \times 5 + 4}{5} = \frac{10 + 4}{5} = \frac{14}{5} ).
Step 2: Multiply by 3
Now, multiply by 3 to find the total capacity of the bucket:
- ( \frac{14}{5} \times 3 = \frac{14 \times 3}{5} = \frac{42}{5} ).
Step 3: Convert back to a mixed number
Next, convert ( \frac{42}{5} ) to a mixed number:
- ( 42 \div 5 = 8 ) with a remainder of 2.
- So, ( \frac{42}{5} = 8 \frac{2}{5} ).
Thus, the full capacity of the bucket is 8 2/5 gallons.
Answer:
The correct answer is C. 8 2/5.
Explanation:
We know that 1/3 of the bucket holds 2 4/5 gallons of water. To find out the full capacity, we multiply the amount by 3. First, converting 2 4/5 to an improper fraction and then multiplying by 3 gives us the full capacity of the bucket in gallons. Converting the result back to a mixed number provides the final answer, which is 8 2/5 gallons.