A bucket contains `20 1/4` litres of water. A small jug has a capacity of `3/4` litre. How many times the jug has to be filled with water from the bucket to get it emptied?

Answer

To solve the problem step by step, we need to determine how many times the small jug can be filled with water from the bucket to completely empty it.

### Step 1: Convert the mixed number to an improper fraction
The amount of water in the bucket is given as \(20 \frac{1}{4}\) litres. We can convert this mixed number into an improper fraction.

\[ 20 \frac{1}{4} = 20 + \frac{1}{4} = \frac{20 \times 4}{4} + \frac{1}{4} = \frac{80}{4} + \frac{1}{4} = \frac{81}{4} \text{ litres} \]

### Step 2: Identify the capacity of the jug
The capacity of the small jug is given as \(\frac{3}{4}\) litre.

### Step 3: Calculate how many times the jug can be filled
To find out how many times the jug can be filled from the bucket, we divide the total amount of water in the bucket by the capacity of the jug.

\[ \text{Number of times jug is filled} = \frac{\text{Amount of water in bucket}}{\text{Capacity of jug}} = \frac{\frac{81}{4}}{\frac{3}{4}} \]

### Step 4: Simplify the division of fractions
When dividing fractions, we multiply by the reciprocal of the divisor.

\[ \frac{\frac{81}{4}}{\frac{3}{4}} = \frac{81}{4} \times \frac{4}{3} = \frac{81 \times 4}{4 \times 3} = \frac{81}{3} \]

### Step 5: Perform the division
Now, we can simplify \(\frac{81}{3}\).

\[ \frac{81}{3} = 27 \]

### Conclusion
Thus, the jug has to be filled **27 times** to empty the bucket.

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