Ian originally poured 2 gallons of water into the bucket and then added \( \frac{1}{4} \) of a gallon more.
To find the total amount of water in the bucket, we can add these two amounts together:
\[ 2 + \frac{1}{4} \]
To perform this addition, it is useful to express \( 2 \) as a fraction with the same denominator as \( \frac{1}{4} \). The number \( 2 \) can be written as:
\[ 2 = \frac{8}{4} \]
Now we can add \( \frac{8}{4} \) and \( \frac{1}{4} \):
\[ \frac{8}{4} + \frac{1}{4} = \frac{8 + 1}{4} = \frac{9}{4} \]
The result \( \frac{9}{4} \) can also be expressed as a mixed number:
\[ \frac{9}{4} = 2 \frac{1}{4} \]
Thus, the total amount of water in the bucket now is
\[ \frac{9}{4} \text{ or } 2 \frac{1}{4} \text{ gallons.} \]
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