To determine the remaining amount of gasoline Frank has after using \( \frac{3}{4} \) of a gallon from the 3 gallons he initially bought, we can perform the following calculation:
- Start with the total amount of gasoline: \( 3 \) gallons.
- Subtract the amount of gasoline used: \( \frac{3}{4} \) gallon.
We start with the equation:
\[ \text{Remaining gasoline} = 3 - \frac{3}{4} \]
To perform the subtraction, it's helpful to convert 3 into a fraction with a denominator of 4:
\[ 3 = \frac{12}{4} \]
Now we can rewrite the equation:
\[ \text{Remaining gasoline} = \frac{12}{4} - \frac{3}{4} \]
Now, we can subtract the two fractions:
\[ \text{Remaining gasoline} = \frac{12 - 3}{4} = \frac{9}{4} \]
Thus, the remaining amount of gasoline Frank has is \( \frac{9}{4} \) gallons.
So, the answer is:
\(\frac{9}{4}\)