To simplify the mixed number \( 81 \frac{1}{4} \) into an improper fraction, you can follow these steps:
- Multiply the whole number by the denominator: \( 81 \times 4 = 324 \).
- Add the numerator to this result: \( 324 + 1 = 325 \).
- Write this sum over the original denominator: \( \frac{325}{4} \).
So, the simplified form of \( 81 \frac{1}{4} \) is \( \frac{325}{4} \).