Change the following improper fraction to a mixed number with the fraction part reduced to lowest terms. \[ \frac{57}{22} \]

To convert the improper fraction \(\frac{57}{22}\) to a mixed number, we start by dividing the numerator by the denominator. When we divide 57 by 22, we find that 22 fits into 57 two times (because \(2 \times 22 = 44\)). Subtracting 44 from 57 gives us a remainder of 13. Thus, we can express \(\frac{57}{22}\) as \(2\frac{13}{22}\). Furthermore, the fraction part \(\frac{13}{22}\) is already in its simplest form since 13 is a prime number and does not share any common factors with 22 other than 1. So, the mixed number is \(2\frac{13}{22}\).