1. The problem asks to convert the improper fraction $\frac{15}{2}$ into a mixed number. 2. A mixed number consists of a whole number and a proper fraction. 3. To convert, divide the numerator by the denominator: $15 \div 2 = 7$ remainder $1$. 4. The whole number part is $7$. 5. The remainder $1$ becomes the numerator of the fractional part, with the original denominator $2$. 6. So, $\frac{15}{2} = 7 \frac{1}{2}$. 7. Final answer: $7 \frac{1}{2}$.