1. The problem is to understand the mixed number 15 1/2, which represents the number of days Gerry kept the book. 2. A mixed number consists of a whole number and a fraction. Here, 15 is the whole number and 1/2 is the fraction. 3. To work with this number in calculations, it is often useful to convert it to an improper fraction or a decimal. 4. To convert 15 1/2 to an improper fraction, multiply the whole number by the denominator and add the numerator: $$15 \times 2 + 1 = 30 + 1 = 31$$. 5. So, 15 1/2 as an improper fraction is $$\frac{31}{2}$$. 6. To convert 15 1/2 to a decimal, divide the numerator by the denominator and add the whole number: $$15 + \frac{1}{2} = 15 + 0.5 = 15.5$$. 7. Therefore, 15 1/2 equals 15.5 days. 8. This means Gerry kept the book for fifteen and a half days.