1. The problem states that Jemima sleeps for 8 hours in one day and asks for the fraction of the day she is awake. 2. We know there are 24 hours in a day. 3. The time Jemima is awake is the total hours in a day minus the hours she sleeps: $$24 - 8 = 16$$ hours. 4. To find the fraction of the day Jemima is awake, we write the awake hours over the total hours in a day: $$\frac{16}{24}$$. 5. Simplify the fraction by dividing numerator and denominator by their greatest common divisor, which is 8: $$\frac{16 \div 8}{24 \div 8} = \frac{2}{3}$$. 6. Therefore, Jemima is awake for $$\frac{2}{3}$$ of the day. 7. This fraction is in its simplest form.