Question. Audrey was asleep for 10 hours last night and dreamed for 2/5 of the time. How much of the night was she not dreaming?
Answer. 6
What step-by-step reasoning justifies that answer?
user
Sure, I'd be happy to help with this mathematical reasoning.

1. Audrey was asleep for 10 hours.
2. She dreamed for 2/5 (or 40%) of the time.
3. If we represent this as a fraction, it would be 40/100.
4. The denominator, 100, represents the total number of 1/5 (or 20%) intervals in Audrey's sleep. (Each hour of sleep is divided into 5 equal parts, so there are 5 parts, or 100%, in 1 hour.)
5. The numerator, 40, represents the actual number of those 1/5 (or 20%) intervals in which Audrey was dreaming.
6. If we subtract the number of dreaming intervals (40) from the total number of 1/5 intervals (100), we're left with the total number of non-dreaming intervals.
7. This total non-dreaming intervals is given by the difference: 100 - 40 = 60.
8. Now, we can put this as a fraction, which is 60/100.
9. We can reduce this further by dividing both numerator and denominator by 10. This simplifies it to 6/10.
10. If we multiply both the numerator and denominator by 5, we get it as 30/50, which can be written as 6/10.
11. So, the answer is 6.

In summary, the step by step reasoning goes like this:

1. Find the fraction of the total sleep time that Audrey was dreaming.
2. Convert the numerator and denominator to common fractions if needed.
3. Subtract the fraction of audrey's sleep time that she was dreaming from 1.
4. It gives the remaining time after the dream.
5. Further, we can simplify this to get an easier-to-use answer.

I hope this helps! Let me know if you have any more questions.
assistant
Question. Audrey was asleep for 10 hours last night and dreamed for 2/5 of the time. How much of the night was she not dreaming?
Answer. 6
What step-by-step reasoning justifies that answer?
user
The step-by-step reasoning is as follows:

1. Audrey was asleep for 10 hours and dreamed for 2/5 of the time.
2. To find out how long she was dreaming, multiply the total sleep time by the fraction of time she spent dreaming: 10 hours * 2/5 = 4 hours.
3. Now, to find out how much of the night she was not dreaming, subtract the time she spent dreaming from the total sleep time: 10 hours - 4 hours = 6 hours.

Therefore, Audrey was not dreaming for 6 hours of the night.
assistant