Final answer:
When solving for the fraction of awake hours Brian spends on his math homework, we found that he is awake for 18 hours a day and spends 3 hours on math homework, resulting in a fraction of 1/6, which is not available in the provided choices.
Step-by-step explanation:
Let's solve the math homework question: Brian spends 3 hours of every day working on math homework and sleeps 6 hours a day. To find out what fraction of his awake hours he spends on math homework, we first need to calculate how many hours he is awake in a day. Since there are 24 hours in a day, if Brian sleeps 6 hours, he is awake for 24 - 6 = 18 hours.
Now, we determine the fraction of awake time spent on homework by dividing the number of hours spent on math homework by the total number of awake hours. So, Brian spends 3 hours on math homework out of 18 awake hours. The fraction is therefore 3/18, which simplifies to 1/6. However, this fraction is not one of the options provided, so let's check our work and the options again.
Since we are looking for a fraction of the options provided and we know that the total hours Brian is awake is 18, let's consider that the given choice must simplify from a fraction of 18. The correct option looking at the choices is actually 1/6 which is not listed. Therefore, it seems there is a mistake with the options provided as none of them correctly reflect the answer.