Writing fraction division story problems

We're told that Daryl spent 24 and one-fourth hours writing a chapter of a novel. Then they asked us, what are some things that 24 and one-fourth divided by three-fourths could represent in this context?

So, my understanding of this is they really just want us to be a little bit creative about what division by a fraction could represent in a given context.

Well, one, I encourage you to pause your video and think about that a little bit before I think about it. But one thing I think about is, well, if I took 24 and one-fourth and if I were to divide it into chunks of three-fourths of an hour—because this is in hours—how many chunks would I have?

So, this could represent, let's say, that he spent 45 minutes, which is the same thing as three-fourths of an hour. Three-fourths hours of an hour, I should say, three-fourths of an hour. Each day, how many days did it take him? Did it take? And then you could evaluate this 24 and one-fourth divided by three-fourths. We've talked about how to evaluate that in other videos, so that's one context.

Another one could be some type of a comparison. So, let's say that 24 and one-fourth is three-fourths of the amount of time that he spent doing something else. So, let's say—this is now a completely different context—I'm gonna put a line here. I'll do it a different color just to make it clear it's a different context.

So, another one could be to justify doing this division. He spent three-fourths as long writing as he spent illustrating the chapter. And so then the question is, how long did he spend illustrating? How long did he spend illustrating?

Now I really want you to think about this one. My brain actually—this one takes a little bit longer for my brain to process. But when you think about it, if you divide by a fraction that is less than one, you're going to get a number larger than the one that you're dealing with.

Or another way to think about it is the time spent illustrating—I'll write it like this—the time illustrating times three-fourths should be equal to the time spent writing. Because it says he spent—or he spent, I forgot to write that—he spent three-fourths as long writing as he spent illustrating.

So, time illustrating times three-fourths should be time writing or 24 and one-fourth. So, something times three-fourths is equal to 24 and one-fourth. Then 24 and one-fourth divided by four should be equal to time illustrating.

So these are the two contexts that I can think of that might make sense, but you might be able to think of others.