Comparing fractions word problems

We're told that Katie made a table to show how much time she spent on homework last week. So, we can see the different subjects and then how much she spent in terms of hours.

So, on math, she spent three-fourths of an hour, reading seven-eighths of an hour, writing three-sixths of an hour, and then science five-tenths of an hour. They ask us on which activities did Katie spend more than two-thirds of an hour. So, pause this video and see if you can figure that out.

All right, so we essentially have to figure out which of these fractions are greater than two-thirds of an hour or which are greater than two-thirds. This is all in terms of hours.

First, let's just think about representing two-thirds. Let me do it like this, and I'm going to hand-draw it so it's not going to be perfect. If this is a hole right over here, I could split it into three equal sections. So, I'm going to try to do that. Let me see, does that look about right? So, three equal sections, so that would be a third, that would be a third, and then that would be a third.

Then, two-thirds would be two of them, so I'll pick these first two. Well, it doesn't have to be those first two. So, that's one third and then two thirds.

Now, let's see if we can draw a similar visual for each of these. So, what about three-fourths? Once again, let's make this a whole. Now, if I'm going to think in terms of fourths, I have to divide it into four equal sections.

So, let's see, if I divide it, that'll be two equal sections, and then I could divide each of those into two equal sections. So, let's see, maybe something like this and then like this. So, it's hand-drawn, but these are four equal sections.

This would be a fourth, that would be a fourth, and that would be a fourth, and that would be a fourth. Four fourths make a hole, so three of those fourths would be one, two, and then three.

You can see, and I've drawn it pretty close; it's not perfect because it's hand-drawn, but you can see that three-fourths is more of a whole than two-thirds. It's greater than two-thirds. So, Katie spent more than two-thirds of an hour on math because three-fourths is greater than two-thirds.

I like this one right over there. I'll just put a square circle around the ones that she spent that extra time on or that are greater than two-thirds of an hour.

Now, let's think about reading, which is seven-eighths. To compare that, I will once again make a hole here, and then I want to think about seven-eighths.

So, I'm going to split it into eight equal sections. Let's see, that will split into two equal sections, and then I can go to four equal sections, and then if I split each of those into two, this would be eight equal sections.

So, it looks something like this—not perfect, but I think it will get the job done. Each of these are an eighth, so seven-eighths are going to be one, two, three, four, five, six, and seven eighths.

Clearly, once again, it's greater than our two-thirds that we have in purple. So, she spent more than two-thirds of an hour on reading.

Now, what about writing three-sixths? What would that look like? Well, I'll do another one right over here. So, if that is a hole, well actually, let me split it into thirds first. Since we already have a bit of a reference there, we can look up there, and we can see those are thirds.

If we split each of those into two, we're going to have six because we'll have six equal sections. So, it would look something like that. Then, three of those six—well, that's one, two, and three.

So, we can see that three-sixths is less than two-thirds, so I'm not going to circle that one. She didn't spend more than two-thirds of an hour on writing.

And then last but not least, science five-tenths. Once again, we can make a hole here, and let's see, I want to do it into ten equal sections. So, that's two equal sections.

Then each of these I can do into five equal sections. Let's see, one, two, three, four, five. I can do a little bit neater than that. Three, four, and five. Then one, two, three, four, and five.

I can make it a little bit neater, but I think this will get us to where we need to be. So, these are each a tenth. I could write 1/10, 1/10. I could do that for all ten of these, but we care about five of these tenths.

So, one, two, three, four, five of those tenths. And notice five-tenths is the exact same thing as three-sixths. Like three-sixths, it is less than two-thirds.

So, which activities did Katie spend more than two-thirds of an hour on? Clearly, math and reading.