Comparing fractions word problems

- [Instructor] We're told that Katie made a table to show how much time she spent on homework last week, and so we can see the different subjects and then how much she spent in terms of hours. So in math, she spent 3/4 of an hour, reading, 7/8 of an hour, writing, 3/6 of an hour, and then science, 5/10 of an hour. And then they ask us on which activities did Katie spend more than 2/3 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 2/3 of an hour? Which are greater than 2/3? And this is all in terms of hours. So first let's just think about representing 2/3, so let me do it like this, and I'm going to hand draw it so it's not going to be perfect. But if this is a whole right over here, I could split it into three equal sections, so I'm gonna try to do that. Let me see, does that look about right? So three equal sections, so that would be 1/3 that would be 1/3, and then that would be 1/3, and then 2/3 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 1/3 and then 2/3. So let's see if we can draw a similar visual for each of these. So what about 3/4? So once again, let's make this a whole. And now if I want to think in terms of fourths, I have to divide it into four equal sections, so let's see. If I divide it, that will be two equal sections, and then I can 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, and so this would be a fourth, that would be a fourth, and that would be a fourth, and that would be a fourth. 4/4 make a whole, so three of those fourths would be one, two, and then three. And so you can see, and I've drawn it pretty close. It's not perfect 'cause it's hand drawn, but you can see that 3/4 is more of a whole than 2/3. It's greater than 2/3. So Katie spent more than 2/3 of an hour on math because 3/4 is greater than 2/3, so I like this one right over there. I'll just put a square or circle around the ones that she spent that extra time on or the more, the greater than 2/3 of an hour on. And I'll think about reading, 7/8. So to compare that, I will, once again, make a whole here, and then I want to think about 7/8, so I'm gonna split into eight equal sections. So let's see, that will split into two equal sections, and then, 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 may look something like this. Not perfect, but I think it will get the job done. So each of these are 1/8, so 7/8 are going to be one, two, three, four, five, six, and 7/8. Clearly, once again, greater than our 2/3 that we have in purple. So she spent more than 2/3 of an hour on reading. Now what about writing? 3/6, what would that look like? Well, I'll do another one right over here. So if that is a whole, well, actually let me split it to thirds first, since we already have a bit of a reference there. We can look up there and we can see. Those are thirds and if we split each of those into two, we're going to have sixths, 'cause we'll have six equal sections. So it would look something like that, and then three of those six, well, that's one, two, and three. So we can see that 3/6 is less than 2/3 so I'm not gonna circle that one. She didn't spend more than 2/3 of an hour on writing, and then last, but not least, science. 5/10. Well once again, we could make a whole here, and let's see. I want to do into 10 equal sections, so that's two equal sections, and 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, and 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 get to. So these are each 1/10. I could write 1/10, 1/10, I could do that for all 10 of these, but we care about five of these tenths, so one, two, three, four, five of those tenths. And notice, 5/10 is the exact same thing as 3/6, and like 3/6, it is less than 2/3. So which activities did Katie spend more than 2/3 of an hour on? Clearly, math and reading.