Comparing unit fractions

- [Instructor] So which of the following numbers is greater, 1/3 or 1/5? Pause this video and try to answer that. All right, now let's think about this together. And the way that I can best think about it is by visualizing them. So let's imagine a whole. So this is a whole right over there. And then let's say that this is another whole right over there, I'm gonna try to make these rectangles about looking about the same. And now, how would I represent 1/3? Well, I would divide this whole into three equal sections. And so I'm gonna try to divide it into three equal sections. So that's three equal sections right over there. Now they're supposed to be three equal sections, these are hand-drawn so give me a little slack. But one of these three equal sections, well that's 1/3. So that is 1/3 right over there. Now what about 1/5? Well then I would try to divide this in five equal sections. So one, two, three, four, and five equal sections. And so 1/5 would be just one of these fifths. So it would be that right over there. So when you compare it like this, what's larger 1/3 or 1/5? And if it isn't obvious just yet, I could drag this one over, so that we can compare them, so that we can compare them directly. And you can see very clearly that 1/3 covers more of the whole, it's a larger fraction of the whole than 1/5 is. So 1/3 is greater than 1/5. And so you might have noticed an interesting pattern or might start thinking about a pattern. You might have been tempted when you saw the five here, five is larger than three, but 1/5 is less than 1/3 or 1/3 is greater than 1/5. And that is generally true, that the larger the denominator, the smaller the fraction is going to be. Why is that? Because you're dividing your whole into more equal chunks. So if you're only dividing into three, if it's one of three of the whole, 1/3 of the whole, or if it's one of three equal chunks of the whole, it's gonna be bigger than one of five equal chunks of the whole. And so based on this, how would you compare these two numbers? How would you compare 2/3 to 2/5? Well, same idea here. 1/3 is bigger than 1/5, so 2/3 is definitely going to be bigger than 2/5, and you can see it here. 2/3 is that, while 2/5 is that right over there. And I can do another example where I haven't even drawn it out. How would you compare four over six to four over eight? So 4/6 versus 4/8? Well, same idea. 1/6 is larger than 1/8. 1/6 is greater than 1/8, because the denominator here is smaller. We have the same numerator, but the denominator is smaller. So four of the bigger things is going to be larger than four of the smaller things. So 4/6 is greater than 4/8.