Comparing fractions visually

We have four fractions written over here. And what I want you to do is think about which of these fractions is the smallest value, which of these is the largest value, and which of these might be equal. And there's two ways that you could do it. You could try to plot them on a number line, or you could try to depict them visually. So pause the video now and try it on your own. So let's plot these on a number line. So let me give ourselves another little number line right over here. Let me see, I can draw one. So let's say this is my number line-- draw it as straight as I can. So that's my number line. That is 0. Let's say that this is 1, and then that is 2. So let's first try to plot where 1/2 is on the number line. So we can split the section between 0 and 1 into 2 equal sections. And 1/2, would mean that I would have gone one of those 2 equal sections. So if I just go that far, I should be at 1/2. So this right over here is 1/2. Now let's think about 2/4. Well, to do 2/4, we want to split the section between 0 and 1 into 4 equal sections. So let's do that. So 0-- so that's 1 equal section, 2 equal sections, 3 equal sections, and 4 equal sections. So where we do end up if we go 2 out of those 4 equal sections? Well we would end up-- 1, 2 equal sections, so we end up right over here. 2/4, we end up at the exact same place. So at least based on how we've drawn the number line, it looks like 1/2 is equal to 2/4. Let me write that down. 1/2 is equal to 2/4. Now what about 4/8? Well let's split the part of our number line between 0 and 1 to 8 equal sections. So if we take each of those 4 equal sections and split them into 2-- So now we have 1, 2, 3, 4, 5, 6, 7, 8. I can't draw it perfectly, but I'm trying to make them equal sections. Now it's 8 equal sections. And now we're going to go 4 of them. Starting at 0, we're going to go 1, 2, 3, 4. So we end up at the same place again. This is also equal to 4/8. So 1/2 is equal to 2/4, which is equal to 4/8. Now, what about 3/8? Well, we've already split our number line into 8 equal sections-- let's go 3 of them. 1, 2, 3. So 3/8 is right over here. 3/8 is less than 1/2, it's less than 2/4, it's less than 4/8. It is a smaller number. Let's see if that also makes sense when we try to visually depict or try to visually draw these fractions. So I've done that right over here. And this is one 1/2. So all of these rectangles are the exact same size. And this purple one over here I've split into 2 equal sections, and we shaded in one of them. So we see that this is 1/2. Now here I shaded in 2 out of the 4 equal sections, and you see that this looks the exact same size as the 1/2 right over here. We started with rectangles of the same size. If you shade in 1/2 or 2/4, it looks exactly the same. And that makes sense, because if you took this one right over here, if you took this first one and you divided each of your 2 equal sections into 2 equal sections, so you split it again, then you see that this is equal to 2/4. Now what about 4/8? Here I've split it up where I have this one, this one, this one, and this one shaded in. But if you rearrange them, you could see that you could get exactly the same amount of the rectangle shaded in. And if you want to see that, divide each of these 4 into 2-- so divide those into 2 and those into 2. Notice I now have 1, 2, 3, 4 out of the 8 equal squares shaded in. These two things are equal. So let me make it clear. This is an equal fraction, which is an equal fraction of that which is equal fraction of that And here, this is 3 out of 8. You see that it's less than this region right over here. This one we've literally filled in half of the entire rectangle-- 4 out of the 8. If we did 4 out of the 8 here, we would have also had to fill in this one right over here, which we didn't. We only filled in 3 out of the 8. So it makes sense that 3/8 is a smaller part of our whole than 4/8, or 2/4, or 1/2. And likewise, it's a smaller number.