 How shall we divide two fractions? Well, let's start off by illustrating our actual process of division using the bar model. So for example, 2 thirds divided by 5, and let's go ahead and take a look at that. We'll use a partative division approach. So we're going to take 2 thirds and divide it to 5 equal pieces. So we'll start with our model for 2 thirds. We'll take a unit divided to 3 equal pieces. We'll take 2 of those equal pieces. So that's our model for 2 thirds. We want to divide it by 5. So that means that we want to divide this into 5 equal parts. So I'll do the division horizontally. And our division is to divide it into equal parts and then take one of those parts. So I'll go ahead and take that one part there. Let's consider how big this part is. This is two parts, two of these little rectangles, out of a total of 5, 10, 15 altogether. So this is 2 thirds divided by 5. It's going to be 2 parts equal to 1 15th. And so 2 thirds divided by 5 is 2 15ths. Well, what if we're dividing by fractions? For example, let's start off with a whole number divided by fraction, 3 divided by 1 half. So I'll use a quotative division approach this time. So we'll find out how many pieces of size 1 half could fit into 3. And generally speaking, our quotative division approach is going to be a little bit easier to handle. So let's go ahead and take our bar representing 3. So now I have 1, 2, 3. And I want to find how many 1 halves fit here. So 1 half is just the unit divided into two parts. So here's my unit. And so now I've divided that into two pieces there. And while I'm at it, I might as well break the rest of them into size 1 half. So here's my 3, 1, 2, 3. And it's been divided into, quotatively, pieces of size 1 half. And now I could just count 1, 2, 3, 4, 5, and 6. So there's a total of six pieces. And so that tells me that 3 divided by 1 half gives you 6. Well, what about dividing a fraction by another fraction? So again, we'll take the fraction 1 half divided by 1 6. And again, it's convenient to take a quotative approach. How many of these does it take to make up this? So let's draw our 1 half, look something like that. And continuing our pattern of dividing both horizontally and vertically, I want to take a look at how big those 1 6 pieces are. So we'll divide the bar into six parts, and we'll take one of them. So remember, 1 half is this entire left or right, left side of the bar. 1 6 consists of these two pieces here. And so I can handle my division. How many of these things do I need to make up one side? Let's go ahead and collapse that. So there's 1, 2, 3. So I need 3 of the 1 6 to make up 1 half. So 1 half divided by 1 6 is going to be our quotient, which is equal to 3. What if we try 3 over 4 divided by 2 over 7? Again, it's convenient to approach this problem quotatively. So we'll make our model of 3 4s, looking something like that. Again, we'll need a model for 2 7s. And again, it's convenient if we take our divisions in two different directions. So 2 7s would be something like this. So again, there's my original divided into 4 divided by 7. This is 2 7s. And it turns out to be 8 of these little rectangles here. So if I want to take my amount 3 quarters, how many of these 8 blocks would it take? Let's start counting. So there's 1 block of 8, 2 blocks of 8. We don't have enough to make a third block of 8, because the block of 8, there's only five rectangles left over before we fill up our 2 7s. So what's that going to be? Well, that's 1, 2, and 5 out of the 8 pieces that we need. So that tells us that a quotient is going to be 2 and 5 8s.