So, let's think about all the different ways that we can represent 7/9. So let's just visualize 7/9. So here I have 9 equal sections and 7 ninths you represent as 7 of those equal sections. So let me get myself a bigger thing to draw with so that I can fill this in fast. I don't like how that looks, I'm going to use the paintbrush. So here we go, so that's 1, 2, 3, 4, 5, 6, and 7. So that's one way of representing 7 ninths, we already know that, that's not too interesting. So let's see if we can represent it as the sum of other fractions. So let's imagine, maybe we can represent it as, let's do it as 2 ninths (let me get another brush here) so let's represent it as 2 ninths. 2 over 9, plus ( I don't know) maybe 3 over 9, but that doesn't quite get us to 7 ninths yet. 2 over 9 plus 3 over 9, that's going to get us to 5 over 9 so we need 2 more, so that's going to be plus another 2 over 9. Plus another 2/9, so what would this look like? So let's just draw another grid here, so this is going to look like (so I'm going to put it right below it so we can look at what it looks like). So we have 2 ninths, this here is 2 ninths well we have nine equal sections. So 2 ninths is going to be, 1 and 2. And then we're going to add 3 more ninths, so one, two, three, so we add 3 ninths. And then 2 more ninths, that's 1 and 2. So notice, when I added 2 ninths to 3 ninths to 2 ninths, this equals 7 ninths. And we know that when we add a bunch of fractions like this that have the same denominator, we can just add the numerators. And this is why, this is 2/9 and 3/9 and 2/9 and they give me 7/9. Actually, let's do this again, this is a lot of fun. So let me draw my grid again. And then, let's see what we can do. So let me get my pen tool out and make sure my ink isn't too thick. And let's add a couple of ninths. So let's add 1/9 and let's add 2/9 and then we could add (I dunno), maybe we could add 3/9. And then we could add, that won't get us, let's see 1/9. I'm going to try to add 4 fractions here. So first I'm going to try to add 1/9 and see where that get's us. 1/9 is going to get us right over here. So that's 1/9, so let's say we add 2/9 to that. So that's 1 and 2, so that still doesn't get us there. So that's 3/9, 1 plus 2 is 3. So let's add 4 ninths. So 4/9. So let's see where this get's us. Actually, why not. And so that's going to get us 1, 2, 3, 4. So that looks like it got us all the way. Because 1+2+4=7 so that's 7/9. So what could we put here? We could actually put 0/9. Why not? So we could put in 0/9. And how would we visualize that? Well we're saying none of these. So this is 1/9 plus 2/9 plus 4/9 equals 7/9. So these are all different ways to decompose the exact same fraction.