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so let's think about all of the different ways that we can represent 7 9 7 9 so let's just visualize seven ninths so here I have nine equal sections and seven ninths you could represent as seven of those equal sections so let me get our set 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 one two three four you know where this is going five six and seven so that's one way of representing seven ninths we already know that that's not too interesting but let's see if we can represent seven ninths as the sum of other fractions so let's imagine maybe we can represent it as let's do it as two ninths give my use a different brush here so it's represented as two ninths two over nine plus plus I don't know let's see maybe three over nine but that doesn't quite get us to seven ninths yet two over nine plus three over nine is going to get us to five over nine so we're going to need two more so it's going to be plus another 2 over nine plus another 2 over 9 plus another 2 over 9 so what would this look like so let's let's just draw another grid here so this is going to look like I'll try to do it right below it so that we can see how they match up so we have two ninths we have two ninths this two ninths right over here well we have each of these is 1/9 we have nine equal sections so two ninths is going to be so we're going to get one and two and then we're going to add three more nights so one one two three so we had three nines right over there and then two more nights and then two more nights one one and two so notice when I added two nines to three nines to two ninths this equals seven ninths and we know that when we add a bunch of fractions like this that have the same denominator we can just add the numerator and this is why this is two 9s plus 3 9 times two 9s is going to give me seven nine so let's do this one more time this is actually a lot of fun so let me draw my grid again let me draw my grid and then let's let's see what we can do so let me get my pen tool out and tool out make sure my my ink is a - they call this is fine and let's add a couple of nights here so let's add let's add first 1/9 and I'm going to stride all the 9s in blue and let's add two nights and then we could add I don't know maybe we could add give some space here so we can add more and maybe we could add three nights three nights and then we could add let's see that won't get a cc 1/9 election let me just write this I'm going to try to add four fractions here so let's head first 1/9 see where that gets us so 1/9 is going to get us right over here so that's 1/9 so let's say we add two nights to that so two nights two nights get my little paintbrush going on so that's one and two more two nights so that still doesn't hat get us there this gives us a total of three nights one plus two is three three nights so let's do that a no let's add let's add let's add 4/9 4/9 and I'll do that in this blue color so four nights that's well that's different enough four nights so let's see where this gets us actually well why not so 4/9 and so that's going to get us one two three four so that looks like it got us all the way because one plus two plus four is going to give us seven seven nine so what can we put here well we could say zero nine why not so we could put in we could call this one right over here zero nine and why would we visualize that well let's lure saying none of these no no ninths right over here so this is 1/9 plus two 9s plus 4/9 is equal to seven nine so these are all different ways to decompose the exact same fraction