Representing 1 as a fraction

so let's say that this circle looking thing represents a whole we've already seen a couple of situations we said hey look we could divide this into two equal pieces and if we shade in one of them so one of these equal pieces that would be one-half and then if we shade in two of them this would be two halves so let me call it that in a little bit better so this right over here I've divided into two equal pieces and I'm shading in two of these equal pieces so what fraction of the whole do I have shaded in well we've seen this multiple times this is two halfs two halfs of the entire figure and we see we've shaded in the entire figure so this is equal to this is equal to one whole one whole and we could do that we don't have to just split it into two equal parts we could split it into let's see we could split it into three equal parts so let's say we were to split into three equal parts let me do that my best attempt to draw three equal parts three equal parts looks like a Mercedes symbol and that's my best I can draw a little bit better job of that be clear that I'm trying to make them equal so that's three equal parts and then if we were to actually shade in the three equal parts if we were to shade in the three equal parts so that would be one of the three so that's 1/3 2/3 2/3 and three thirds so once again 3/3 3/3 is equal is equal to one whole now what if we were to do something on some level even simpler what if we just take our whole and we divide it into only one equal section well I've already done that this is one equal section right over here and then I were to select that one equal section so I were to select it so let me color it in so I have one section and I'm going to shade it in so what fraction what fraction of the whole do I now have shaded in well I had one equal section to begin with I had one equal section to begin with and I shaded in that one equal section so I have one once of this shaded in and this is also clearly an entire hole so this is also equal to a hole and I think you see a pattern here two seconds three thirds or one one these all represent the exact same value they all represent a hole and you would also see this if you were to draw a number line so if you were to draw a number line so this is 0 this is 1 we could keep on going well this is 1 1 if I always say well between 0 & 1 I just have one eye divided into 1 equal chunk well that's just this whole thing right over here and if I were to move one of those equal chunks I would get I would get 2 I get to 1 if I divide it into 2 equal chunks if I divide it into 2 equal chunks and if I if I jump if I make 2 jumps 1 2 jumps I still end up at 1 if I divide it into 3 equal sections so let's say 1 1 2 3 equal sections and I make 3 jumps 1 2 3 I end up at 1 again so two seconds 3/3 1 1 or 1 over 1 these all are another are different ways of representing the number 1 or 1 hole