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so we've got this fraction written here 2/3 what I want you to do is pause this video and try to think of any other fractions that are the same that are equivalent to this fraction right over here that essentially represent the same number so to do that let's let's visualize what two-thirds is so let me draw a hole here let me draw a hole and I'm gonna divide it into three equal sections so that is my hole we drive three equal sections I'm gonna try to draw make them as equal as I I can do a little better job than that so that's one two three three equal sections and so two-thirds would represent two out of those three equal sections so I second spray-paint this so that's one third right over here and then this is two-thirds so we have two of the three equal sections so that is two-thirds and I'll let me copy and paste that so we can think about other ways to represent this fraction so copy and then let me paste it I'll do it once and then and I'll do it another time and I could do this multiple times but I'll do two other times right over here so there's a couple of things we can do the first option is we could take this and we could divide we could draw a horizontal line that draws that divides each of these three sections into two sections so let's do that into two sections so now how many equal sections do I have I have one two three four five six equal sections six equal sections and how many of those equal sections are actually shaded in now well we see it's one two three four four six so notice four six is the exact same fraction of the whole as two-thirds these are equivalent fractions we could say that 2/3 is equal to 4/6 now we could do something very similar instead of dividing each of those each of these thirds into two we could divide each of these thirds into three so I could draw three horizontal lines here so let's see one two three so now I have divided what was in three equal sections and I have three many three times as many sections I have one two three four five six seven eight nine equal sections and then which of those are actually shaded in we have 1 2 3 4 5 6 6 so 2/3 which is equal to 4 6 is also equal to six ninths these are all all three of these are equivalent fractions two-thirds four six and six nines and if you were to put them on the number line the same thing what happens let's do that let's draw a number line here let's say that's a zero and I'm just gonna focus on between zero and one and obviously we can go beyond that go beyond that and let's divide it first into thirds so this is one-third and two-thirds so we already know this is this would represent one-third and this is two-thirds it's we've gone to of the equal spaces of the three on the way to one we've divided the section between zero and two one and two three equal spaces now what would four sixths be well now we just have to divide this into six equal spaces so one two three four five six and four sixths that would be four out of the six spaces a lot on the way to one so one two three four so this number is also equal to four six and you could do the same thing if you wanted to think about ninths so instead of instead of dividing each of so what we could do we could put one two three four five six seven eight nine now I've split this part of our number line between 0 and 2 and 1 into 9 equal spaces well what would six ninths be well 1 2 3 4 5 6 once again the exact same point of the number line it's an equivalent fraction six nines is equal to 2/3 is equal to 4/6