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what we're going to talk about in this video is the idea of a fraction we'll see there's many ways to think about a fraction but first we'll think about the most fundamental so let's say that I have this square and this is the hole we can consider this a hole so let me write that down this is a hole it is a complete square now what I'm going to do is divide this into four equal parts so with one cut like that I've divided it into two equal parts and then with another cut like this I could divide it into four four equal parts so there are four equal parts and now what I'm going to do is I'm going to select one of those equal parts so let's say this part right over here I am going to select that so the question is what fraction of the hole is the part that I have shaded in red well it is one out of the four equal parts right I've shaded in one out of one two three four equal parts so we write this as this fraction this piece represents one-fourth of the hole and there's two ways that you can think about this you could view this as one of the four equal parts or you could view this as a hole divided by four would get you exactly this much now let's do another one and this time let's think about how we would how we could represent one over 8 so 1 over 8 well we could divide this hole in this case the hole is this rectangle looking thing we could divide the whole into eight equal parts so let's do that so here I've divided into two equal parts that looks pretty good and now I can divide each of those into two equal parts to get me four equal parts and then if I were to divide each of those into two equal parts into two equal parts I will have I will have eight equal parts and it's not exact obviously I've drawn it by hand but hopefully this gets you a sense so now I have eight equal parts eight equal parts and now I'm going to select exactly one of them and that will represent 1/8 and I could select any one of these but I'll just do this one to show you does not have to be necessarily the first one so once again this square right over here that I'm shading in red represents 1/8 of the hole now let's look at a few more examples where I've shaded them in ahead of time and what I want you to do right now is pause the video and either in your head or on a piece of paper write down if you consider this this purple thing the hole what fraction does this red part represent if you consider this blue part the hole what fraction does this red part represent if you view this yellow triangle as a hole what fraction does this red part represent and so I encourage you to pause the video now well let's look at each of these so in this case for this rectangle we have three equal parts and we've shaded in one of them so this red rectangle this red rectangle right over here represents one-third of the hole now over here in this kind of pie looking thing this circle looking thing we have one two three four five equal parts five equal parts and we have shaded in one of those five equal parts so this little slice of the pie this represents one-fifth this right over here is one-fifth of the entire of the entire fraction or of the of the entire pie now this one's interesting you might be tempted to say well I've got four parts and then I've shaded in one that must represent one-fourth but remember it needs to be four equal parts and it's pretty clear looking at this that this part right over here is not equal in size to this part right over here or this part right over here these are not four equal parts so we cannot say that this is one-fourth of the triangle so you cannot say that