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Visualizing division with arrays

Sal uses arrays to represent division expressions.

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Video transcript

- [Instructor] We have three different pictures here, and my question to get us warmed up is which of these could represent 20 divided by four? Pause this video and see if you can figure that out. All right, so let's go through each of these. And, actually, let's think about what each of them could represent. So how many total circles do we have in this picture right over here? Let's see, we have one, two, three, four, and then we have four groups of four. So four, eight, 12, 16. So this looks like 16 circles. 16 circles divided into, we could do it as divided into groups of four, or we could actually also view it as divided into four equal groups, because both of those are true. And we see that that is going to be equal to four. So this one over here, it's really representing 16 divided by four, not 20 divided by four. Now, what about this one? Let's see, here, it looks like we have one, two, three, four, five groups of one, two, three, four, five. So this looks like 25 circles divided into groups of five, or divided into five equals groups, which is, of course, equal to five. So this is 25 divided by five, not 20 divided by four. Now, but what about this one? So let's see, we have one, two, three, four, five, and we have, one, two, three, four groups of five. So five, 10, 15, 20. So we definitely have 20 circles there. And we have divided it into four equal groups. We have divided it into four equal groups, and so that's exactly what we're talking about, or what we started talking about. This is 20 divided by four. And you can see, when you take 20 and divide it into four equal groups, then you get one, two, three, four, five circles per group. And we're done.