Identifying multiples

- [Instructor] In this video, we're gonna start thinking about what it means for something to be a multiple of a number. So, we're asked, which of the following numbers is a multiple of nine? So, pause this video and see if you can figure that out. All right, now let's do it together. And one way to think about a multiple, a multiple is a number that you can get to by multiplying the number, in this case nine, by a whole number. So we could figure out the multiples of nine by skip counting, that's one way to do it. So you could go from nine, and then you add nine to that, you get to 18. You add nine to that, you go to 27. You add nine to that, you are going to get to 36. You add nine to that, 45. Add nine to that, 54. Add nine to that, 63. Add nine to that, you get 72. Add nine to that, you get to 81. And we could keep going. But to figure out whether these are multiples, you really just have to say, hey, are any of these numbers in this list? Now, if one of these numbers are larger than 81 we would have to keep going to see it's included. But we can see that 46 sits between two multiples of nine. 46, that sits closer to 45 but it sits in there, it sits between two multiples. So that's not going to be a multiple. Another way to think about it is, for something to be a multiple, if you divide by nine, you're not going to get a remainder. But if you divided 46 by nine, you are going to get a remainder. You're not going to be able to divide nine into it evenly. So I am just going to, I'm going to take that one out of the contention. 77 is right over here, it's between 72 and 81. Once again, it's between two multiples but not a multiple. 39 is between 36 and 45, so not a multiple, between two multiples. Rule that out. And we can see very clearly that 18 is a multiple. If I was doing this on my own, I would just maybe be skip counting in my head. I'd be going, nine, all right I don't see a nine. 18, oh, I see an 18, there you go. Specially if I'm only going to pick one choice. Let's do another example. Which of the following shows only multiples of eight? So, pause this video and think about that. All right, well, I could do it choice by choice here. So, let's see. This first one, is four a multiple of eight? Well, four, it can divide into eight. We could say that eight is a multiple of four, but four is not a multiple of eight. What whole number am I going to multiple eight by to get to four? So we can rule this out. And you can think about what they're showing here. These are actually multiples of four, not multiples of eight. We can skip count here. Four, eight, 12, 16, 20, 24, 28. These are multiples of four, not multiples of eight. Some of the multiples of four are also multiples of eight. Eight is a multiple of eight, 16 is a multiple of eight, 24 is a multiple of eight, but not all of the multiples of four are multiples of eight. And I think you might be seeing a little pattern here, which ones are multiples of eight. Now, what about this choice right over here? 16 is eight times two. 24 is eight times three. 32 is eight times four. 40 is eight times five. In fact, we can skip count. Eight then 16, 24, 32, 40, then 48, 56, so on and so forth. But these are all multiples of eight, so I like this choice. And then over here, one, two, four, and eight. Well, these are showing numbers that can be divided into eight without a remainder. You could think of them as factors of eight. You could say, hey, I could multiply one times eight to get eight. I could multiple two times four to get eight. But these are not multiples of eight. What whole number can I multiply eight by to get one or to get two or to get four? In general, your multiples of a number are going to be that number or larger than it. I was about to say that number or multiples of it but then I realized I can't use multiples to define multiples. It would be that number or larger numbers than it. And if you were to skip count with that number, you would hit all of the multiples.