Examples identifying multiples

In this video, we're going to 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 9. So pause this video and see if you can figure that out.

All right, now let's do it together. One way to think about a multiple is a number that you can get to by multiplying the number, in this case 9, by a whole number. So we could figure out the multiples of 9 by skip counting; that's one way to do it.

You could go from 9, and then you add 9 to that; you get to 18. You add 9 to that; you go to 27. You add 9 to that; you are going to get to 36. You add 9 to that; 45. Add 9 to that; 54. Add 9 to that; 63. Add 9 to that; you get 72. Add 9 to that; you get to 81. 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 is larger than 81, we would have to keep going to see if it's included. But we can see that 46 sits between two multiples of 9. 46 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 9, you're not going to get a remainder. But if you divide 46 by 9, you are going to get a remainder; you're not going to be able to divide 9 into it evenly. So I am just 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, eighteen, oh I see an 18. There, there you go. Especially 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 for a multiple of eight. Well, four 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 multiply 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: 4, 8, 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; sixteen is a multiple of 8; 24 is a multiple of 8. But not all of the multiples of 4 are multiples of 8.

I think you might be seeing a little pattern here: which ones are multiples of 8. Now, what about this choice right over here? 16 is 8 times 2; 24 is 8 times 3; 32 is 8 times 4; 40 is 8 times 5. In fact, we could skip count: 8, 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: 1, 2, 4, and 8. Well, these are showing numbers that can be divided into 8 without a remainder. You could think of them as factors of 8. You could say, hey, I can multiply 1 times 8 to get 8. I can multiply 2 times 4 to get 8. But these are not multiples of 8. What whole number can I multiply 8 by to get 1 or to get 2 or to get 4?

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 I realized I can't use multiples to define multiples. It would be that number or larger numbers than it, and it would have to... and if you were to skip count with that number, you would hit all of the multiples.