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Estimating division that results in non-whole numbers

Sal uses estimation to find quotients that are non-whole numbers.

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Video transcript

- [Instructor] So let's think about something a little bit. What do you think 17 divided by two is going to be? Well, you might immediately realize that it's not obvious what you need to multiply two by in order to get to 17. There's no whole number that I could put here that gets us to 17. We know that two times, let's see, two times eight is a little bit less than that. Two times eight is equal to 16. And we know that two times nine is going to be a little bit more than that, is equal to 18. And so this question mark, two times question mark is equal to 17. This helps us know that our question mark, our unknown value here is going to be between eight and nine. It is going to be eight point something. So let's do another example. If someone were to ask you, hey, let's think about 18 divided by four. And you don't have to figure out exactly what it is just yet, but I want you to think about what two consecutive whole numbers is 18 divided by four, whatever that is, what is that between? Well, we could do something similar. We could say, all right, let's see, four times four is equal to 16, so that doesn't quite get us to 18. We could say that four times five is equal to 20, so that's more than 18. So four times question mark is equal to 18. This helps us realize that because 18 is between 16 and 20, this question mark right over here is going to be between four and five. So 18 divided by four is going to be four point something. Now, another way of thinking about or estimating what division might result in is through an inequality. So if I were to say 87 divided by nine, how would you compare that to 10 over here? So there's a couple of ways you could compare it. You could say, hey, maybe this is greater than 10. Maybe it's equal to 10. Maybe it is less than 10. So pause this video and see if you can figure that out. What would you put here? Is it less than, greater than, or equal to 10? Well, we know it's not equal to 10. We know that 90 divided by nine is equal to 10. And let's see, if we go one multiple of nine less than that, we know that 81 divided by nine is equal to nine. And so 87 divided by nine is in between these two values. Let me do this in another color. So 87 divided by nine is going to be something in between nine and 10. And so it is going to be less than 10. So the whole point of this video is to start to get us a little bit comfortable with this idea of dividing where we might get an answer that is not a whole number. And in the future we'll learn how to compute that, but for now we're just learning to estimate and just get a sense of, hey, okay, this is going to be between eight and nine. This is going to be between four and five. This is going to be between nine and 10, which just means it's going to be nine point something, which means it's going to be less than 10.