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Estimating when adding multi-digit numbers

Let's learn about estimating when adding multi-digit numbers. We see how to round numbers to the nearest 10 and then add them together to get an approximate sum. This technique is helpful for us when we need to make quick mental calculations and don't require an exact answer.

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Video transcript

- [Instructor] Let's say that we run an egg farm, and yesterday, we went out and we collected 398 eggs from the chickens, and then today, we went out and we collected 251 eggs from the chickens. And what we're curious about is, roughly how many eggs do we now have that we've collected over the last two days? Well, there's a few ways we could do that. We could just add 398 to 251, and figure out what that is equal to. But let's say that we don't have a lot of time, and we don't have paper, and we want to do it in our heads, and we don't care about the exact number. We want to know roughly how many eggs do we have? Well, that's where the tool of estimating is useful. So instead of saying the exact amount of eggs, we could say, how many do we roughly have? And that's what this squiggly equal sign means, it means, hey, we don't have to get the exact number, but how many do we roughly have? And so we will be estimating. And the way that we can do that is that we can round each of these numbers to a number that is close to them, but that's easier to add in our heads, and then we add those two numbers. So pause this video, and see if you can do that on your own before we do it together. Alright, now let's do this together. Let's start with 398, and let's round it to the nearest 10. So, 398, you can view this as, we have a nine in the 10s place, but you could view this as 39 10s, and eight. The 10 that it is right directly above is exactly 39 10s and zero ones, or 390, and then the next ten would be if we go up to 40 10s, which would be the same thing as 400. Now, which one would we round to? Well, 398 is closer to 400 than it is to 390, and we've talked about in the rounding videos that you can see that this right over here is five or greater, so we would round the 10s place up. So we would round to 400. And so, 398, we round to 400. And then we're going to add that to 251, what's that rounded to the nearest 10? So I'll do that again, right over here. 251. The 10 that is right below that is going to be 250. The 10 that is right above that is going to be 260. Once again, you could view this as 25 10s and one. And 251 is clearly closer to 250, we can round down. Another way to think about it is, you look at the 10s place, and then you look at the ones place, and you say, hey, this is less than five, so I'm gonna round down to on the 10s place, so we get to 250. So when you round 251 to the nearest 10, you're going to get 250. Now, I encourage you, add these two in your head. What would this be equal to? Well, the way that I think about it in my head, and there's a lot of different ways to approach addition, but you could say, alright, I can think about the hundreds. I have four hundreds, and I'm adding that to two hundreds, and let me do this in a new color. So if I have four hundreds, and I'm adding it to two hundreds, well, that's going to be six hundreds. And if I have zero 10s, and if I'm adding it to five 10s, well, I'm still going to have five 10s, and then I have zero ones in either cases, so I'm still going to have zero ones. And so there you have it. We were able to estimate 398 plus 251 as being roughly 650.