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Solving 3-digit addition in your head

Sal shows some techniques for doing mental addition, such as making groups of 10 and 100.

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Video transcript

- [Voiceover] What I want to do in this video is go over some techniques for doing mental addition. Now, if I saw something like 355 plus 480, if you have some paper around, you could write these numbers down and do your traditional addition, but you might want to be able to do these in your head, so how do you do it? Well, the way to think about it is, can we add or subtract from these numbers so that one of these numbers might become a little bit simpler? So for example, I have 480 here. What would I have to do to 480 to, say, get it to 500? It's almost 500. Well, I could add 20 to 480, but I can't just add 20. I would would also have to take away 20, so what happens if I take away 20 from 355 and add it to 480? So what am I talking about? So this is going to be the same thing as, so let me take away 20 from this. So that's going to be 335 and let me add 20 to this, so 480 plus 20 is 500, and the whole reason why I took away 20 and I added 20 is I said, well what do I have to add to 480 to get to 500? And I could have done that in my head. Okay, I need to add 20. 355 minus 20 is 335. But now this problem is much, much simpler to compute. 335 plus 500, well, it's going to be three hundreds plus five hundreds, it's going to be equal to 800 and then we have 35. 835. Now, to make it a little bit clearer what we did, remember, we wanted to take 20 from here and put it over here, so we could break up 355, we could say that it's going to be equal to, it's going to be equal to, let's break it up into 335 and 20, and remember, the whole reason why I picked 20 is because I'm going to want to add that to 480, but I'm just doing it step-by-step here, so plus 480, and now I can just change the order with which I add, so I could say, this is going to be equal to 335 plus 20 plus 480, and instead of adding the 335 and 20 first, I could add the 20 and 480 first, so I could add these two characters first, and so then I'm going to be left with, this is going to be equal to 335 plus, what's 20 plus 480? Well, that was the whole point. I picked 20 so that I can get to 500. 20 plus 480 is going to be 500 and then, now, you can add them. This is going to be 835. So this is just a longer way of saying what I did here. I took 20 from 355, so I can make the 480 into a 500. Let's do a couple more examples of this, and remember, the key is just thinking about how could I add or take away from one of the numbers to make them simpler? So over here, I have 18 plus 704. So there's a couple ways we could tackle this. One way, we could try to get the 704 to be equal to 700. So, we could say that this is the same thing as 18 plus, I could write 700 plus 4, or I could write it as 4 plus 700, like that, and then I could put the parentheses around this first, and then I could just switch the order in which I add, so this is the same thing as 18 plus 4 plus 700, and now I could add the 18 and the 4 first. Now what's 18 plus 4? It's 22, and then I have plus 700, and now this is pretty easy to compute, and all of these are going to be equal to each other, so let me just write it like that. 22 plus 700, I could do that in my head. That's going to be 722. Now, I know what you're thinking. Hey, this is supposed to be a technique for doing something in my head? I can't write all this stuff down in my head. The reason why I'm writing this down this way is that you see what's really going on. But you could do it a lot quicker. You could just say, hey, let me take 4 from the, I'm closing my eyes right now as I'm talking, just so I can pretend like I'm doing it in my head. Okay, let me add 4 to 18 and take away 4 from 700, well that's going to be the same thing if I add 4 to 18, this is going to be 22, and if I take away 4 from 704, that's going to be plus 700. 22 plus 700 is 722. Now, there's another way that you could tackle it. You could say, well, let me actually, instead of taking away 4, let me add some number, some value here, so I get to, I don't know, say 710. That seems a little less ideal for me, but you could do it. Well, let's see, if I added 6 to 704, I'll get to 710. So how about I break off 6 from the 18 and add it to the 704? So I could write it like this. I could say that 18 is 12 plus 6 and then plus 704 which is the same thing as 12 plus 6 plus 704, and then I could add these first, and I could have 12 plus 710 and I might be able to say, Okay, that's going to be 722, but this method right over here doesn't seem anywhere near as intuitive as doing this, as trying to get the 704 to 700 by taking 4 from here and adding it over here. Let's do one more example of this. So, 275 plus 595. Well, my gut reaction is, can we get this 595 to be equal to 600? So this is going to be equal to, so if I add 5 to 595, I get 600. Let me do that in the same color. So I'm going to add 5 to it to get 600. I have trouble switching colors. So, 600, but I can't just add 5, I also have to take 5 away from here, so taking 5 from there, that would be 270, so this becomes 270 plus 600, and this is easier for me to compute in my head. This would be two hundreds plus six hundreds is equal to eight hundreds. I have seven 10's plus zero 10's, so 800, and then I have no one's. 870. Now, another way that you could have tried to tackle it is like, let's try to get this 275 to, let's try to get it to 300. So, we could say this is the same thing as 300. We could say this is the same thing as 300. And to get there, I just added 25, but if I add 25 from this number, I'm going to have to take 25 from this number. So I could subtract 25 from here, and then I would get 300 plus 95 minus 25 is going to be 70, so it's going to be 570. 570, and this is also easy to compute. 300 plus 570 is 870. And there's other ways that you can tackle this including the traditional way of writing it down on paper and whatnot. But hopefully this gives you a little bit of a toolkit for being able to solve these things maybe in your head.