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Addition using groups of 10 and 100

Sal rewrites addition problems to make them easier to solve.

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Video transcript

- [Voiceover] So, let's do some practice problems on Khan Academy exercises that make us rewrite an addition problem so that we can get them to rounder numbers. Numbers that might be multiples of 10, or multiples of 100. So, let's see here, I have 63 plus 427, and that seems kind of hairy, you know, it feels like I wanna write those things down, but maybe I could take away from one of them, and give it to the other one so that they both become round numbers, and it's clear that 63, if I were to give three away I would get to 60, and if I were to give those three to 427, it would get to 430, and 60 plus 430 is a much simpler problem. So, let's think about what this question is saying. Well, it's just taking a step by step through that process. It's just saying 63 plus 427 is going to be equal to 60 plus what plus 427? So, the 60 plus what, this is gonna to be the same thing as 63, cause we have 427 in both places, so 63 is 60 plus three. Well, that makes sense. On this next step, they just change the order. 60 plus three, and then adding 427 is the same thing as doing 60 plus, and then adding the three to the 427 first. So, we're just taking this three and moving it from the 63 to the 427. Well, three plus 427, that's just 430. And now this addition problem became a lot simpler. 60 plus 430, we can do that in our head. We're just adding six 10's to this, right over here, so it's gonna be 490, and we're done. Let's do a couple more examples of this. So, over here, we want to, let's see, we want to add these two numbers, and let's maybe see if we can 'em a little bit a rounder number. So, over here, we're breaking up the 275 into 270 and something. Well, that's gonna be 270 plus five. Notice, the rest is still the same, plus 595, plus 595. Now, why are we doing that? Well, if we take five from 275 and give it to 595, which is what we're doing here, the 595 can get to 600. It's gonna make the calculation easier. So, once again, here we're adding the 270 and the five first, and then we're adding the 595, but we could change the order in which we do it. We could add the five to the 595 first, and then add the 270. So, this is the same thing as 270 plus, five plus 595 is 600, that's the whole reason why we took five from the 275 is so that we can add it to the 595 and get 600, and now we can do this in our head. 270 plus six 100's, well we're just gonna increase our 100's by six, so it's gonna be 870. Let's do a couple of more examples here. Fill in the blank. 51 plus 83 is the same thing as blank plus 84. Well, they increased 83 by one to 84, so we gotta decrease 51 by one. So, this is gonna be the same thing as 50 plus 84. Now, why would anyone care about this? Why would they do that? Well, I find this easier to calculate, because now I just have to say eight 10's plus four ones, plus another five 10's. Well, that's gonna be 13 10's and four ones, or 134. So, I find this a little bit easier, but the important thing is if we add to one number, we gotta take away the same amount from the other number in order to not change the value of this addition problem, of this expression. Let's do one more. 138 plus 710 is the same as blank plus 700. So, we had 710, and it's now 700. So, we took 10 away from that number, so we have to give it to the other number. So, 138, we have to add 10 to that, so that's gonna be 148. Now, why was that useful? Well, 148 plus 700, you can do that in your head. That's gonna be 848, and that's easier to compute than what we just had over here.