Regrouping to add 1-digit number | Addition and subtraction | 1st grade | Khan Academy

So, we have the number 35. The 3 is in the tens place, so it represents 30 or 3 tens—one 10, two groups of 10, three groups of 10. And then the 5 is in the ones place, so it represents five ones. We see them right over here—one, two, three, four, five.

Now, we want to take that 35 or those 3 tens and 5 ones and add 6. 6 ones. The 6 is in the ones place—one, two, three, four, five, six ones. And I encourage you to pause the video and try to do that. Add 35 to 6.

So let's think about it now. So I'm gonna start with the ones. So I have 5 ones, and I want to add 6 ones. So what's that going to be altogether? Well, 5 ones plus 6 ones, that's going to be 11 ones. And I still have 3 tens, so we could say it's going to be 3 tens, 3 tens and 11 ones. 3 tens, I could write, plus 11 ones here.

Now this is a little bit of a problem because we can't write a two-digit number in the ones place or in any one of the places. I can't, this number isn't going to be 311. It's going to be 3 tens and 11 ones. But how can I rewrite this, or how can I regroup things so that I only have a single-digit number here? I have zero, one, two, three, four, five, six, seven, eight, or nine here instead of a two-digit number—the 1 one.

Well, I can regroup. I can say, "Look, I have enough ones here to create a group of ten." I could take 10 of them, so let's take these 10 right over here and put them together and make a new group of ten. So, a new group of ten right over there.

So if I take, so just to be clear, what I just did, I just took these 10, these 10 ones, and I stuck them together and I turned it into this new group of ten. So now what do we have? So when you regroup like this, you see that you have one, two, three, four tens. 4 tens.

And how many ones do you have now? 4 tens plus? Well, I've regrouped all of these 10 ones and all I have left is this 1 one right over there. So I could write this as 4 tens plus 1 one. Once again, 3 tens and 11 ones—that's the same thing as 4 tens and 1 one.

And so we can write that over here, we can write this as 1 one and 4 tens. Now how could you get this if you weren't, if you didn't do it like this and drawing everything out and regrouping like this? This is actually what you should be doing in your head, but another way of thinking about it, you could say, "Alright 5 plus 6," that's going to be 11 ones, but I can't write an 11 here in the ones place.

So I could say, "That's going to be the same thing as 1 ten plus 1 one." 1 ten plus 1 one. Sometimes it's taught that 5 plus 6 is 11, carry the 1, but really what you're doing is you're saying, "5 plus 6 is 1 ten plus 1 one."

And, in fact, an 11, the number 11 right over here. So if I were to write the number 11, the number 11 has a 1 in the tens place and a 1 in the ones place, so it's 1 ten plus 1 one. So you're just saying that 5 plus 6 is 11, which is the same thing as 1 ten and 1 one, and then you add your tens together—1 ten plus another 3 tens is going to be 4 tens.

But I really want you to appreciate what's going on. You're not just blindly saying, "Oh, 5 plus 6 is 11, so I'm going to write 1 of the ones here and write the 1 in the tens place here." You're doing it because you're regrouping. You're regrouping that group of ten. You're saying, "Hey I could take 10 of these ones and I can turn them into a new group of ten, and that would just leave me 1 in the ones place. 1 in the ones place, and I've just turned all the other ones into a new group of ten."