Adding three digit numbers with regrouping | Addition and subtraction | Arithmetic | Khan Academy

We have three different addition problems right over here.

And what I want you to do so you get the hang of things is to pause the video and try them on your own.

But as you do them, I want you to really keep in mind and think about what the carrying actually means.

So I assume you've tried on your own.

Now I'll work through them with you.

So we have 9 + 6.

9 ones + 6 ones.

Well 9 + 6 is 15.

Well, we could write the 5 in the ones place, and then we carry the 1.

But what did we just do?

What does this 1 represent?

Well, we put it in the tens place.

1 ten represents 10.

So all we said is that 9 + 6 is equal to 10 + 5, is equal to 1 ten + 5, which is equal to 15.

Now, in the tens place, we have 1 + 0 + 9, which is 10.

And so we can write 0 and carry the 1.

1 + 0 + 9 is 10.

Now what does that really mean?

Well this is 1 ten + 0 tens + 9 tens, which is 10 tens.

10 tens is 100.

Or another way of thinking about 100, it's 1 hundred, and 0 tens.

So that's all that carrying represents.

So now we have 1 + 7 + 9.

That is going to be 17.

Now, we have to remind ourselves, this is in the hundreds place.

So this is actually 1 hundred, plus 7 hundreds, plus 9 hundreds, or 17 hundreds.

Or 1 thousand, 7 hundreds.

And of course we have this 5 here.

And we are done.

Now let's try to tackle this one.

Now the reason why I wrote it that way is to make sure that we remind ourselves to align the proper places under the appropriate places.

So this problem we could rewrite as 373 + 88 (stacked vertically).

We want to write the ones under the ones place, and the tens under the tens place, so that we're adding the appropriate place values.

So 3 + 8 is 11.

The 1 in the ones place, and the 1 in the tens place.

10 + 1 is 11.

1 + 7 is 8.

8 + 8 is 16.

But this is actually 16 tens.

So let me just write down the 16.

What is 16 tens?

Well, that's 160.

So this 6 is a sixty.

And then I have 100.

1 + 3 is 4.

But these are actually hundreds, so it's 4 hundreds.

So we get 461.

Now finally, 9 + 3 is 12.

2 ones, and 1 ten.

12 is the same thing as 10 + 2.

Now in the tens place: 1 + 4 + 9 is 14.

So we write the 4, and carry the 1.

But remind ourselves, this is actually 10 + 40 + 90, which is 140.

Which is the same thing as 40 + 100.

And then 1 + 1 + 2 is 4.

But this is the hundreds place.

So this is actually 1 hundred, plus 1 hundred, plus 2 hundreds or 4 hundreds.

And we're done.