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## Arithmetic (all content)

### Course: Arithmetic (all content) > Unit 2

Lesson 16: Addition with regrouping within 1000# Using place value to add 3-digit numbers: part 2

Learn to use regrouping to add 536+398. Created by Sal Khan.

## Want to join the conversation?

- Why is it that you can only "carry the one" and never "carry the two"?(165 votes)
- Good question. When you add two numbers, you are adding pairs of digits, as in the video. Those pairs can never add up to more than 18, (or 19 when you are carrying 1) .

But if you are adding three or more numbers, the digits you add together can add up to more than 18, in which case, you might have to carry two, three, or more.

Let' s try 276 + 499 + 387`276`

+499

+387

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2 Two units

2 Carry two tens

62 Six tens and two units

2 Carry two hundreds

1162 One thousand, one hundred, six tens and two units(184 votes)

- why did Sal do it in expanded form?(45 votes)
- Sal was trying to show you why adding the numbers in each column and carrying the digit works. He wants you to understand that we aren't just adding single digit numbers. Instead, they have place value (units, tens, hundreds, etc)(53 votes)

- You can carry the two or any other number?(15 votes)
- Yes, it doesn't matter what the integer is, as long as it is of a greater place value that you are adding up, it should be carried over to the respective place value. For example:
`18`

28

15

9

+14

¨¨¨¨¨¨¨¨¨

84

When you add up the numbers in the ones place, you get 34. You then carry the thirty over to the tens place and represent it as a 3.(4 votes)

- What if you were adding in the ones place and you had to carry 100

(Or a 1000 in the situation of the ten's place, and so on)?(12 votes)- my bro this is because 9 is a single digit number so there is no need of carrying.(2 votes)

- I do not get it(8 votes)
- In life, is there math involved?(4 votes)
- Yes. For example, if you go out to a store to buy a product, you will calculate the cost of what you have and what you will pay. Math comes in handy by helping you calculate not just costs of what you have and what you will pay, but will also calculate what you will need for taxes, fees, and maybe even warranty (depending on what product you get).(11 votes)

- you can only carry two when you have a twenty something(4 votes)
- It is not possible to end up with a twenty something when adding only two numbers together. So your (correct) statement means that in order to carry two, you have to be adding more than two numbers together.

Have a blessed, wonderful day!(5 votes)

- how many three-digit numbers have three different digits?(4 votes)
- The answer is 648. There are several ways to arrive at this.(4 votes)

- What if you were adding in the ones place and you had to carry 100

(Or a 1000 in the situation of the ten's place, and so on)?(4 votes)- This might be an example of the situation that you're asking about.
`+9.9999`

+0.0003

-------

?

To add these two decimals, the 3+9 = 12. Write a 2 in the ten thousandths' place. Carry the 1.

Then 9+0+1 = 10. Write a 0 in the thousandths' place. Carry the 1.

Then 9+0+1 = 10. Write a 0 in the hundredths' place. Carry the 1.

Then 9+0+1 = 10. Write a 0 in the tenths' place. Carry the 1.

Then 9+0+1 = 10. Write a 0 in the units' place and a 1 in the tens' place.

Final answer after all that carrying:`+9.9999`

+0.0003

-------

10.0002(3 votes)

- What's the difference between adding and adding with regrouping? Don't you get the same Answer?(4 votes)
- Depends on how you add. If you don't regroup, there is a larger chance that you have gotten the wrong answer. As you know, you can't put two digits in the ones slot, or in the tens slot, etc. If you don't regroup, then things may get confusing and cause your answers to be wrong. So, adding with regrouping is a way to help make things less-confusing.(2 votes)

## Video transcript

Now, let's do the exact
same addition problem that we did in the last video. But I'm going to expand out
these numbers so that we really understand what's
going on when we're doing all of this carrying. So this 5 is in
the hundreds place. So it really represents
5 hundreds or 500. 3 represents 3 tens because
it is in the tens place. So it represents 30. And the 6, well, it just
represents 6 ones or 6. Likewise, this 3 represents 300. This 9 is 9 tens or 90. And this 8 just
represents 8 ones or 8. And now we can add these two up. Now let's start in the
right-most column-- this ones column. 6 plus 8, we've
already figured out, is equal to 14, which is
the same thing as 10 plus 4. So let's write the
part that's not a multiple of 10 in
this ones column. So let's put that 4 there. And the part that
is a multiple of 10, we can now carry into
this tens column. And that's just to keep track
of it-- just to make sure that we don't lose
that 10, we're putting it into the tens column. Now we can add all the tens. 10 plus 30 plus 90, we've
already figured out is 130. Well the part that is
not a multiple of 100, we can write in this tens
column-- so the 30 part. And then the part that
is a multiple of 100, we can put in the
hundreds column. So we could put the
100 right over here. Notice, we've just
carried the 1. But essentially, we've carried
100, because we put a 1 in the hundreds place. 10 plus 30 plus
90 is 100 plus 30. This is equal to 100 plus 30. That's all we've done. Now we can add the hundreds. 100 plus 500 plus 300 we've
already figured out is 900. So we can write it as 900. And we're done! We've figured out that
500 plus 30 plus 6, plus 300 plus 90 plus 8, is
equal to 900 plus 30 plus 4, which is the same thing as 934. So hopefully this gives
you a little bit more sense of what we're doing when we
"carry the 1" every time. 6 plus 8 is 14. We carried the 1. That 1 represents 10. It represents this
10 right over here. Just so we don't
lose track of it. Then we say that 10 plus
30 plus 90 is equal to 130. So that's 30 plus 100. Then we add the hundreds
together and we get 900.