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

Lesson 16: Addition with regrouping within 1000

Learn to use regrouping, or carrying to add 709+996, 373+88, and 149+293. Created by Sal Khan.

## Want to join the conversation?

• Well good question, regrouping is technically carrying but subtraction (plz give me a vote 🥺)
• ok I will
(1 vote)
• What is "regrouping"? Is it the carrying of the 1s? Or is it the moving the 88 under the 373 as in the middle problem? I learned addition about 60 years ago, and the term "regrouping" wasn't used back then?
EDIT: I figured it out from the lesson on subtraction. It's both "carrying" and "borrowing". Thanks anyway! My mistake.
• Regrouping is carrying of the 1's in an addition problem, and borrowing of the 1's in a subtraction problem. So regrouping in addition and subtraction problems is the exchange of 10 ones for a ten (or the reverse exchange), 10 tens for a hundred (or the reverse exchange), 10 hundreds for a thousand (or the reverse exchange), and so on.

Have a blessed, wonderful day!
• why is the middle one horizontal at in the video?
• As Sal explain from onward, the reason it was initially horizontal, is to remind us, how we have to put the numbers vertically, with the ones aligned, and the tens aligned.
It's just a reminder that an addition might be presented in a test in this (horizontal) notation, and that we have to arrange them in the specific way to carry out the addition procedure.
• Whats 5543+7820 equals what?
• What is 53+53+53+53+53 is it let me think....... if my caculations are correct it is....... 265 am I right?
• yes u are!!
• can you make it harder
• it coudava makes sense
• whah is a adding a 5 numder like 10890+16547=
• Q: 10890+16547

A: Lets use a similar method to solve this.

1.
‎‎
‎‎ ‎ ‎‎‎10890
+‎ 16547‎ ‎ ‎ ‎ ‎ ‎ ‎ <-‎ ‎ Let's first add the one's digit. 7+0 is 7
----------
‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎‎‎ 7

2.
‎ ‎ ‎ ‎ ‎ ‎ ‎ ¹
‎‎ ‎‎ ‎‎ ‎‎‎10890
+‎ 16547‎‎ ‎<-Now let's add the tens digit. 4+9 is 13 so we need to carry
----------
‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎37

If we keep continue this process, we can get the answer 27437.
• This is super, duper EASY!!
• I really do not understand.

## Video transcript

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 it on your own. Now I'll work through them with you. So we have 9 plus 6. 9 ones plus 6 ones. Well 9 plus 6 is 15. Well, we can write the 5 in the ones place, and then we can carry the one. But what did we just do? W.hat does this 1 represent? Well, we put it in the tens place-- one 10 represents 10. So all we've said is that 9 plus 6 is equal to 10 plus 5. Is equal to one 10 plus 5, which is equal to 15. Now, in the tens place, we have 1 plus 0 plus 9 which is 10.. So we can write 0 and carry the 1 1 plus 0 plus 9 is 10. Now what does that really mean? Well this is 1 ten plus 0 tens plus 9 tens, which is 10 tens. 10 tens is 100. Or another way to think about 100, it's 1 hundred, and 0 tens. So that's all that carrying represents. So now we have a 1, plus a 7, plus a 9. That is going to be 17. Now we have to remind ourselves, this is in the hundreds place. This is actually 1 hundred plus 7 hundred plus 9 hundred 17 hundred. Or 1 thousand, 7 hundred. 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 we rewrite as-- let me do that same green color-- we could rewrite this as 373 plus-- we want to write the ones place under the ones place, and the tens place under the tens place, so that we're adding the appropriate values. So 3 plus 8 is 11. The 1 in the ones place, and the 1 in the tens place. 10 plus 1 is 11. 1 plus 7 is 8. 8 plus 8 is 16. 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 60, and then I have a hundred. 1 plus 3 is 4. But these are actually hundreds, so it's 4 hundreds. So we get 461. Now finally, 9 plus 3 is 12. 2 ones, and 1 ten. 12 is the same thing as 10 plus 2. Now in the tens place, 1 plus 4 plus 9 is 14. So we write the 4, and carry the 1. But remind ourselves this is actually 10 plus 40 plus 90, which is 140. Which is the same thing as 40 plus 100. And then 1 plus 1 plus 2 is 4. But this is the hundreds place. So this is actually 1 hundred, plus 1 hundred, plus 2 hundred, or 4 hundred. And we're done.