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# Multi-digit subtraction with regrouping: 7329-6278

Sal subtracts 7329-6278 using regrouping. Created by Sal Khan.

## Want to join the conversation?

• hello. can any one explain me the "subtraction by addition" in a visual way?

the steps says:
1. take the "complement" of the number we are subtracting
2. add it to to the number we are subtracting from
3. discard the extra "1" on the left

example: 9 - 7 7compliment is 3 therefore 9+3 =12 we discard the 1 on the left and answer is:2

but I do not understand how it works actually?
• Wow, I've never heard about "Subtraction by Addition" before. It is pretty cool! I will try to explain it as best I can! In a visual way, say we have 9 - 7, we could see that as 9 boxes, but we crossed out 7 of them, leaving us with 2 boxes:
``[ ][ ][X][X][X][X][X][X][X]``

When we take the compliment of a number, we basically just add the number we take the compliment to. In this case, it is the number 10, right?
The complement to 7 is 10 - 7.

In our first equation we had 9 - 7 = ?
If we would to add 10 to both sides, we would get:
9 + 10 - 7 = ? + 10
And we know that 10 - 7 is the complement. So we get
9 + (complement of 7) = ? + 10
But since we had to add it to both sides, we have an extra + 10 to our answer, right? So to get the correct answer, we must remove that extra + 10. We can see it as:
9 + (complement of 7) - 10 = ?

So we have 9 boxes
``[ ][ ][ ][ ][ ][ ][ ][ ][ ]``

We add "complement of 7" more boxes (which is 10 - 7) So we add 10 and remove 7
``[ ][ ][ ][ ][ ][ ][ ][ ][ ]  [ ][ ][ ][X][X][X][X][X][X][X] ``

And then we remove the extra 10.
``[ ][ ][X][X][X][X][X][X][X]  [X][X][X][X][X][X][X][X][X][X]``

And we are done. The answer is 2.
• what if all the numbers are small and on the bottom is all big like this: 10000-76899
• than it becomes a negative number. i have to do it all the time in algerbra
• This doesn't make any sense. If you add a 100 to 20 wouldn't it make 120?😕😕😕😕😕
• YES 100+20= 120 go check on a calculator.
(1 vote)
• why can't you just put all like the adding in one video, the multiply in another all together then to have it going to video then you gotta turn to the next so why?
• I think addition is too much to show in a single video....Unless the video is ridiculously long..
• Some one said that 1+1 is not 2, is it true?
(1 vote)
• 1 + 1 must be 2 ....
let's say you have 1 apple. i give you 1 more. you now have 2
(1 vote)
• okay i don't understand why we need to see it as hundreds why can't we just see it as the combination it is just really weird to me and i just don't see why. Please tell me if you can answer this thx.
(1 vote)
• ok really can anybody answer this question please.Now why do we have to see it as hundreds it is sillly please answer this thx goodbye
(1 vote)
• how do you do times tables in algarithim
(1 vote)
• Sal does two examples in this video, which example is better??
(1 vote)
• how long did it take to make this vidio
(1 vote)

## Video transcript

We have 7,329 minus 6,278. So let's go place by place and see if we can subtract. 6,278 is clearly less than 7,329, so we should be able to do this. So first, we go to the ones place. We're subtracting an 8 from a 9. That seems pretty straightforward. That's just going to be a 1, a 1 in the ones place. It literally just represents 1. Then we go to the tens place. And we're trying to subtract a 7 from a 2. And this is really representing 70. And this is really representing 20. Well, now we're hitting a bit of a stumbling block. So we're going to have to regroup or borrow. And to understand what we're doing, let's rewrite both of these numbers. So 7,329-- 7 we can rewrite as being equal to 7,000. Plus 300-- so this 3 in the hundreds place is representing 300. The 7 in the thousands place is 7,000. 3 in the hundreds place is 300. The 2 in the tens place, that's two 10's, or 20. And then the 9 in the ones place is just going to be 9. So this is another way of representing 7,329. And then down here, we have the 6 in the thousands place. Well, that's going to be 6,000. And we're subtracting, so minus 6,000. And then here, we have a 2 in the hundreds place. And once again, we're going to be subtracting all of these. So we're going to be subtracting 200. And then here in the tens place, we have our 7. And we're subtracting it. So seven 10's, that's 70. And then we are subtracting that 8. And what we've already done is said, hey, look. Subtracting 8 from 9? That's just going to be 1. But then we got over here, and we said, hey, how are we going to subtract 70 from 20? And the key here is to regroup some of the value up here and give it to the tens place, so that we can subtract 70 from it. And the most natural place to go is one place value above. So we could take 100 from the 300. So then it will become 200. We're going to give 100-- we're going to give that 100 to the tens place. So it is going to become 120. Notice, 200 plus 120 is 320. 300 plus 20 is 320. We have not changed the value of the number. We've just changed what place we're representing it in. If we wanted to do it here, we could say-- and when you think of it this way, this is really regrouping, and this is really what's happening. But if you want to think of it in a borrowing framework, you could say, hey, let's take 1 from the 3. Although it's a 300, so you're really taking 100. That becomes a 2. And you give that 1 to the tens place. And so that becomes a 12. Now, what was really happening is you took 100. You gave it to the 20. It became 120. But now you can subtract. Here, you'd say, well, what's 120 minus 70? Well, 120 minus 70 is going to be 50. Over here you could say, well, what's 12 minus 7? Well, that's 5. But it's still representing the same thing. 12 10's is 120. Seven 10's is 70. And they give you five 10's, which is the same thing as 50. This 5 represents that 50. And then we can go to the other places. You say 2 minus 2. Well, that's zero 100's. And then 7,000 minus 6,000 is 1,000. And once again, right over here, 200 minus 200 is zero 100's. And then 7,000 minus 6,000 is 1,000. So this is going to be 1,000 plus 0 plus 50 plus 1, which is the exact same thing as 1,051. The important thing is to visualize-- you don't have to write this out every time. But to make sure you visualize in your head that this 3 is representing 300, that this 2 represents 20, that when you're taking 100 from the 300, then you would represent that as a 2 in the hundreds place. And then when you give 100 to the tens place, it's essentially that the two 10's will become 12 10's. Because you're giving it 10 more 10's. You're giving it 100. So hopefully, that makes some sense.