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Worked example: Subtracting 3-digit numbers (regrouping twice)

Sal using regrouping (borrowing) to subtract 913-286. Created by Sal Khan.

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• Can you regroup in subtraction?
• Yes, you can regroup in subtraction but it is more commonly called BORROWING instead of regrouping. If you are taking 68 away from 243, you would need to regroup, because you wouldn't be able to take 8 ones away from 3 ones, so you would have to regroup or BORROW from the tens column. You would also need to regroup because you wouldn't be able to take 6 tens away from 3 tens (since we just borrowed one of the tens), so we would need to borrow from the hundreds.
243=2 hundreds, 4 tens, 3 ones but it also equals 2 hundreds, 3 tens, 13 ones
now we can take the 8 ones in 68 away from the 13 ones in 243, which leaves us with 5 ones
So now we have 243=2 hundreds, 3 tens, 13 ones but it also equals 1 hundred, 13 tens, 13 ones
now we can take the 6 tens in 68 away from the 13 tens in 243, which leaves us with 7 tens
we can also take away the 0 hundreds in 68 from the 1 hundred in 243, which leaves us with 1 hundred
• What are some tricks/methods I can learn in order to solve this problem (and other 3-digit problems) mentally? I can solve addition and subtraction problems mentally if they are one or two-digit numbers but whenever it's a 3-digit I get stumped because I lose track of the numbers I'm regrouping. Thank you.
• If you're having trouble with this, try using a piece of paper for help. I'm in middle school, and even now i sometimes have to do addition and subtraction on paper. There's no shame in using a piece of paper or showing your work
• is the expanded form different the original way?
• you're just adding zeros. the expanded form is just a bit easier. Like if you don't exactly get the number. say, 7,483,655. in expanded form it would be 7,000,000+400,000+80,000+3,000+600+50+5
• Why do we have to regroup twice? Why can't we just regroup all of the numbers in one , single process?
(1 vote)
• If you regroup all at once it is possible that you mix up all the numbers and you get the answer wrong, but if you take your time and regroup one by one, you will get it write because you are neat.
• i dont understand subtraction why cnat we subtract 300-500?
ans: yes we can we get a negative number -200
im confused?because people say you cannot subtract a small number by big number?
(1 vote)
• You can subtract a smaller number from a larger number. Younger level teachers don't want to confuse their children, so they say that you can't do this. In higher math, teachers say you that you can.

I hope this helps!
• Why does Sal have 100 in the tens place and 13 in the ones place?
(1 vote)
• You always subtract by starting from the right most digits.
3-6 doesn't work, so you borrow a 10 from the tens place, making 13 ones leaving 0 tens.
Looking ahead, you realize that you can't take 8 from 0, so you borrow from the hundreds, putting 10 in the tens and leaving 8 in the hundreds.
He expanded each place, making the 10 tens a hundred.

Video transcript

So let's subtract 286 from 913. But first I'm going to do it in a slightly different way. I've taken each of these numbers, and I've expanded them out. This 9 in the hundreds place represents 900. This 1 in the tens place represents 10. This 3 in the ones place represents 3. Likewise, 286 is the same thing as 200 plus 80 plus 6. So let's try to subtract going place by place. So if we start in the ones place, we have a problem immediately. 3 is less than 6. How do we subtract a larger number from a smaller number? We also have a problem in the tens place, 80 is larger than 10. How do we subtract a larger number from a smaller number? And you might guess the answer here is regrouping, sometimes called borrowing. We're going to take value from one place and give it to another. So let's say this scenario right over here, where we have this 3, and we want to take some value from one of the other places. Well, I could take 10 from the tens place, so then this is going to become 0. And if I give that 10 to the ones place, so 10 plus 3 is 13. Notice I haven't changed the value. 900 plus 0 plus 13 is still 913. Now, this solved the problem for the ones place. I can now subtract 6 from 13. But it made the problem in the tens place even worse. I now have to subtract 80 from 0. What do I do? Well, luckily, I can go to the hundreds place. I could take 100 from 900, so then I'm left with 800. And I could you give it to the tens place. So if I give it to the tens place, then this is going to be 100. Notice this still adds up to 913. 800 plus 100 plus 13 is 913. Why is this valuable? Well, now in every column, I'm subtracting a smaller number from a larger. You might say, wait, isn't there a positive sign here? But we have this negative out here. So we're subtracting 6 from 13. We're subtracting 80 from 100, subtracting 200 from 800. So let's do it. 13 minus 6 is 7. 100 minus 80 is 20. 800 minus 200 is 600. So we're left with 600 plus 20 plus 7, which is 627. Now let's do the exact same thing here, but we're not going to expand out the numbers. So 6 is greater than 3, what do we do? Well, we can regroup from the tens place. We can take 10 from here so we're left with 0 tens and give that 1 ten to the ones place. So you give 10 to the 3, it becomes 13. But now we have a problem in the tens place. How do we subtract 8 from 0? Well, we could take 100 from the hundreds place, so 900 becomes 800, and give that 100 to the tens place. So you give the 100 to the tens place, 100 plus 0 tens is 100. 100 is the same thing as 10 tens. And so now we are ready to subtract. 13 minus 6 is 7, 10 minus 8 is 2. Remember, this is really 10 tens minus 8 tens to get 2 tens. 100 minus 80 to get 20. And then finally, we have 800 minus 200 to get 600-- 627.