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## 3rd grade

### Course: 3rd grade > Unit 3

Lesson 7: Subtracting with regrouping within 1000- Worked example: Subtracting 3-digit numbers (regrouping)
- Subtracting 3-digit numbers (regrouping)
- Worked example: Subtracting 3-digit numbers (regrouping twice)
- Worked example: Subtracting 3-digit numbers (regrouping from 0)
- Subtract within 1000

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# Subtracting 3-digit numbers (regrouping)

Sal uses regrouping (borrowing) and place value to subtract 629-172. Created by Sal Khan.

## Want to join the conversation?

- When Sal writes the second line in the second problem, why does he put a parenthesis around the bottom row?(75 votes)
- Sal wrote the second number in expanded form. But we are subtracting the second number, so we need to put the subtraction sign. He could have put negatives for each place value, but that loses the sense that we have expanded the number.(78 votes)

- at1:27, do you have to take away 100? or can you take away just 1?(6 votes)
- Well,it depends on what strategy you are using to subtract.If you're just doing standard algorithm then, you would just write that you are borrowing "1" but if you want to say the accurate value of the number then you would say that you're borrowing 100, which is what you are actually borrowing!

Hope this helps!(3 votes)

- how would do one with a zero like 800-546(2 votes)
- Borrow/Regroup from the 8 into the tens place, then borrow/regroup from the tens place into the ones place. Just work from left to right.

I use multiple lines as there is no way to indicate crossing out a number for subtraction by 1.`11`

800

-497

----

4 -> Reach the 9 notice it's greater than 0 so subtract one to borrow

31 -> Reach the 7 notice it's greater than 0 so subtract one to borrow again

303(5 votes)

- for home schoolers like me why is there a line in the seven?(2 votes)
- The line through the seven is a way that Sal differentiates 7 from other numbers. You do not need to write a line through your sevens. For instance, Z and 2 look a lot alike, therefore I write a line through my Z's to differentiate them from my 2's. Doing so helps me to avoid confusion and mistakes while doing my problems.(3 votes)

- Why did you put () around the bottom number thats expanded(2 votes)
- The entirety of the number 172 is being subtracted, so the parentheses signals that the subtraction is distributed to every part of the 172. Without the parentheses, Sal would not be subtracting the whole 172, but would be subtracting just 100 and then adding 72.(2 votes)

- I understand the metod, however I need help with this example: 5000-2999. Using this method the result is 2101.(2 votes)
- I'll try to work through this for you, but unfortunately this isn't rendered in a fixed width font so working my be a little mucky. Basically you need to borrow all away from the thousands back to the ones to get. 4 9 9 10 (4000 + 900 + 90 + 10 = 5000)

(sub)

5000

2999

=>

borrow 1 x 1000, then again 1x100, then again 1x10; finally add the 10 to the ones column to get:

4 9 9 10

2 9 9 9

------------

2 0 0 1.

Add add it back up to check:

2999

2001

--------

5000(2 votes)

- is regrouping/borrowing the same as carrying?(1 vote)
- They're similar operations, it's just a matter of the direction. With carrying, you're moving 10 ones (or 10 tens, 10 hundreds, etc) up to a higher place in order to make sure we can write the number with only single digits in each place. With borrowing, you are moving 10 to a lower place in order to make it possible to easily subtract the digits in that place. So they come from the same idea - both are rearranging how we represent a number, but for slightly different purposes.(3 votes)

## Video transcript

I've written the same
subtraction problem twice. Here we see we're
subtracting 172 from 629. And all I did here is I
expanded out the numbers. I wrote 629 as 600 plus 20
plus 9, and I rewrote 172, the one is 100. So that's there. This is 7/10. It's in the tens
place, so it's 70. And then the 2 is 2 ones,
so it just represents 2. And we'll see why this
is useful in a second. So let's just start
subtracting, and we'll start with the ones place. So we have 9 minus 2. Well, that's clearly just 7. And over here we could
also say, well, 9 minus 2, we have the
subtraction out front. That is going to be 7. Pretty straightforward. But then something
interesting happens when we get to the tens place. We're going to try to
subtract 2 minus 7, or we're going to try
to subtract 7 from 2. And we haven't learned
yet how to do things like negative numbers, which
we'll learn in the future, so we have a problem. How do you subtract a larger
number from a smaller number? Well, luckily we have
something in our toolkit called regrouping, sometimes
called borrowing. And that's why this is valuable. When we're trying to
subtract a 7 from a 2, we're really trying to
subtract this 70 from this 20. Well, we can't subtract
the 70 from the 20, but we have other
value in the number. We have value in
the hundreds place. So why don't we take 100 from
the 600, so that becomes 500, and give that 100
to the tens place? If we give that 100 to the tens
place, what is 100 plus 20? Well, it's going to be 120. So all I did, I didn't
change the value of 629. I took 100 from
the hundreds place and I gave it to the tens place. Notice 500 plus 120
plus 9 is still 629. We haven't changed the value. So how would we do
that right over here? Well, if we take 100
from the hundreds place, this 600 becomes
a 5, 500, and we give that hundred
to the tens place, it's going to be 10 hundreds. So this will now become a 12. This will now become a 12. But notice, this 12 in the
tens place represents 12 tens, or 120. So this is just another
way of representing what we've done here. There's no magic here. This is often called borrowing,
where you say hey, I took a 1 from the 6, and I
gave it to the 2. But wait, why did
this 2 become a 12? Why was I able to add 10? Well, you've added
10 tens, or 100. You took 100 from here, so
600 became 500, and then 20 became 120. But now we're ready to subtract. 12 tens minus 7 tens is 5 tens. Or you could say
120 minus 70 is 50. And then finally, you
have the hundreds place. 5 minus 1 is equal to 4, but
that's really 500 minus 100 is equal to 400. 500 minus 100 is equal to 400. And so you get 457, which
is the same thing as 400 plus 50 plus 7.