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### Course: Class 3>Unit 3

Lesson 2: Subtracting by regrouping

# 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?
• 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.
• at , do you have to take away 100? or can you take away just 1?
• 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!
• for home schoolers like me why is there a line in the seven?
• 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.
• how would do one with a zero like 800-546
• 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``
• I understand the metod, however I need help with this example: 5000-2999. Using this method the result is 2101.
• 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.

2999
2001
--------
5000
• is regrouping/borrowing the same as carrying?
• 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.
• Why did the 20 become a 12 if we are borrowing from the hundreds?
• Great question! When we borrow from the hundreds place, we're actually taking 100, which is the same as 10 tens. So when we add that to the 20 (which is 2 tens), we get 12 tens, or 120.