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## Arithmetic (all content)

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

Lesson 17: Subtraction with regrouping within 1000- Worked example: Subtracting 3-digit numbers (regrouping)
- Worked example: Subtracting 3-digit numbers (regrouping twice)
- Worked example: Subtracting 3-digit numbers (regrouping from 0)
- Subtract within 1,000 using place value blocks
- Subtract on a number line
- Subtract within 1000
- Subtracting in your head (no regrouping)

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

Learn to use regrouping (borrowing) and place value to subtract 971-659. Created by Sal Khan.

## Want to join the conversation?

- Is there another way to subtract?(12 votes)
- Yes. There is a system called Vedic math with a variety of tricks for subtraction, multiplication, division, and even algebra. If you google Vedic math, you might find some tricks that you like!

Here’s a Vedic method of subtraction.

For each column where we subtract a larger digit from a smaller digit, we put down the difference but put a bar on top of the digit (for example, subtracting 5-7 gives 2bar). Think of bar digits as “negative” digits.

Then we need to convert our answer to a normal number without bar digits.

For each group of bar digits, we treat any group of 0’s immediately to the left of the group as bar digits as well.

Then we use the rule “subtract all from 9 except last from 10” within each group of bar digits, and subtract 1 from the normal (nonzero) digit immediately to the left of the group.

Example: 5234197-1439428

From left to right:

5-1=4, 2-4=2bar, 3-3=0, 4-9=5bar, 1-4=3bar, 9-2=7, 7-8=1bar.

So we have

4 2bar 0 5bar 3bar 7 1bar.

Place a bar on the 0 because it’s immediately to the left of a group of bar digits. Now we have

4 2bar 0bar 5bar 3bar 7 1bar.

We now have two groups of bar digits. Subtracting all from 9 except last from 10 within each group and subtracting 1 from the digit just left of each group gives final answer 3794769.(9 votes)

- can you do the problem 267,442 - 209,650(16 votes)
- well yes and if you don't know how to do it then do it verticle way!(1 vote)

- can u add 1000 in a negative?(7 votes)
- yes, but you would really just be doing subtraction

for example 1,001 + -1,000 = 1(6 votes)

- how do you make a website(6 votes)
- Hey! You can actually learn how to code websites and design them with code right here on khan academy! https://www.khanacademy.org/computing/computer-programming/html-css?ref=resume_learning , start coding :)(5 votes)

- Do you subtract 3 digit numbers like you add 3 digit numbers?(4 votes)
- no subtraction is slightly diffrence when regrooping(5 votes)

- can you regroup with muliplying(4 votes)
- Yes you can regroup with multiplying. You just do it differently.(4 votes)

- why would you subtract the bottom numbers arn't they supose to be subtract that same way as the top?(3 votes)
- how do yall like do this stuff(2 votes)
- Not everyone likes it, but we just have to do it when we go to school and I guess it's better to understand it.(2 votes)

- can you subtract add muteply(1 vote)
- What? Can you explain this in a way that makes since as what you have now looks like gibberish.(1 vote)

- I got confused about the bottom half, why couldn't you just add the addition to the top and bottom, and then just add the subtraction sign . It's almost like seeing two different math problems, so I'm pretty confused about that. Any help on why you did that would be great thanks?(1 vote)
- If you are subtracting a positive number from a negative number, you could use your method too. Actually, that's easier.(3 votes)

## Video transcript

Let's try to subtract
659 from 971. And as soon as you start trying
to do it, you face a problem. You go to the ones
place, and you say, how am I going to
subtract a 9 from a 1? And the answer lies in
regrouping, taking value from one of the other
places here and giving it to the ones place. And to understand that
a little bit better, let me rewrite
these two numbers. Let me expand it out. So this 9 is in the hundreds
place, so it represents 900. The 7 is in the tens place,
so it represents 7 tens. And then, this 1 is in the ones
place, so it just represents 1. And then down here,
this 6 represents 600. This 5 represents 5 tens, or 50. And then, this
9-- well, it still just represents 9 ones, or 9. And we're subtracting this. We're subtracting
600 plus 50 plus 9. Or another way of thinking
about it, we're subtracting 600, we're subtracting 50,
we are subtracting 9. So let's work it out over here. So this is the
exact same problem, just written a little
bit differently. And we still have
the same issue. How do we subtract a larger
number from a smaller number? And the solution lies
in trying to take value from one of the other places. And the easiest place to go
is-- look, we've got 70 here. Why don't we take 10 from here,
and we'll be left with 60, and give that 10
to the ones place. So if you add 10 to
1, what do we have? Well, then we're
going to have 11. Notice, I have not changed
the value of the number. 971 is the same thing
as 900 plus 60 plus 11. It's still 971. And now we can
actually subtract. 11 minus 9 is 2. 60 minus 50 is 10. And 900 minus 600 is 300. So this subtraction should
result in 300 plus 10 plus 2, which is 312. Now, let's do the
exact same thing here, but we're going to do it
without expanding it out. So same issue-- how do
we subtract a 9 from a 1? Well, let's take a 10
from the tens place. We're going to regroup. So we're going to get
rid of one of these tens, so we're only going to have 6
tens left in the tens place. And we're going to give
that 10 to the ones place. So 10 plus 1 is 11. Now we are ready to subtract. 11 minus 9 is 2. 6 minus 5 is 1. 9 minus 6 is 3. We get-- let me do
that same color-- 312.