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Lesson 4: Adding and subtracting within 1,000

# 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?
• 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.
• Do you subtract 3 digit numbers like you add 3 digit numbers?
• no subtraction is slightly diffrence when regrooping
• how is it possible to subtract with negatives?
• Subtracting a negative number is the same thing as adding its opposite. The opposite of -6, for example, is 6. So 5 minus negative 6 is the same thing as 5 plus 6.
• When I learn how to use negative numbers, would it be strange for me to not regroup, but to allow the ones place to go negative?
• Yes and no. If you were doing 86 - 19, you would not want to write the answer as 7-3 or 7negative3.
However, because 80 - 10 = 70 and 6 - 9 = -3, you can think of the answer as 3 less than 70, which would be 67.

Have a blessed, wonderful day!
• what if there is 0 in the middle?
• You go on to the next best digit. Here's an example:
406
-137
__
To start, you would subtract the 7 in 137 from the 6 in 406. Since 7 is bigger than 6, you would have to "borrow" 1 from the 0, but you can't. Instead, you would move on to the 4 in 406, take a 1 from it and "give" it to the 0, so it's now 10, then you would take 1 from the 10, so it's now 9, and add it to the 6, so it's now 16. Now it looks like this:

39 (1)6
-137
__
Now you go on about how you would normally do it, and there you go! The answer is 269!
• Isn't addition used in a way to check you answer in subtraction. How do you do it?
• Its quite simple really, you add the answer from the subtraction problems to one of the numbers in the subtraction problem, and if the number equals the other number, then u did it right, for an example, 20 - 15 = 5, so you do 5+15 = 20 if this is correct then your answer is correct
• Thank you, but I have one more question... If you need to regroup 4 zeros and the top number is 1 how would you get the answer if there is not enough tens or hundreds to go around?
• You can just keep regrouping! Here's an example:
10,000 = 10,000 + 000 + 00 + 0
10,000 = 9,000 + 1,000 + 00 + 0
10,000 = 9,000 + 900 + 100 + 0
10,000 = 9,000 + 900 + 90 + 10

so if you we're subtracting 9,897 from 10,000 you could do the following:

10,000 = 9,000 + 900 + 90 + 10
9,897 = 9,000 + 800 + 90 +7
giving you: (9,000 - 9,000) + (900 - 800) + (90-90) + (10-7)
which equals: 0,000 + 100 + 00 + 3
finally giving you the number: 103

In this way, you can never run out of places (as long as your top number is larger than you're bottom number!)
• Could we use the standard method tu subtract a multi-digit number that is larger than the number we are subtracting from? (e.g. 104-137)
• You could find 137-104 using the standard method (or another valid method). Then attach a negative sign in front of your answer.
• what happens if you don't have enough to subtract from the number like 96-100
• You go into negatives. 96 - 100 = -4, because 100 is 4 more than 96. If you don't have enough to subtract a number from a lower one, the answer is in negatives.
• Would you be able to subtract odd fractions with different denominators?
• No.You need the denominators to be the same size in order to subtract fractions..

## 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.