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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?(73 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.(76 votes)

- If it was 29-72,how would you borrow?(7 votes)
- Actually, this get's more complex in numbers. There are such numbers that are NEGATIVE. These are numbers below 0. If it is -12 degrees in winter, it is VERY cold! You can watch Sal's videos on negative numbers to learn more.(4 votes)

- I so confused! can you subtract negitave numbers!(13 votes)
- You can subtract negative numbers. But, to subtract negative numbers, you have to learn a few special rules.

When subtracting a negative number, the negative number being subtracted becomes positive.

4 - (-)3 (Because we are subtracting a negative number -3, the number becomes +3.)

4 + 3 = 7

When subtracting a positive number from a negative number, you do something similar to adding.

-4 - 3 = -7 (Instead of ending up with -1, I ended up with -7. However, -7 is actually worth less than -1.)(11 votes)

- This is outstanding how do you make these videos for my students(8 votes)
- can you make these easier?(6 votes)
- Why do you need a second video for regrouping(4 votes)
- This is just practice to help. You don't necessary "need" any video if you're confident with her math.

But this video can also strengthen your regrouping skills and your subtracting 3-digit numbers.

Later, this will help you in math, eventually. =)(4 votes)

- at1:27, do you have to take away 100? or can you take away just 1?(5 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!(1 vote)

- Are you a Mathematician(5 votes)
- Is it not when you borrow instead of 20 when you borrow a hundred it becomes 30 because that

is what my teacher says but I don't know?(4 votes) - Everyone will respet that they made this =}(4 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.