Subtracting 3-digit numbers (regrouping)

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.