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 1 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 1 so it just represents 2 and we'll see why this is useful in a second so let's just start subtracting 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 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 tool kit called regrouping sometimes called borrowing and that's why this is valuable when we're trying to subtract the 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 a hundred from the 600 so that becomes 500 and give that hundred to the tens place if we give that hundred to the tens place what is a hundred plus 20 well it's going to be 100 and it's going to be 120 so all I did I didn't change the value of 629 I took a hundred from the hundreds place and I gave it to the tens place notice 500 plus 120 plus nine 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 five five hundred and we give that hundred to the tens place it's going to be ten hundreds so where this will now become a 12 this will now become a 12 but notice this 12 in the tens place represents ten so it 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 one from the six and I gave it to the tuba way why is this why did this to become a 12 why was I able to add 10 well you've added 10 tens or a hundred you took a hundred from here so 600 became 500 and then 20 became a hundred and 20 but now we're ready to subtract 12 tens minus seven tens is five tens or you could say 120 minus 70 is 50 and then finally you have the hundreds place five minus one is equal to four but that's really five hundred minus 100 is equal to four hundred five hundred minus 100 is equal to four hundred and so you get 457 which is the same thing as four hundred plus 50 plus seven