Worked example: Subtracting 3-digit numbers (regrouping from 0)

Let's try to subtract 164 from 301, and I encourage you to pause this video and try it on your own first. So let's go place by place, and we can realize where we have to do some borrowing or regrouping. So in the ones place, we have an issue. 4 is larger than 1. How do we subtract a larger number from a smaller number? We also an issue in the tens place. 6 is larger than 0. How do we subtract 6 from 0? So the answer that might be jumping into your head is oh, we've got to do some borrowing or some regrouping. But then you might be facing another problem. You'd say, OK, well, let's try to borrow from the tens place here. So we have a 1. If we could borrow 10 from the tens place, it could be 11. But there's nothing here in the tens place. There's nothing to borrow, so what do we do? So the way I would tackle it is first borrow for the tens place. So we have nothing here, so let's regroup 100 from the hundreds place. So that's equivalent to borrowing a 1 from the hundreds place. So that's now a 2. And now in the tens place, instead of a 0, we are going to have a 10. Now, let's make sure that this still makes sense. This is 200 plus 10 tens. 10 tens is 100, plus 1. 200 plus 100 plus 1 is still 301. So this still makes sense. Now, the reason why this is valuable is now we have something to regroup from the tens place. If we take one of these tens, so now we're left with 9 tens, and we give it to the ones place, so you give 10 plus 1, you're going to be left with 11. And we can verify that we still haven't changed the value of the actual number. 200 plus 90 is 290, plus 11 is still 301. And what was neat about this is now up here, all of these numbers are larger than the corresponding number in the same place. So we're ready to subtract. 11 minus 4 is-- let's see, 10 minus 3 is 7, so 11 minus 4 is 7. 9 minus 6 is 3, and 2 minus 1 is 1. So we are left with 137.