Worked example: Subtracting 3-digit numbers (regrouping)

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.