Video: Subtracting Three-Digit Numbers: Regrouping Hundreds

You can regroup a hundred to help you solve subtraction problems. Find 712 − 460.

03:44

Video Transcript

You can regroup 100 to help you solve subtraction problems. Find 712 take away 460.

In this problem, we’re going to need to regroup 100 to help us find the answer. We’ll see why we need to do this when we get there. But to begin with, let’s subtract the ones. 712 contains two ones, and we need to subtract zero ones. Two take away zero equals two. So, our answer has two ones.

Next, we need to subtract the tens. 712 has one 10, and we need to subtract six tens. But six is larger than one. How can we take away six tens from one 10? Well, we know we definitely can subtract six tens because the number we’re subtracting from is 712. There are plenty of tens in 712 to take six tens from. It’s just that at the moment there aren’t enough tens in the tens column, so we need to regroup our number slightly so that there are enough tens in the tens column to take away six tens from.

And the way to do this is to take one of our one hundreds, we’ve got seven of those, and to regroup it into tens. Let’s just go through what this means. Here’s what one of our 100s looks like. Remember, we’ve got seven of these in 712. Now, if we take one of our 100s and regroup it into tens, we’ll have 10 tens. Both of these are worth exactly the same amount. We’ve just grouped them in a different way.

By regrouping one of our hundreds, instead of having seven hundreds, we can cross this through because we now have six hundreds. And we’ve swapped our 100 for 10 tens. So, in our tens column, we now have 11 tens. We already had one 10, and now we have an extra 10 tens. To show that we have 11 tens. We can write a one next to the one we already had. The little one we’ve written represents 10 more tens.

Now, it might look like we’ve changed the number on the top. Instead of 712, we now have six hundreds, 11 tens, and two ones. But if we work it out, we can see that six hundreds, 11 tens and two ones is exactly the same as 712. All we’ve done is regroup 100. And this will now help us to find the answer. We can now subtract six tens from our 11 tens. 11 take away six leaves us with five tens.

Finally, we can subtract the hundreds digits. And remember, we’re not subtracting 400 from 700. By regrouping 100, we now only have six hundreds in this column. 600 take away 400 leaves us with 200.

We worked through the subtraction column by column, but because we were unable to take the number of tens that we wanted to take away, we had to regroup 100 to help us to continue to work out the subtraction. 100 is the same as 10 tens. And by swapping one of our hundreds for 10 tens, we could then subtract the number of tens that we needed to. 712 take away 460 equals 252.

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