Subtracting in your head (no regrouping)
At about 103s Sal says '11 minus 8 is 13' (should be 3; he means 71 tens - 8 tens = 63 tens). A note flags this.
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Sal shows a mental way to subtract that starts from the hundreds place and moves right without regrouping: subtract the hundreds, then the tens, then the ones. He uses it for 301 - 169 = 132, 913 - 286 = 627 and 721 - 88 = 633, and stresses that any method is fine if you understand what the digits mean.
You'll be able to
- subtract 3-digit numbers in my head by taking away hundreds, then tens, then ones.
- explain that the digits I subtract stand for hundreds, tens or ones.
Key words
- regrouping
- Trading a ten for 10 ones (or a hundred for 10 tens) so you can subtract in each place.
- place value
- The value of a digit depends on its place: hundreds, tens or ones.
Transcript
What I want to do in this video is show you a way of subtracting numbers that is different than the regrouping technique. And this is closer to what I actually do in my head. And this might not be what you see in school, so be careful while you're looking at this.
Some people might not fully approve of what I'm about to show you. But the idea, the reason why I'm showing you this is to understand that there's not just one way to do things. As long as you understand the underlying principles, what these numbers represent, and you do things that make sense, you should be OK.
And what's neat about this technique is that we don't have to regroup. We're just going to start with the hundreds place and keep on moving. So, for example, if I think of 301, I first want to subtract 100. So 300 minus 100 is going to get me to 200. Now I need to subtract 60.
And so I can think about what is 20-- two, zero-- minus 6. So this is essentially saying what is 200 minus 60? Well, 20 minus 6 is 14. So I just subtract, and now I'm left with 14. And so now the problem has resulted in 141 minus 9. So I really just have to think about what-- well, or I could do what 141 minus 9 is.
Well, 141, it's a little bit more mental computation than you might be used to. But 141 minus 9 is going to be 132. So we are left with 132. Let's do this one, same technique. And I encourage you to pause the video and try it yourself, this same technique. Well, 9 minus 2, it's really 900 minus 200.
You're going to be left with 700. Then 71 minus 8, let's see, 11 minus 8 is 13. So you're going to be left with 63. And now we have to subtract 633 minus 6. 13 minus 6 is 7. So it's going be 627. And once again, try to pause the video and do it on your own. So I don't have any hundreds to subtract, so I can immediately go to 72 minus 8, which is really 720 minus 80.
But let's just think in terms of 72 minus 8. Well, 12 minus 8 is 4, so 72 minus 8 is going to be 64. So now this is the same thing as 641 minus 8. Well, 41 minus 8 is going to be 33. I have to do a little bit of mental computation here. So this will result in 633.
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