Methods for subracting 3 digit numbers

Hello! In this video, we're going to think about techniques for subtracting three-digit numbers. So, let's say we wanted to figure out what 357 minus 156 is. Pause this video and see if you can somehow figure this out. You don't have to be able to, because we're going to work through it together, but it doesn't hurt to try a little bit.

All right, now let's do it together. One way to think about it is, what if we were to break up the 156 into its different place values? We could view it as 100, 50, and 6. So then, this could be rewritten as 357 minus 100, minus 100, minus 50 (that's 5 tens right there), and then minus 6. Now, does this help us? Pause this video and see if you can figure out what this would be.

Well, many of you probably said, "All right, if I have 357 and I take away 100, well then I'm going to be left with 257." Then, if I take 50 away from that—250 away from 205; well, I have five tens here and I'm going to take away 5 tens. So, I'm going to be left with 0 tens, and I'm going to be left with 207.

Then, if I took 207 and I subtracted 6 from that (so 207 minus 6), that of course is going to be equal to 201. I just took away those six ones, and I had seven ones on top of the two hundreds before to get us to 201. So, this is one very good technique for being able to subtract numbers.

And it doesn't just apply to three-digit numbers; you can do this with many-digit numbers. But there's other things that you could be doing. You could, for example, try to adjust the numbers to make the subtraction easier. For example, you could say, "Hey, wouldn't it be nice if instead of subtracting 156, I only had to subtract 150?"

There is a way that you could do that. As long as whatever you add or subtract to one of these numbers, you do to the other, then the difference will be the same. So, there is a situation where you subtract 6 from both of these numbers before you try to find the difference.

Let me write this out. So, let's say you wanted to subtract 6 from both. What would this be? Well, 357 minus 6—well, we're just going to take six ones away from the seven ones here, so it’s going to be 351.

Now, minus 156 minus 6—well, that just gets us to 150. And this might be, for many of you, a little bit more straightforward to compute. You might realize, "All right, if I have three hundreds and I take away one of those hundreds, I get two hundreds." If I have five tens and if I take away those five tens, I'm going to be left with zero tens.

If I have one one, and if I take away no ones, I'm still going to have one one. Or, you could say, "Look, 300 minus 100 is 200, 51 minus 50 is just one." So, that was pretty helpful.

Another technique is to, instead of going 150, you might say, "Well, what if I wanted to subtract 160?" Well, in that situation, you could add 4 to both of these numbers. Add four to both—what would happen then? Pause this video and try to figure that out.

Well, what's 357 plus 4? 357 plus 3 gets us to 360, plus another one gets us to 361. And if I add 4 to 156, that is 160. And since I added 4 to both, I added the same amount to both, the difference is going to be the same.

So, if you look through this: 300 minus 100 is 200; it’s left. Then, 61 minus 60 that gets us to—gets us to 201. What I just kind of did in my head, if I wanted to write it out, we could say this is the same thing as 361 minus 100 minus 100.

I could break it out completely like I did up here, or I could break it out partially. I could just break out the hundreds place and then break out the 60. So, minus 60—I guess you could view that as I broke out the tens and I didn't write the ones.

But you can see 361 minus 100 would be 261, and then you take 60 away from that, once again, you would be left with 201. So, the big takeaway here is there's many different ways to approach subtraction with however many digits you have.

This just gives you a glimpse of different methods, and some will be more convenient in different situations, depending on what numbers you are dealing with.