Strategies for subtracting more complex decimals with tenths

Some more examples subtracting decimals. So let's say we want to figure out what 2 - 1.2 is. Pause this video and see if you can calculate this.

So, there's multiple ways to tackle this. One way is you could say, look, this is the same thing as 2 - 1, 2 - 1 - 2/10. This is 2 - 1 and 2/10. So you are subtracting 1, and we're subtracting 2/10. Now, 2 - 1 is pretty straightforward to compute; 2 - 1 is going to be 1.

Then we need to subtract 2/10 from that. So, one is the same thing as 10/10. We could say this is 10/10. Write it this way: 10/10. And we're going to subtract 2/10. What is that going to give us?

Well, that's going to give us—if we have 10/10 and we take away 2/10—that's going to give us 8/10. Let me write it down here: 8/10, which is the same thing as 0.8 or 8/10. One way to think about this is if you're subtracting 0.2 from one.

If you view this one as a 1.0 instead of expressing this as 1 and 0/10, we are thinking about this as 0 ones and 10/10. When you think about it as 0 ones and 10/10, well, 10/10 minus 2/10—it's easier to then think about, well, 10 of something minus two of something is going to be eight of something. It’s going to be 8/10.

Now we can also visualize this on a number line. So, for example, let me draw a number line here: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9—that's 1, 1, 2, 3, 4, 5, 6, 7, 8, 9. That is two, so we're starting at two, and we're subtracting 1 and 2/10.

So one way to think about it is we first subtracted one. We first subtracted one, and then we subtracted 2/10. That got us to the point 8/10 on the number line. Another way to think about this—and the whole point here is to see multiple strategies and for you to think about what strategy you like the most and to realize they all get you to the same place, if you're thinking about it in a reasonable way—is you could view this: What's the difference between two and 1.2?

So 1.2 sits here on the number line. So what's the difference between two and 1 and 2/10? Another way to think about it is how many tenths do you have to add to one and 2/10 to get to two? Well, if you've already got 2/10, you need to add another 8/10 to get to the next whole.

So, you have to add 8/10, or you have to add 0.8. So, the difference between 2 and 1.2 is equal to 0.8. Let's do a few more examples that get a little bit more involved.

So let's say we want to calculate what 3.8 minus 1.5 is. Pause the video and see if you can calculate this. Well, just like before, we could view this as 3 - 1. So we're subtracting the ones plus 8/10 - 5/10. Notice we have 3 and 8/10 minus 1 and 5/10.

And so now we can figure out, okay, 3 - 1, that's just going to be equal to 2. And then 8/10 minus 5/10—well, that is 3/10. So this is going to be 2 and 3/10, which of course we could write as 2.3. That seemed pretty straightforward.

Let's do one that's a little bit more involved. Let's say we want to calculate 4 and 5/10 or 4.5 minus 2 and 8/10 or 2.8. Pause the video and see if you can calculate this.

So you might want to do the exact same thing. You might say, okay, well, this is the same thing—let's think about the ones—this is 4 - 2 plus 5/10 - 8/10. 4 and 5/10 minus 2 and 8/10—that's exactly what we have up here.

You'd say, all right, 4 - 2, that is 2, but then you get to 5/10 minus 8/10, and there's multiple ways to tackle this. But you might say, well, how do I take away 8/10 if I've only got 5/10 here?

And there's a bunch of strategies that you could think about. You could say, hey, what if I can get some more 10ths here? So this is 5/10 minus 8/10. What if I could get some more 10ths here? And the best way I could think of it is like: what if I were to break up these ones because one is 10/10?

So, I could view a two as 1 + 1, or I could view this as 1 + 10/10. So if you view a two as 1 and 10/10, you can then just add those; you can then figure out what is 10/10 + 5/10 - 8/10.

What is that going to be? Well, this is a little bit more straightforward. 10/10 + 5/10 is going to be 15/10. And if you have 15/10, and you take away 8/10, you're going to be left with 7/10.

So, this gets us to 1 + 7/10. So all of this, when you compute it, that is 7/10, which I could write as 0.7, which is equal to 1 and 7/10. Now, there's other strategies that you could do here.

One strategy—this is the one that I typically do in my head—is I write this as 4.5 - 2.5 - 0.3 or 4 and 5/10 - 2 and 5/10 - 3/10. Now, why did I write it this way? Because I find this pretty straightforward to compute. And then, once I get that answer, I just have to take away 3/10.

So for example, well, if I have 5/10 here, and I'm taking away 5/10, those are going to knock each other out, and so I'm just going to be left with 4 - 2, which is going to be 2. And then I have to take away the 3/10.

And this is a pretty straightforward way of doing it in your head. So what's 3/10 less than 2? Well, you can visualize a number line in your head. Well, that's going to be 1 and 7/10. And if this feels strange how I got—oh, one, I wrote 1 and 7/10.

And if this seems strange how I got there that fast, just think about this: this is the same thing as 1 + 1 - 3/10, and this one right over here is the same thing as 10/10. So, 10/10 minus 3/10—that over there is going to be 7/10.

So it's going to be 1 and 7/10, which is what we got before. So, the whole point here is to appreciate there's multiple strategies for subtracting decimals—some that you can do a little bit more automatically.

But it's really good to think about what's going on in your head, and some strategies are actually better in your head than on paper, or at least easier in your head.