Introduction to adding decimals tenths

In this video, we're going to introduce ourselves to the idea of adding decimals, and I encourage you, as we work through these problems, to keep pausing the video and seeing if you can think about it on your own before we work through it together. We're going to build up slowly, and in future videos, we're going to find out faster ways of doing it. But the way we're learning it in this video and the next few is to really make sure we understand what is happening.

So, let's say we wanted to add 0.1 to 0.8, or you could say we're adding one tenth to 8/10. Pause this video and see if you can figure that out. Well, there are a couple of ways to think about it. You could say, "Hey, look! 0.1, that is 1/10th, and 0.8, that is 8/10." So if I have one of something, and I add eight more of that something, so I have one tenth, and I'm going to add eight more tenths, well, I'm going to end up with nine of that something. In this case, we're talking about tenths, so that is going to be equal to 9/10.

That's one way to think about it. Another way we could think about it visually, so let's say we take a whole, and we were to divide it into tenths, which we have right over here. If we say this whole square as a whole, we've divided it into ten equal sections. So, each of these white bars you can view as a tenth. We have one tenth, so let me fill that in. So 1/10. Whoops! That's not what I wanted to do. We have one tenth right over there, and to that, we want to add 8/10.

So, 1, 2, 3, 4, 5, 6, 7, 8. And so how many total tenths do I now have? Well, let's just count them up. We have this one here: 1, 2, 3, 4, 5, 6, 7, 8. These are really saying the same thing. All of this together is going to be… let me do that a little neater. All of this together is going to be 9/10.

Now, in either case, how do we write 9/10 in decimal form? Well, we go to the tenths place, which is one space on the right side of the decimal. We say, "Hey, we have nine tenths." This is the tenth space right over here, so that's just saying we have nine tenths. We have nine, we have nine of these tenths right over here.

So, let's keep building. Let's try to do… let's do another example. So, let's say that we… let me clear all of this out. So, let's say that we want to add… do these with different colors. So, let's say we want to add… I have trouble. It's my pen isn't working. Let's see… let's say we want to add… my pen is… oh, here we go.

Let's say we want to add three tenths, and to that we want to add 9/10. What is that going to be? Well, you could use the same idea. If you say this is 3/10, and this is 9/10, plus 9/10, we have three of something, and if I add nine of them, well, that's going to be 12. 3 + 9 is 12, so we could say this is going to be equal to 12/10.

Now, this one might be a little bit counterintuitive: 12/10, what does that mean? Well, one way to think about it, this is 10/10 plus 2/10. And what are 10/10s? Well, if I have 10/10s, this right over here is one whole, so that is going to be one. So we have one and 2/10.

So how do we write one and 2/10? Well, we could write it as in the one's place, we just write a one, and in the tenths place, we write our 2/10. So you could say it's equal to 1.2, or you could say it's equal to 1 and 2/10, which is the same thing as 12/10.

Now, if we want to see that visually, let's get our diagram out again. So actually, I'm going to put two of these here: one and then a second one. And we want to add… so let's start with the 3/10.

So let me color these in really fast. So use that light blue color, so that is 1/10. This is 2/10. Just coloring them in really fast, and this is 3/10. And then to that we're going to add 9/10. So to that, we're going to add: 1, 2, 3… I'm not coloring them in fully—4, but you get the idea—5, almost there—6. I need to color faster—7, 8, 9.

So there you have it. I have added 9/10. You notice I've colored in nine—I've colored in yellow—nine of the tenths. And before, I had three of the tenths colored in. And when you add them all together, what happens? Well, the 3/10 plus the 7/10 right over here, they made a hole. So this right over here is our one, and then we also have another 2/10 left over. And so this is where this is our 0.2 or 2/10. So it's going to be 1 + 2/10, which is 1.2.

So hopefully, this gives you a good sense of how we think about adding decimals. And even though in the future we're going to figure out faster ways of doing it or more systematic ways of doing it, this is still the way that— that I still do it in my head. If someone walks up to me on the street and says, "Hey, add 0.3 to 0.9," that's how I think about it.