Introduction to adding decimals: tenths

- [Instructor] 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. Now we're going to build up slowly, and in future videos we're gonna find out faster ways of doing it. But the way we're learning it in this video in the next view 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 1/10 to 8/10. Pause this video and see if you can figure that out. Well there's a couple of ways to think about it. You could say, hey look 0.1, that is 1/10, and 0.8, that is 8/10. And so if I have one of something and I add eight more of that something, so I have 1/10, and I'm gonna add eight more tenths, well I'm gonna 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. So if we say this whole square is a whole, we divide it into 10 equal sections. So each of these white bars you can view as a tenth. So we have 1/10, so let me fill that in. So 1/10, woops that's not what I wanted to do. We have 1/10 right over there. And to that we want to add 8/10. So one, two, three, four, five, six, seven, eight. And so how many total tenths do I now have? Well let's just count 'em up. We have this one here. One, two, three, four, five, six, seven, eight, nine. 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 tenth's place, which is one space on the right side of the decimal. We say hey we have 9/10. This is the tenth's space right over here. So that's just saying we have 9/10. We have nine of these tenths right over here. So let's keep building. 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 because 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 3/10, 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, well if I have three of something and I add nine of them, well that's going to be 12. Three plus nine 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 10/10? Well if I have 10/10, 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 then in the tenth's place, we write our 2/10. So you could say it's equal to 1.2, or you could say it's equal to one 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 gonna put two of these here. So 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. Use that light blue color. That is 1/10. This is 2/10. Just coloring 'em in really fast. And this is 3/10. And then to that we're gonna add 9/10. So to that we're gonna add one, two, three. I'm not coloring them in fully. Four, you get the idea. Five, almost there. Six. I need to color faster. Seven. Seven. Eight. Nine. 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 'em all together, what happens? Well the 3/10 plus the 7/10 right over here, they made a whole. 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 gonna be one plus 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 gonna figure out faster ways of doing it, or more systematic ways of doing it, this is still the way 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.