Adding decimals with ones and tenths parts

Last video, we got a little bit of practice adding decimals that involved tths. Now let's do slightly more complicated examples.

So let's say we want to add four to 5.7, or we could read the second number as 5 and 7/10. Pause this video and see if you can do this.

So the way that my brain tries to tackle this is I try to separate the whole numbers from the tenths. You can view this as being the same thing as 4 + 5 + 7/10. All I did here is I broke up the 5 and 7/10 into 5 + 7/10. The reason why my brain likes to do that is because I can then say, "Okay, 4 + 5, that's just going to be equal to 9."

Then I just have to add the 7/10, so it's going to be 9 and 7/10. I can rewrite this as going to be equal to 9 and 7/10. And 9 and 7/10 I could write as 9.7. Even though in future videos we're going to learn other ways of adding decimals, especially larger, more complicated decimals, this is still how my brain adds 4 + 5.7, especially if I need to do it in my head.

I say, "Okay, 4 + 5 is nine, and then I have that 7/10," so it's going to be 9 and 7/10 or 9.7.

Now let's do another example where both numbers involve a decimal. So let's say I want to add 6.3 to 7.4. So, 6.3 + 7.4. Once again, pause this video and try to work through it on your own.

Well, my brain does it the same way. I break up the whole numbers and the decimals. And once again, there are many different ways of adding decimals, but this is just one way that seems to work, especially for decimals like this.

So we could view this as 6 and 3/10. I'm breaking up the 6.3, the 6 and 3/10 into 6 + 3/10, plus 7 and 4/10, which is 7 + 4/10. Then, you can view this as 6 + 7, plus 3/10, plus 4/10.

So if you add the ones here, you have 6 ones and 7 ones. That's going to be equal to 13. And then 3/10 and 4/10, well if you have three of something and then you add four of that, that's going to be 7/10.

We would write 7/10 as 0.7, 7 in the tenth place. And then what's 13 + 7/10? Well, that is going to be 13. This is going to be equal to 13.7.

13.7, and we are done. Let me do one more example that will get a little bit more involved. So let me delete all of these.

So let's say I wanted to add 6.3 to, and I'm going to add that to 2.9. Pause the video and see if you can figure this out.

Well, let's do the same thing. This is going to be 6 and 3/10, so 6 + 3/10, plus 2 + 9/10. Or you could view this as 6 + 2, so I'll put all my ones together: 6 + 2, and then I'll put my tenths together: plus 3/10 + 9/10.

And so the 6 + 2 is pretty straightforward. That is going to be equal to 8. And now what's 3/10 + 9/10? This is going to get a little bit interesting.

3/10 + 9/10, and I could write it out. I could say this is 3/10, this is 9/10. Well, 3/10 + 9/10 is equal to 12/10. This is going to be 12/10. But how do we write 12/10 as a number?

Well, 12/10 is the same thing as 10/10 plus 2/10. The reason why I broke it up this way is that 10/10 is one whole. So this is going to be equal to one.

So when you add these two together, it's 12/10, which is the same thing as 1 and 2/10. So 1 + 2/10. Or, well, let me just write it that way.

So this I can rewrite as plus 1 plus 2/10. And then I think you see where this is going. I could add the 8 and the 1, and I get 9 and 2/10. So 9 and 2/10, so it's going to be 9.2.

Now, the reason why this one was a little bit more interesting is I added the ones. I got 6 + 2 is 8, but then when I added the tenths, I got something that was more than a whole. I got 12/10, which is 1 and 2/10.

And so I added one more whole to the 8 to get 9, and then I had those 2/10 left over. This is really good to understand because in the future, when you're adding decimals, you'll be doing stuff like carrying from one place to another.

This is essentially what we did when we added the 3/10 plus the 9/10. We got 12/10, and so we added an extra whole, and then we had the leftover 2/10. Hopefully, that makes some sense.