Andding decimals with hundredths

Let's get some practice adding numbers that involve hundreds. So, pause this video and see if you can add these two numbers. See what you get.

Alright, now let's work through this together. Now, there's many different ways to add decimals, and you'll learn more systematic, faster ways of doing it in the future. But I'll show you the few ways that my brain might think about it.

So, one way to think about it is you could say that this is 53 hundredths. You could read this as either five tens and three hundredths or 53 hundredths. So you could say this is 53 hundredths, and to that you're going to add 4242 hundredths.

And so, if I have 53 of something and I'm going to add 42 of that same something to it, what am I going to get? Well, what's 53 plus 42? Well, in my head I say, well, 50 plus 40 is ninety, and three plus two is five. So, it's going to be 9595 hundredths.

And if I wanted to write that as a pure number, I would write that as zero point nine five, which I could read as ninety-five hundredths or nine tens and five hundredths.

Now, the other way we could have thought about it is we could have broken these numbers up. We could have said that this first number is five tenths plus three hundredths, and then the second number we could have rewritten as four tenths plus two hundredths.

We make sure my decimals plus two hundredths, and then we could have separately added the tenths and the hundredths. So, you have five tenths plus four tenths. So, five tenths plus four tenths, and then you could separately add three hundredths plus two hundredths.

So, three hundredths and a little trouble saying that plus two hundredths. And so, what do I get? Well, five tenths and four tenths, we've done this in previous videos. If I have five of something, and I had four of it, that's going to be 9/10, so it's going to be 9/10, and then the three hundredths plus two hundredths, that's going to be five hundredths.

So, plus 0.05, and then 9/10 plus five hundredths is going to be—and I'm saying hundredths kind of strange—is going to be nine tenths and five hundredths, which you could also say as 95 hundredths.

Let's do another example, one that's a little bit more involved. So, let's say I want to add 68 hundredths and 233 hundredths. What is this going to be? And like always, pause the video and see if you can figure it out on your own.

Well, there's a couple of ways to think about it. One way we could split up the tenths and the hundredths. Actually, let's do it that way. So, if we could rewrite this first number as six tenths plus eight hundredths, and the second number we could write as three tenths plus three hundredths.

Let me do that in that orange color. So, three tenths plus three hundredths. And so, if I add this, so if I add the six tenths and the three tenths, so let me just do that, I'm going to write every step here. If you're doing this in your head, if you're doing this on paper, you wouldn't necessarily write every step here.

So, those are the tenths, and then separately I'm going to add the hundredths. So, plus eight hundredths plus three hundredths. So, six tenths plus three tenths, we've done this in previous videos, that's hopefully pretty straightforward by this point. If it's not, I encourage you to review some of those earlier videos, so that's going to be nine tenths.

Now, what's this going to be? Well, you could view this as eight hundred plus three hundred. So, I have eight of something and I add three of something, that's going to get eleven of that something, 1100.

So, how do we write 1100 as a decimal? Well, one way to write it—you could just view this as 0.1. This is 1100; many people would read this as 1100. Or you could view this as equaling ten hundredths plus one hundred hundred, and ten hundredths right over here is one tenth.

So, you could view this as one tenth and one hundred. And when you add everything together, what you get? Well, you get nine tenths plus 1/10 plus 100.

Well, now this is going to get interesting still. So, let's see, let me rewrite this. So, it's going to be nine tenths, and this one, let me write it plus 1/10 plus that one hundredth leftover. So, plus that one hundred.

So, what is this going to be? So, 9/10 and one tenth. That's going to be nine tenths and one tenth is going to be ten tenths, which is the same thing as one whole. So this is just going to be equal to one, so it's going to be one plus one hundredth.

So, it's going to be one and one hundred, and we are done. As I keep mentioning, in future videos we're going to learn maybe faster ways of doing this—maybe ways that you might be able to do a little bit more automatically.

But it's really important to think about what we just went here and how we were able to think, okay, 1100 is the same thing as 1/10 and one hundredths. And then taking that tenth, and then adding it to the nine tenths that we had and said, hey, that's a hole.

In the future, we're going to be doing things like carrying with decimals, but this is essentially what is happening underneath. Conceptually, it's really important to get a sense of that before you learn the faster methods.