Adding decimals with ones, tenths and hundredths

Let's do some more involved examples using decimals.

So, let's say we want to add four and 22 hundredths to 61 and 37 hundredths. Like always, I encourage you to pause the video and try to figure it out on your own.

Well, the way that my brain tries to tackle it is it says, "All right, I have 4 and 22 hundredths and 61 and 37 hundredths. How about I add the 4 plus the 61?" So it's going to be 4 + 61. Then separately, let me add the 22 hundredths to the 37 hundredths.

So then I'm going to add 22 hundredths plus 37 hundredths. So, 4 + 61 is going to be equal to 65. Then, 22 hundredths + 37 hundredths, well what's 22 + 37? Let's see, 20 + 30 is 50, and then 2 + 7 is 9. So it's going to be 59 hundredths. So it's going to be 65 and 59 hundredths, which we can write as 65 and 59 hundredths.

Now, like I've mentioned in previous videos, there are many different ways of adding decimals, and in future videos, we'll learn arguably faster ways of doing it. But I want to show you multiple ways, so you get a sense of at least ways to approach it. This is the way that I do it in my head. If someone said, "Hey, something costs $61.37 and then you had to pay $4.22 in tax, how much would you have to pay in total?" This is how I would actually do it in my head; I would get $65.59.

Let's do another example. So let's say that we have 3 and 53 hundredths, and we want to add that to 4 and 72 hundredths. Like always, pause this video and see if you can figure it out on your own.

So like we did in the previous example, we could say, "All right, we could add the ones, 3 ones plus 4 ones," so it's going to be 3 + 4. Then we could add the hundredths, and we could say plus 53 hundredths plus 72 hundredths. Now, 3 + 4 is pretty straightforward; that's just going to be equal to 7.

But what is 53 hundredths plus 72 hundredths? Well, what's 53 + 72? Well, 3 + 2, let me write it this way. This is 53 hundredths, and this is 72 hundredths. Well, 3 + 2 is going to be equal to 5, and then 50 + 70 is equal to 120. So this is going to be 125 hundredths, or 1 and 25 hundredths.

So how do we write 125 hundredths as a decimal, or as just, well just as a number? Well, there are a couple of ways to think about it. You could view this as 100 hundredths plus 25 hundredths. The reason why I picked 100 hundredths is because 100 hundredths make a whole. Plus 25 hundredths, so 100 hundredths is just going to be 1. So this is going to be 1 plus 25 hundredths, so I could write this as 1 + 0.25.

And remember, I'm adding that to the 7 here, so it's going to be 7 plus the 1 plus the 25 hundredths. So when we added the 53 hundredths plus the 72 hundredths, we got 125 hundredths, which is the same thing as 1 and 25 hundredths. Now, we could add in the ones to the other ones, and so this is going to be 7 + 1, which is equal to 8, and 25 hundredths, so 8.25.

Now, I'm going to introduce you a little bit to how people might tackle this more systematically. I want you to think about how this is the exact same thing that we just did.

So what you're going to see in the future is people saying, "Okay, line up the decimals," so 3.53 plus 4.72. The reason why people say line up the decimals is so that you're adding the right places to the right places.

Then they say, "All right, well just go place by place and add it up," which is essentially what we just did, but without doing it in such an organized way. Here, I did it this way so that you really get the understanding of what's going on.

But you could say, "All right, I have 3 hundredths plus 2 hundredths," so I'm adding in the hundredths place. So 3 hundredths plus 2 hundredths is 5 hundredths. Then you could say, "Okay, then I have 50 hundredths plus 70 hundredths," which I did over here, or you could view this as 510 plus 710.

510 and 710 is going to be equal to 1210, but you can't write 1210 in the tenths place. But what you can do is, so you can't write, so 5 + 7 is going to be 1210, but 1210 is the same thing as 1 and 210. So you can write the 210 in the tenths place, and then you take the one and you put it in the ones place.

So 510 + 710 is 1 and 210, and then you add the ones up. So you get 1 + 3 + 4, which is 8. So it's 8 and 2/10 and 5 hundredths, or 8 and 25 hundredths, or 8.25. The exact same thing, any way that you try to tackle it.

But hopefully, it makes sense what's actually going on. You're adding hundreds to hundreds, tenths to tenths, ones to ones. When you say you add tenths to tenths and you get something that's larger than one, well that part that is a whole number, you can put in the ones place. We’ll get much, much more practice with this in future videos.