Adding decimals with hundredths
There are different ways to add decimals involving hundredths. One method is to combine the total number of hundredths, while another involves breaking the numbers down into tenths and hundredths and adding them separately. A more complicated example shows how these techniques can be used to arrive at a whole number plus a fraction. Understanding these concepts is important before moving on to faster methods.
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- [Instructor] Let's get some practice adding numbers that involve hundredths. 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 is 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 a few ways that my brain might think about it. One way to think about it is you could say that this is 53/100. You could read this as either 5/10 and 3/100, or 53/100. You could say this is 53/100. Hundredths. And to that you're going to add 42/100. 42/100. And so if I have 53 of something and I'm gonna 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 90, and three plus two is five. It's going to be 95/100. 95/100. And if I wanted to write that as a pure number, I would write that as 0.95, which I could write as 95/100, hundredths, or 9/10 and 5/100. Now the other way we could've thought about it is we could've broken these numbers up. We could've said that this first number is 5/10 plus 3/100, hundredths. And then the second number, we could've rewritten as 4/10 plus 2/100. Let me make sure of my decimals. Plus 2/100. And then we could've separately added the tenths and the hundredths. So you have 5/10 plus 4/10, so 5/10 plus 4/10, and then you could separately add 3/100 plus 2/100. So 3/100, I have a little trouble saying that, plus 2/100, and so what do I get? Well 5/10 and 4/10, and we've done this in previous videos, if I have five of something and I add four of it, that's gonna be 9/10. So it's gonna be 9/10, and then the 3/100 plus 2/100. Well that's going to be 5/100. So plus 0.05. And then 9/10 plus 5/100 is gonna be, I know I'm saying hundredths kinda strange, is going to be 9/10 and 5/100, which you could also say as 95/100. Let's do another example. One that's a little bit more involved. Let's say I want to add 68/100 to 33/100. 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. We could rewrite this first number as 6/10 plus 8/100, and the second number we could write as 3/10 plus 3/100. Let me do that in that orange color. 3/10 plus... Plus 3/10 plus 3/100. So if I add the 6/10 and the 3/10, so let me just do that. I'm gonna write every step here. If you're doing this in your head or if you're doing this on paper you wouldn't necessarily write every step here. Those are the tenths. And then separately I'm gonna add the hundredths. Plus 8/100, plus 3/100. Plus 3/100. 6/10 plus 3/10, 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. That's going to be 9/10. If I have six of something and then I add three of them, in this case we're talking about tenths, I'm gonna get nine of them, so 9/10. And so what's this going to be? Well you could view this is as 8/100. 8/100 plus 3/100. If I have eight of something and I add three of something, that's gonna get 11 of that something. 11/100. How do we write 11/100 as a decimal? Well one way to write it, you could just view this as 0.11. This is 11/100. Many people would read this as 11/100. Or you could view this as equaling 10/100, 10/100 plus 1/100. Hundredth. And 10/100 right over here is 1/10. You could view this as 1/10 and 1/100. 1/10 and 1/100. When you add everything together, what do you get? Well you get 9/10, plus 1/10, plus 1/100. Well now this is gonna get interesting still, so let's see. Let me actually rewrite this. It's gonna be 9/10, and this one let me write it plus 1/10, plus that 1/100 leftover. Plus that 1/100. What is this going to be? 9/10 and 1/10, that's going to be, 9/10 and 1/10 is going to be 10/10. 10/10, which is the same thing as one whole. This is just going to be equal to one. It's going to be one plus 1/100. It's going to be one and 1/100, and we are done. As I keep mentioning in future videos we're gonna learn maybe faster ways of doing this. Maybe ways that you might be able to do it 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 11/100 is the same thing as a tenth and a hundredth, and then taking that tenth, and then adding it to the 9/10 that we already had and say, hey that's whole. In the future, we're gonna be doing things like carrying with decimals, but this is essentially what is happening underneath conceptually. It's really important you get a sense of that before you learn the faster methods.