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Adding decimals with ones, tenths and hundredths

CCSS Math: 5.NBT.B.7

Video transcript

- Let's do some more involved examples using decimals. So, let's say we wanna add four and 22 hundredths to 61 and 37 hundredths. Like always, I encourage you to pause the video and try to figure out on your own. Well the way that my brain tries to tackle it, is it says, alright, I have four and 22 hundredths, and 61 and 37 hundredths, how about I add the four plus the 61, so it's gonna be four plus 61, and then separately let me add the 22 hundredths to the 37 hundredths, so then I'm gonna add 22 hundredths plus 37 hundredths, and so four plus 61 is going to be equal to 65, and then 22 hundredths plus 37 hundredths, well, what's 22 plus 37? Let's see, 20 plus 30 is 50, and then two plus seven is nine, and so it's going to be 59 hundredths. So 59 hundredths, so it's gonna be 65 and 59 hundredths, which we can write as 65 and 59 hundredths. Now like I've mentioned in previous videos, there's many different ways of adding decimals, and in future videos we'll learn arguably faster ways of doing it, but I wanna show you multiple ways so you get a sense of ways to approach it, and this is the way that I do it in my head if someone said hey, something cost $61.37, and then you had to pay $4.22 in tax, how much did 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 three and 53 hundredths, and we wanna add that to four 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 can say alright, we could add the ones, three ones plus four ones, so it's gonna be three plus four, and then we could add the hundredths, and we could say plus 53 hundredths, plus 53 hundredths, plus 72 hundredths, plus 72 hundredths, now the three plus four is pretty straightforward, that's just going to be ... Yup, blue color, this is just going to be equal to seven, but what is 53 hundredths plus 72 hundredths? Well, what's 53 plus 72? I'm going to write it this way, this is 53 hundredths, hundredths, and this is 72 hundredths, well, three plus two is going to be equal to five, and then 50 plus 70 is equal to 120, so this is going to be 125 hundredths, 125 hundredths, so how we write 125 hundredths as a decimal or just as a number? Well, there's a couple of ways to think about it, you could view this as 100 hundredths, hundredths, plus 25 hundredths, plus 25 hundredths, and the reason why I picked 100 hundredths, is because 100 hundredths make a whole, plus 25 hundredths, and so 100 hundredths is just going to be one, so this is going to be one plus 25 hundredths, so I could write this one plus 0.25, and remember, I'm adding that to the seven here, so it's gonna be seven, plus the one, 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 one and 25 hundredths, now, the one, we could add in the ones to the other ones, and so this is going to be seven plus one, is equal to eight, eight and 25 hundredths, so 8.25. Now, I'm going to introduce you a little bit to how people might tackle this more systematically, and 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 are gonna say oh you line up the decimals, so 3.53 plus 4.72, and the reason why people say line up the decimals is so that you're adding the right places to the right places, 4.72, and then they say alright, we'll just go place by place and add it up, which is essentially what we just did without doing it as organized of a way here, and I did it this way so that you really get the understanding of what's going on. But you could say alright, I have three hundredths plus two hundredths, so I'm adding in the hundredths place, so three hundredths plus two hundredths is five hundredths, and then you could say okay, then I have 50 hundredths plus 70 hundredths, which I did over here, or you could view this as five tenths plus seven tenths, and five tenths and seven tenths is going to be equal to 12 tenths, but you can't write 12 tenths in the tenths place, but what you can do, so five plus seven is going to be 12 tenths, but 12 tenths is the same thing as one and two tenths, so you can write the two tenths in the tenths place, and then you take the one and you put it in the ones place, so five tenths plus seven tenths is one and two tenths, and then you add the ones up, and so you get one plus three plus four is eight, so it's eight and two tenths and five hundredths, or eight 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 hundredths to hundredths, tenths to tenths, ones to ones, and when, 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, and we'll get much much more practice with this in future videos.