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  • - [Narrator] Let's see if we can add

  • five and 2/5 to three and 4/5.

  • Pause this video and see if you can figure out what this is.

  • All right, now let's do this together.

  • We've had a little bit of practice

  • adding mixed numbers in the past.

  • And so one way to think about it is,

  • you could view five and 2/5 as five plus 2/5.

  • And then to that we're going to be adding three and 4/5,

  • which you could view as three plus 4/5.

  • And then you could just change the order

  • with which you are adding,

  • and say, all right,

  • well, I could say five plus three,

  • so that's five plus three,

  • and then to that I could add 2/5 and 4/5,

  • so, plus 2/5, plus 4/5.

  • Now what is that going to get me?

  • Well five plus three is going to be equal to eight.

  • Eight plus, and then if I have 2/5,

  • and I add four more fifths to that,

  • well now I'm going to have 6/5.

  • Two of something plus four of that something

  • is going to be six of that something,

  • and the something in this case are fifths.

  • So now I'm going to have 6/5.

  • So some of you might be tempted to say,

  • "Hey, isn't this just going to be equal to

  • eight and 6/5?"

  • And you wouldn't be completely wrong if you said that.

  • But pause this video and think about

  • why this feels a little bit off.

  • Well, the reason why this isn't standard,

  • is the fractional part of this mixed number 6/5

  • is greater than one.

  • So there's a whole inside of this 6/5.

  • So the standard way to do this is

  • see if we can break out that whole.

  • Now what do I mean by that?

  • Well I could rewrite eight plus 6/5

  • as eight plus 6/5 is the same thing

  • as a whole, or 5/5 plus 1/5.

  • And why is this useful?

  • Well 5/5 is the same thing as one.

  • And so now I can say this is going to be equal

  • to eight plus one whole is nine,

  • that's eight plus the 5/5,

  • and then what I have leftover is 1/5.

  • So nine and 1/5.

  • And so this is the direction

  • that people will traditionally go in.

  • Now there's another way that you could approach it,

  • which is really the same idea,

  • we're just writing things a little bit differently.

  • We could write this as five and 2/5

  • plus three and 4/5,

  • and notice the way that I wrote it.

  • I put all the fractions in the fraction column,

  • I guess you could call it that way,

  • and I put all of our whole numbers underneath each other,

  • and if I had multiple digits here,

  • I would align them according to place value.

  • And then what we could do is we could say,

  • okay 2/5 plus 4/5 is going to be 6/5.

  • We could write 6/5 there.

  • But we say, hey, there's something a little bit

  • fishy about 6/5.

  • That's really the same thing as 5/5 plus 1/5,

  • or you could say that's the same thing as one and 1/5.

  • 6/5 is equal to one and 1/5,

  • and so what you could do is,

  • you could write the 1/5 part in the fractions column,

  • and then the one well now you're going to be regrouping that

  • into our whole numbers,

  • so you put a one right over there.

  • Notice, 2/5 plus 4/5 is one and 1/5,

  • which is the same thing as 6/5.

  • And then you add the whole number part.

  • One plus five plus three is nine.

  • So you get nine and 1/5.

  • But hopefully you realize

  • that these are really the same idea,

  • just different way of writing things

- [Narrator] Let's see if we can add

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