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  • - [Instructor] In this video we're gonna try to figure out

  • what 1/2 plus 1/3 is equal to.

  • And like always, I encourage you to pause this video

  • and try to figure it out on your own.

  • All right, now let's work through this together.

  • And it might be helpful to visualize 1/2 and 1/3.

  • So this is a visualization of 1/2

  • if you viewed this entire bar as whole,

  • then we have shaded in half of it.

  • And if you wanted to visualize 1/3 it looks like that.

  • So you could view this as this half

  • plus this gray third here,

  • what is that going to be equal to?

  • Now one of the difficult things is we know how to add

  • if we have the same denominator.

  • So if we had a certain number of halves here

  • and a certain number of halves here,

  • well then we would know how many halves we have here.

  • But here we're trying to add halves to thirds.

  • So how do we do that?

  • Well we try to set up a common denominator.

  • Now, what do we mean by a common denominator?

  • Well what if we could express this quantity

  • and this quantity in terms of some other denominator.

  • And a good way to think about it is

  • is there a multiple of two and three

  • and it's simplest when you use the least common multiple

  • and the least common multiple of two and three is six.

  • So can we express 1/2 in terms of sixths

  • and can we express 1/3 in terms of sixths?

  • So we can just start with one over two

  • and I made this little fraction bar a little bit longer

  • 'cause you'll see why in a second.

  • Well if I wanna express it in terms of sixths,

  • to go from halves to sixths,

  • I would have to multiply the denominator by three.

  • But if I want to multiply the denominator by three

  • and not change the value of the fraction,

  • I have to multiply the numerator by three as well.

  • And to see why that makes sense, think about this.

  • So this, what we have in green,

  • is exactly what we had before but now

  • if I multiply it the numerator and the denominator by three,

  • I've expressed it into sixths.

  • So notice, I have six times as many divisions

  • of the whole bar.

  • And the green part which you could view as the numerator,

  • I now have three times as many.

  • So these are now sixths.

  • So I now have 3/6 instead of 1/2.

  • So this is the same thing as three over six

  • and I want to add that or if I want to add this to what?

  • Well how do I express 1/3 in terms of sixths?

  • Well the way that I could do that, it's one over three,

  • I would want to take each of these thirds

  • and make them into two sections.

  • So to go from thirds to sixths I'd multiply the denominator

  • by two but I'd also be multiplying the numerator by two.

  • And to see why that makes sense,

  • notice this shaded in gray part is exactly

  • what we have here but now we took each of these sections

  • and we made them into two sections.

  • So you multiply the numerator and the denominator by two.

  • Instead of thirds, instead of three equal sections,

  • we now have six equal sections.

  • That's what the denominator times two did.

  • Instead of shading in just one of them,

  • I now have shaded in two of them

  • because that one thing that I shaded

  • has now turned into two sections.

  • And that's what multiplying the numerator by two does.

  • And so this is the same thing as 3/6

  • plus this is going to be 2/6.

  • And you can see it here.

  • This is 1/6, 2/6, and now that everything is in terms

  • of sixths, what is it going to be?

  • Well it's going to be a certain number of sixths.

  • If I have three of something plus two of that something,

  • well it's going to be five of that something.

  • In this case, the something is sixths.

  • So it's going to be 5/6.

  • I have trouble saying that.

  • And you can visualize it right over here.

  • This is three of the sixths, one, two, three,

  • plus two of the sixths, one, two, gets us to 5/6.

  • But you could also view it as this green part

  • was the original half and this gray part

  • was the original 1/3, but to be able to compute it,

  • we expressed both of them in terms of sixths.

- [Instructor] In this video we're gonna try to figure out

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A2 denominator numerator shaded multiply express visualize

Adding fractions with unlike denominators introduction

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    林宜悉 posted on 2020/03/27
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