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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?

• 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.

• 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.

• we now have six equal sections.

• That's what the denominator times two did.

• 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

A2 初級

# 有不同分母的分數加法簡介 (Adding fractions with unlike denominators introduction)

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林宜悉 發佈於 2021 年 01 月 14 日