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• - [Instructor] Let's say we wanted to figure out

• what one half minus one third is equal to.

• And we can visualize each of these fractions.

• One half could look like that where if I take a whole

• and if I divide it into two equal sections,

• one of those two equal sections would be a half

• and you see that shaded in green here.

• And then from that, we're trying to subtract a third

• and we can visualize a third this way.

• That if this whole thing is a whole,

• I divide it into three equal sections

• and one of those three equal sections is a third.

• So what we wanna do is take away this gray box

• from this green box and figure out

• how we can mathematically say what is left over.

• So pause this video and see if you can have a go at this.

• And I'll give you a hint, it will be useful

• to be able to represent your halves and thirds

• in terms of a different denominator.

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

• So the way that we can approach this is

• to get a common denominator.

• If I can express both fractions

• in terms of the same denominator,

• it's going to be a lot easier to subtract.

• And the common denominator that's most useful

• is to find the least common denominator.

• And the smallest number

• that is both a multiple of two and three

• is actually two times three, or six.

• So what if we were to write each of these numbers

• in terms of sixths.

• So how can we rewrite one half in terms of sixths?

• I always have trouble saying that.

• Well if I start with one half and if I multiply

• the denominator by three,

• that's going to get us to sixths

• and so I don't change the value of the fraction.

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

• As long as I multiply both the numerator

• and the denominator by the same thing.

• Well, then that's still going to be equal to one half

• and you can visualize what that looks like.

• If you take each of these two equal sections

• and turn them into three equal sections,

• well then you're gonna have a total of six equal sections

• or sixths.

• Two times three in the denominator

• and the part that was shaded in in green

• which was just one of those sections

• is now three times as many sections.

• So your one half is now equal to three over six.

• And we can do the same thing over here.

• how do we express it in terms of sixths?

• Well to go from three to six I would multiply it by two,

• and so I also wanna do that in the numerator

• so that I don't change the value of the fraction

• and we can visualize that.

• Notice, if you take all three sections

• and you turn each of them into two sections

• you now have six equal sections.

• So you are now dealing with sixths,

• and that one section before

• is now going to become two sections.

• So this is now going to be equal to two sixths.

• So we can actually rewrite things as

• this is the same thing as

• three sixths minus, minus two sixths.

• And what do you think that is going to be?

• Well if I have three of something

• and I subtract two of them away

• I'm going to be left with one of that something.

• So I'm going to be left with one sixth in this case.

• And we can visualize it just the way

• we visualized everything else.

• If you take two of these gray bars

• or two of these sections from these three sections

• you're just going to be left with one of them.

• This is one of the six equal sections.

- [Instructor] Let's say we wanted to figure out

A2 初級

# 分母が異なる分母を持つ分数の引き算導入 (Subtracting fractions with unlike denominators introduction)

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林宜悉 に公開 2021 年 01 月 14 日