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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.

  • If we start with one third

  • 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

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A2 denominator equal visualize numerator multiply subtract

Subtracting fractions with unlike denominators introduction

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    林宜悉 posted on 2020/03/27
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