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  • - [Instructor] So, what we're gonna think about

  • in this video is multiplying fractions.

  • So, let's say that we wanted to take 2/3

  • and we want to multiply it by four,

  • what is this going to be equal to?

  • Pause this video and try to think about it on your own.

  • Alright, now let's work through this together.

  • And, to help us, I will use a number line,

  • and let's say that each of these hash marks

  • represent a third.

  • So, this is zero, this is 1/3, 2/3, 3/3,

  • 4/3, 5/3, 6/3, 7/3,

  • 8/3, and 9/3, and so where is 2/3 times one?

  • Well, 2/3 times one is just going to be 2/3,

  • we just take a jump of 2/3, so that is times 1.

  • If we multiply by, or if we take 2/3 times two,

  • that'll be two jumps,

  • so one 2/3, two 2/3, three 2/3, and then four 2/3.

  • So, we just took four jumps of 2/3 each.

  • You could view that as 2/3 plus 2/3 plus 2/3 plus 2/3,

  • and where does that get us to?

  • It got us to 8/3.

  • So, notice, 2/3 times four is equal to 8/3.

  • Now, we could go the other way,

  • we could look at a number line

  • and think about what are ways to represent

  • what the number line is showing us?

  • And, on Khan Academy, we have some example problems

  • that do it that way,

  • so I thought it would be good to do an example like that.

  • And, so, let's label this number line

  • a little bit different.

  • Instead of each of these lines representing a third,

  • let's say they represent a half,

  • so zero, 1/2, 2/2, 3/2, 4/2, 5/2,

  • why did I write 5/6, my brain is going ahead,

  • 5/2, 6/2, 7/2, 8/2, and 9/2.

  • And, let's say we were to see something like this.

  • So, if you were to just see this representation,

  • so I'm going to try to draw it like this,

  • so if you were to just see this representation,

  • what is that trying to represent?

  • What type of multiplication is that trying to represent?

  • Well, you could view that as 3/2 plus another 3/2

  • plus another 3/2, 'cause, notice,

  • each of these jumps are three 1/2, or 3/2.

  • So, you could view this as 3/2 plus 3/2 plus 3/2,

  • or another way of thinking about it

  • is this is three jumps of 3/2.

  • So, you can also view this as doing the same thing

  • as three times 3/2, and what are these equal to?

  • Well, 3/2 plus 3/2 plus 3/2, or three times 3/2,

  • it gets you to 9/2.

- [Instructor] So, what we're gonna think about

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A2 初級

数値線上での分数の乗算 (Fraction multiplcation on the number line)

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    林宜悉 に公開 2021 年 01 月 14 日
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