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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

A2 初級

# 數字線上的分數倍增法。 (Fraction multiplcation on the number line)

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林宜悉 發佈於 2021 年 01 月 14 日