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  • - [Instructor] This right over here

  • is an image from an exercise on Khan Academy and it says

  • compare using greater than, less than, or equal to.

  • And on the left, we have 1/4 times 5,000,

  • and we wanna compare that to 5,000.

  • On Khan Academy, you would click on this drop-down

  • and you would pick greater than, less than, or equal to.

  • So what do you think it is?

  • How does 1/4 times 5,000 compare to 5,000?

  • And how do you know your answer is correct?

  • Pick one of these choices as well.

  • Pause the video and have a go at that.

  • Well, one way to think about it,

  • if I'm multiplying 5,000 times some value,

  • that value is going to scale 5,000.

  • It's going to make it smaller or bigger

  • or in certain cases, might not change the size at all.

  • In fact, the ones where you don't change 5,000

  • was you multiply it by one.

  • So one times 5,000 is equal to 5,000.

  • But what do you think is going to happen

  • when you multiply a value

  • that is between zero and one times 5,000?

  • Is that going to be greater than, equal to,

  • or less than 5,000?

  • Well one way to imagine it is on a number line.

  • If this is zero, this is 5,000.

  • This would be halfway between zero and 5,000.

  • And if I then make it the space between zero and 5,000

  • into fourths, this would be 1/4 of the way

  • between zero and 5,000.

  • So this value right over here,

  • that is 1/4 times 5,000.

  • Well, how does this value,

  • 1/4 times 5,000, compare to this value, to 5,000?

  • Well, it's clear that 1/4 times 5,000

  • is less than,

  • is less than 5,000.

  • And in general, if the value is between zero and one

  • that you're multiplying by something else,

  • it's going to make the thing you're multiplying smaller.

  • If this were one, it's not going to change the value.

  • And if this were greater than one,

  • it would make it larger.

  • So let's see these choices.

  • Because we are multiplying 5,000 by a fraction

  • that is less than one.

  • Yeah, that's exactly what's happening.

  • We're multiplying 5,000 by 1/4.

  • So it's going to give us a smaller value than 5,000.

  • I like that choice.

  • Let's just read these other ones.

  • Because we are multiplying 5,000 by a fraction

  • that is equal to one.

  • Well no, 1/4 is clearly not equal to one,

  • so we rule that one out.

  • Because we are multiplying 5,000 by a fraction

  • that is greater than one.

  • Well 1/4 is clearly not greater than one,

  • so we rule that out as well.

  • Let's do another example.

  • So here we're asked,

  • is the product of each expression less than,

  • equal to, or greater than 49?

  • So pause this video and try to figure it out.

  • All right, so this first one is 49 times 7/8.

  • So what do you think that's going to be?

  • Well, 7/8 is less than one.

  • So if I multiply 49 times something less than one,

  • I'm going to get a value that is less than 49.

  • So I like that choice right over there.

  • 49 times 5/2.

  • Well, 5/2 is greater than one.

  • Remember, 2/2 would be equal to one.

  • So 5/2 is greater than one.

  • So if I'm multiplying 49 by a value

  • that is greater than one, I'm going to get a value

  • that is greater than 49.

  • And then last but not least, 49 times 3/3.

  • Well, 3/3 is exactly equal to one.

  • So 49 times one is going to be exactly equal to 49,

  • and we're done.

- [Instructor] This right over here

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A2 初級

分數乘法作為比例的例子 (Fraction multiplication as scaling examples)

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    林宜悉 發佈於 2021 年 01 月 14 日
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