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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?

• 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.

• 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

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