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  • - [Instructor] So which of the following numbers

  • is greater, 1/3 or 1/5?

  • Pause this video and try to answer that.

  • All right, now let's think about this together.

  • And the way that I can best think about it

  • is by visualizing them.

  • So let's imagine a whole.

  • So this is a whole right over there.

  • And then let's say that this is another whole

  • right over there, I'm gonna try to make these rectangles

  • about looking about the same.

  • And now, how would I represent 1/3?

  • Well, I would divide this whole into three equal sections.

  • And so I'm gonna try to divide it into three equal sections.

  • So that's three equal sections right over there.

  • Now they're supposed to be three equal sections,

  • these are hand-drawn so give me a little slack.

  • But one of these three equal sections, well that's 1/3.

  • So that is 1/3 right over there.

  • Now what about 1/5?

  • Well then I would try to divide this in five equal sections.

  • So one,

  • two,

  • three,

  • four,

  • and five equal sections.

  • And so 1/5 would be just one of these fifths.

  • So it would be that right over there.

  • So when you compare it like this, what's larger 1/3 or 1/5?

  • And if it isn't obvious just yet,

  • I could drag this one over,

  • so that we can compare them,

  • so that we can compare them directly.

  • And you can see very clearly that 1/3

  • covers more of the whole, it's a larger fraction

  • of the whole than 1/5 is.

  • So 1/3 is greater than 1/5.

  • And so you might have noticed an interesting pattern

  • or might start thinking about a pattern.

  • You might have been tempted when you saw the five here,

  • five is larger than three, but 1/5 is less than 1/3

  • or 1/3 is greater than 1/5.

  • And that is generally true,

  • that the larger the denominator,

  • the smaller the fraction is going to be.

  • Why is that?

  • Because you're dividing your whole into more equal chunks.

  • So if you're only dividing into three,

  • if it's one of three of the whole, 1/3 of the whole,

  • or if it's one of three equal chunks of the whole,

  • it's gonna be bigger than one of five

  • equal chunks of the whole.

  • And so based on this,

  • how would you compare these two numbers?

  • How would you compare 2/3 to 2/5?

  • Well, same idea here.

  • 1/3 is bigger than 1/5,

  • so 2/3 is definitely going to be bigger than 2/5,

  • and you can see it here.

  • 2/3 is that,

  • while 2/5 is that right over there.

  • And I can do another example

  • where I haven't even drawn it out.

  • How would you compare four over six

  • to four over eight?

  • So 4/6 versus 4/8?

  • Well, same idea.

  • 1/6 is larger than 1/8.

  • 1/6 is greater than 1/8,

  • because the denominator here is smaller.

  • We have the same numerator, but the denominator is smaller.

  • So four of the bigger things is going to be larger

  • than four of the smaller things.

  • So 4/6 is greater than 4/8.

- [Instructor] So which of the following numbers

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A2 初級

単位分数の比較 (Comparing unit fractions)

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    林宜悉 に公開 2021 年 01 月 14 日
動画の中の単語