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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.

• 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

• 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

A2 初級

# 比較組織、部門分數 (Comparing unit fractions)

• 1 0
林宜悉 發佈於 2021 年 01 月 14 日