Solving for the missing fraction Khan Academy English Korean

Solving for the missing fractionYouTube↗ IA↗(long shot)
Education 183.1K views 145 likes 27 dislikes 05 Sep 2015 Show Contributors 1

Khan Academy 9.4M subscribers United States YouTube↗

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Bulgarian Ralitsa Dimitrova

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- [Voiceover] So, we have blank plus one-16th is equal to three halves.

어떤 수 더하기 1/16이 3/2인 식이 있다고합니다

So, I encourage you to pause the video and just figure out what blank is. What plus one-16th is equal to three-halves?

동영상을 멈추고 어떤 수가 무엇일지 생각해 보세요 1/16에 어떤 수를 더해야 3/2이 나올까요?

같이 풀어 봅시다

Now, let's work through this together. One thing that might make it a little bit simpler

좀 더 쉽게 풀기위해

for our brains is if we were to express one-16th and three-halves with a common denominator.

1/16과 3/2을 통분해 줍시다

When we think about a common denominator, we will look at a common multiple of the denominators here.

통분을 하려면 먼저 두 분모의 공배수를 생각해 봅시다

And lucky for us, 16 is already divisible by 2.

다행히도 16은 2로 나눌 수 있죠

It's divisible by 16 as well, so it is the common multiple, or it is the least common multiple of 16 and 2.

또, 16은 16으로도 나눠지니까 공배수 또는 최소공배수 이기도 합니다

There are other common multiples, but the smallest one is going to be 16 times 1, which is also divisible by 2.

다른 공배수들도 있지만 가장 작은 것은 16이에요

So, let's try both of these, let's try both of these fractions. Let's rewrite this equation where both of these fractions

그것도 역시 2로 나눌 수 있죠 그래서 이 식을 16으로 통분합니다

have 16 as their denominators. This one obviously already has it.

16분의 1은 이미 분모가 16이에요

So, let's write that.

So, we're going to have, we're going to have blank plus one-16th, one-16th, is equal to, is equal to, let's see,

_____+ 1/16=( )/16

let's write three-halves as something over 16.

Well, to get our denominator from 2 to 16, we have to multiply by 8.

2에서 16으로 분모를 바꾸기 위해서 8을 곱해주니까

So, we have to multiply the numerator by 8 as well.

분자인 3에도 역시 8을 곱합니다

So, 3 times 8 is going to be 24.

3 곱하기 8은 24이지요

Now, at this point, you might be able to do it in your head.

암산으로도 할 수 있을 거에요

Blank plus one-16th is equal to 24-16ths.

( ) + 1/16 = 24/16 이니까

We could say, okay, this could, this could... We could do this as a certain number of 16ths.

( )는 분모가 16인 분수일것이라는걸 알수 있어요

So, how many 16ths plus one-16th is going to be 24-16ths?

그렇다면 빈칸은 얼마일까요?

Well, 23-16ths.

That's 23-16ths, and I add one more 16th, I'm going to have 24-16ths.

23/16+1/16=24/16 이 맞아요

Another way that you could have thought about it, when we... Actually, you could have even thought about it from the first step, is you could say,

다른 방법은 첫 번째 단계에서도 생각할 수 있었을 텐데

look, if blank plus one-16th is equal to three-halves,

_______+ 1/16 = 3/2이면

then you could say that blank, you could say that blank is going to be equal to three-halves, three-halves minus one-16th, minus one-16th.

_______ = 3/2 - 1/16 이라는 말과 같아요

This is another way that you could have tackled it.

이것은 다른 풀이 방법입니다

If blank plus one-16th is three-halves, then blank is going to be equal to three-halves minus one-16th.

_______+ 1/16 = 3/2이면 _______ = 3/2 - 1/16 입니다

And we know that this is going to be equal to... Three-halves, we already know, it's the same thing as 24-16ths.

앞의 풀이에서 3/2=24/16이니까

So, 24 over 16 minus one-16th, minus one-16th, which we figured out is 23/16ths, which is equal to... I'll just rewrite it again, 23 over 16.

24/16 - 1/16= 23/16입니다

Let's do another example.

다른 문제를 풀어 봅시다

So, here, this is a little bit different.

약간 다른게 생겼네요

I have blank minus three-fourths is equal to two-thirds.

_____ - 3/4 = 2/3라는 식입니다

And there's a couple of ways to think about it.

2가지 풀이가 있어요

If blank minus three-fourths is equal to two-thirds, that, one way to think about it, you can say,

blank, that means that blank is going to be the same thing as two-thirds plus three-fourths. Two-thirds plus three-fourths. Plus three-fourths.

_____= 2/3 + 3/4 라는 식이 나와요

And what is this going to be?

얼마가 되나요?

Well, once again, I could rewrite both of these fractions so they have a common denominator.

두 분수를 통분해 보면

Well, what's the least common multiple of 3 and 4?

3과 4의 최소 공배수는 무엇인가요?

Well, we could look at the multiples of 4 and keep, and, and keep increasing them until we find one that's perfectly divisible by 3.

4의 배수를 구해서 그 중에 3으로 나누어 지는 수를 찾으면 돼요

4 isn't divisible by 3. 8 isn't divisible by 3.

4는 3으로 나눌 수 없고 8도 3으로 나눌 수 없어요

12 is divisible by 3. In fact, it's 3 times 4 is 12.

하지만 12는 3으로 나눌 수 있죠 12는 3과 4의 곱이에요

So, we can rewrite both of these as something over 12. So, this is going to be the same thing as...

이 두 분수를 _____/12 으로 다시 적을 수 있습니다

So, to go from 3 to 12, we multiply it by 4. So, you have to multiply the numerator by 4 as well.

3이 12가 되려면 4를 곱해야 하니까 분자에도 4를 곱해줘요

So, 2 times 4 is 8. Two-thirds is the same thing as eight-12ths.

2곱하기 4는 8입니다 즉, 2/3=8/12입니다

This is going to be equal to eight-12ths plus, and then three-fourths is the same thing as what over 12?

그리고 3/4= ___/12과 같은데

Well, to go from 4 to 12, you have to multiply it by 3, so you have to multiply the numerator by 3 as well.

4에서 12가 되려면 3을 곱해야 하므로 분자에도 3을 곱해줍니다

3 times 3 is 9.

3곱하기 3은 9입니다

And what's that going to be equal to? So, it's equal to this, which is equal to

이 합은 얼마일까요?

eight-12ths plus nine-12ths is going to be, 8 plus 9 is 17. 17-12ths.

8/12 + 9/12= 17/12 이네요

So, you get 17-12ths minus three-fourths is equal to two-thirds.

즉, 17/12 - 3/4 = 2/3이지요

Now, another way that you could have done it is you could have just kept it the same

또 다른 풀이 방법은

and could have said, okay, let me just rewrite, let me just rewrite this, but I'm going to rewrite

문제를 다시 적겠습니다

the fractions so that they have a common denominator.

분모가 같은 식으로요

We already said, well, our common denominator we want to use is 12, at least. We could use 24 or something larger than that. But this would have been the least common multiple,

12가 최소공배수이니까

so this keeps things a little bit simpler.

최소 공배수를 이용하면 훨씬 쉬워져요

And three-fourths, we're going to rewrite this as nine-12ths. 9 over 12 is equal to.

3/4= 9/12이고

And two-thirds, we can rewrite as 8 over 12.

2/3=8/12입니다

And you could assume that this is going to be a certain number of 12ths.

그러고 나면 빈칸에 들어 갈 수가 _____/12라고 생각할 수 있죠

So, blank-12ths minus nine-12ths is equal to eight-12ths.

그래서 ____/12 - 9/12= 8/12입니다

So, if I have blank of something minus nine of something, and I'm left with eight of that something, that means that I had 17 of that something to begin with.

어떤 수 에서 9를 빼 8이 나오려면 어떤 수는 17이지요

17-12ths minus nine-12ths is equal to eight-12ths.

17/12- 9/12 = 8/12 입니다

But either way, you get 17-12ths for our blank.

두 가지 방식으로 빈칸의 답 17/12을 구했습니다

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