쉐도잉 연습: Multiplying Fractions - The Easy Way! - 영상으로 영어 말하기 배우기

In this video we're going to focus on multiplying fractions.

So let's start with a simple example.

Let's multiply 3 over 5 by 4 over 7.

Now for each of these examples feel free to pause the video and try these problems yourself.

See if you can get the answer.

So what do we need to do in this problem?

How can we multiply these two fractions?

When multiplying fractions you need to multiply across.

So we're going to multiply 3 and 4 together.

3 times 4 is 12.

Next, we need to multiply the two denominators together.

5 times 7 is 35.

And so that's it for this problem.

That's all we need to do.

And the answer is 12 over 35.

Now, it's important to check and see if you could reduce the fraction.

And for this example, we can't simplify the fraction.

So the final answer is 12 over 35.

Now let's try another example.

Go ahead and multiply these two fractions.

2 over 5 times 3 over 11.

So once again, we're going to multiply across.

2 times 3 is 6.

And then we're going to multiply 5 and 11.

5 times 11 is 55.

And so this is the answer.

We can't simplify this answer.

Now let's try some examples where we have to simplify the final answer.

So let's multiply 3 over 2 by 4 over 9.

Go ahead and try this.

3 times 4 is 12.

And 2 times 9 is 18.

So we get 12 over 18.

How can we reduce that fraction?

Now, both of these numbers are even, so we can divide 12 and 18 by 2.

12 divided by 2 is 6.

18 divided by 2 is 9.

Now, can we reduce this fraction, or is that the final answer?

6 and 9 are both divisible by 3, so we could divide both numbers by 3.

6 divided by 3 is 2, 9 divided by 3 is 3.

So our final answer is 2 over 3.

Now there's another way in which you can get the same answer.

So once you got to, let's say this part, you could do it this way.

You could say 12 is 6 times 2, and 18 is 6 times 3.

So at this point, you can cancel the 6, and this will give you the final answer of 2 over 3.

So that's another way in which you could reduce a fraction.

Now let's work on another example that's similar to the last one.

4 over 3 times 9 over 8.

So pause the video and work on this example.

So let's multiply across.

What is 4 times 9?

4 times 9 is 36.

And what's 3 times 8?

3 times 8 is going to be 24.

So how can we reduce 36 over 24?

24 and 36 are multiples of 12.

12 times 3 is 36, and 12 times 2 is 24.

So it really helps to know your multiplication tables.

So at this point, we can cancel our 12.

And so the final answer is going to be 3 over 2.

Now let's talk about what to do when multiplying two fractions

that contain large numbers such as this one now what I

don't recommend is multiplying across 24 times 45 it's gonna be a big number let's see what

that number is gonna be if you multiply across that's gonna give you a thousand

and eighty and then if you multiply 27 by 32 that's gonna give you a large number as well.

That's going to be 864.

So what are you going to do to reduce this fraction?

That's not going to be fun and it's going to take a long time.

So there has to be an easier way of getting the answer for this problem.

And the key is to simplify before you multiply.

So, for instance, 28, we can write that as 8 times 3.

27, we can write it as 9 times 3, because 9 times 3 is 27.

Now, 45, you want to break it down into a number with a 9, so you can cancel this 9.

It turns out that 9 times 5 is 45.

And 32, we can represent it as 8 times 4.

So you want to break down these large numbers into smaller numbers in such a way

that you can cancel some of those smaller numbers.

So we can cancel an 8, we can cancel a 9, and we can cancel a 3.

And our final answer is just going to be 5 over 4.

we don't have to simplify any further than this as you

can see this second method is a lot easier than the first so

if you have large numbers I would avoid multiplying them to get even bigger numbers instead simplify before you multiply

so now it's your turn try this 56 over 44 times 55 over 40

go ahead and multiply these two fractions.

So let's not multiply 56 by 55.

Let's avoid that.

56, we can write that as 8 times 7.

44 is 11 times 4.

And 55 is 11 times 5.

40 is 8 times 5.

So we can cancel an 8.

We can cancel an 11.

And we can cancel a 5.

So the final answer is 7 over 4, and that's it.

Now, what if you get a problem that looks like this?

What is 8 multiplied by 5 over 3?

How can you take a whole number and multiply it by a fraction?

The key is to convert the whole number into a fraction.

8 is the same as 8 over 1.

100

In this case, 8 and 5, they're not large numbers, so we can multiply across.

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And we can't really simplify before we multiply in this case.

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So 8 times 5, that's going to be 40.

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And then if we multiply 1 and 3, it's going to give us 3.

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So our answer is 40 over 3 as an improper fraction.

105

Try this one.

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7 over 6 multiplied by 9.

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Go ahead and work on that example.

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So let's rewrite 9 as 9 over 1.

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Now this one we could simplify before we multiply if we want to.

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6, we can write that as 3 times 2.

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And 9 is 3 times 3.

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So we can cancel a 3.

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And so we're left with 7 times 3, which is 21 and 2 times 1 which is 2.

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So the answer is 21 over 2.

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By the way, if you want more videos on fractions, feel free to check out my next video on dividing fractions.

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Which I'm going to post a link to that video in the description section of this video that you're currently watching.

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But now let's get back to our next problem.

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So let's say if we have 12 over 28 times 18 over 30 times 35 over 27.

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How can we multiply these three fractions?

120

So go ahead and try this problem.

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12 we can write

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that as 6 times 2 28 we could say it's 7 times 4 18 we can write

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that as 6 times 3

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but yeah i'm gonna make that 9 times 2 because there's 27 and 27 is divisible by 9

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30 is 6 times 5, 35 is 7 times 5, and 27 is 9 times 3.

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So we can cancel a 9, we can cancel a 7,

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we can cancel a 5, we can cancel a 6,

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and notice that we can also cancel 4.

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2 times 2 is 4.

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So these 2s can cancel the 4 on the bottom.

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So what's our final answer here?

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Notice that every number in the numerators of the 3 fractions have been cancelled.

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So what numbers should we put on top then if there's nothing to write?

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Well, if we think about this, 9 divided by 9.

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The reason why that cancels is because 9 over 9 is 1.

136

7 divided by 7 is 1 So when everything cancels, the number to right is a 1 Now we do have a 3 on the bottom,

137

so our final answer for this problem is 1 over 3 So this is the solution

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✨ 추천 영상

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이 레슨의 어휘와 말하기 포인트

이 B1 수준 말하기 레슨은 영상 “Multiplying Fractions - The Easy Way!”을(를) 바탕으로 합니다. 가장 자주 반복되는 단어는 다음과 같습니다: multiply, fraction, cancel, answer, simplify. 이 영상에는 섀도잉할 문장 137개와 단어 1137개가 있습니다. 말하는 구간의 길이는 10:15입니다. 화자는 분당 약 111단어의 일정한 속도로 말해서 섀도잉하기에 편한 속도입니다. 단어의 89%가 영어에서 가장 많이 쓰이는 3,000단어에 속해 어휘가 쉬운 편입니다.

이 영상의 핵심 어휘

영상에서 가장 어려운 단어 8개를 발음, 뜻과 함께 정리했습니다.

단어	발음	뜻
multiply 동사	/ˈmʌltɪplaɪ/	곱하다
cancel 동사	/ˈkæn.sl̩/	취소하다
fraction 명사	/ˈfɹæk.ʃən/	분수
divide 동사	/dɪˈvaɪd/	나누다, 가르다
pause 명사	/pɔːz/	멈춤, 휴지
denominator 명사	/dɪˈnɒmɪneɪtə(ɹ)/	분모
multiplication 명사	/ˌmʌltɪplɪˈkeɪʃən/	곱셈, 승법
numerator 명사	/ˈnuː.məɹˌeɪ̯.təɹ/	분자

영상에 나오는 구동사

단어	뜻
get over 동사	극복하다

따라 말해 볼 만한 문장

영상에 나오는 짧고 완결된 문장으로, 일상 대화에서 그대로 쓸 수 있습니다:

How can we multiply these two fractions?
That's all we need to do.
We can't simplify this answer.
How can we reduce that fraction?
How can we multiply these three fractions?

이 영상의 문법

화자가 가장 많이 쓰는 문형을 영상 속 실제 표현과 함께 정리했습니다.

문형	영상 속 표현
비교급 -er than / more … than — 두 대상을 비교	further than · easier than
“going to” 미래 be going to + 동사 — 계획이나 곧 일어날 것이 분명한 일	we're going to focus · we're going to multiply · is going to be
의무: must / have to / need to 어떤 일이 필요하다고 말할 때	need to do · need to multiply · have to simplify

주의할 발음

화자는 gonna, we're, can't 같은 축약형과 약화된 형태를 19번 사용합니다. 들리는 대로 짧게 발음하세요.

“sh”와 “zh” 소리: fraction /ˈfɹæk.ʃən/, multiplication /ˌmʌltɪplɪˈkeɪʃən/
긴 단어 — 강세 위치에 주의: divisible [dɪˈvɪzɪbəɫ], denominator /dɪˈnɒmɪneɪtə(ɹ)/, multiplication /ˌmʌltɪplɪˈkeɪʃən/, numerator /ˈnuː.məɹˌeɪ̯.təɹ/

한국어 화자가 어려워하는 소리:

/f/ — ㅍ(/p/)으로 바꾸지 말고 윗니를 아랫입술에 대기: fraction /ˈfɹæk.ʃən/, simplify /ˈsɪmplɪfaɪ/
/v/ — ㅂ(/b/)과 구별하기: divide /dɪˈvaɪd/, divisible [dɪˈvɪzɪbəɫ], convert /kənˈvɝt/
/z/ — ㅈ이 아니라 성대를 울리는 /s/: divisible [dɪˈvɪzɪbəɫ], pause /pɔːz/

이 영상으로 연습하는 방법

먼저 말하지 않고 영상을 끝까지 듣고 모르는 단어를 적어 둡니다.
보통 속도로 한 문장씩 섀도잉하고, 화자의 리듬과 맞을 때까지 반복합니다.
자신의 목소리를 녹음해 원본과 비교하고, multiply, cancel, fraction 같은 단어에 특히 주의합니다.

쉐도잉이란? 영어 실력을 빠르게 키우는 과학적 방법

쉐도잉(Shadowing)은 원래 전문 통역사 훈련을 위해 개발된 언어 학습 기법으로, 다언어 학자인 Dr. Alexander Arguelles에 의해 대중화된 방법입니다. 핵심 원리는 간단하지만 매우 강력합니다: 원어민의 영어를 들으면서 1~2초의 짧은 지연으로 즉시 소리 내어 따라 말하는 것——마치 '그림자(shadow)'처럼 화자를 따라가는 것입니다. 문법 공부나 수동적인 청취와 달리, 쉐도잉은 뇌와 입 근육이 동시에 실시간으로 영어를 처리하고 재현하도록 훈련합니다. 연구에 따르면 이 방법은 발음 정확도, 억양, 리듬, 연음, 청취력, 말하기 유창성을 크게 향상시킵니다. IELTS 스피킹 준비와 자연스러운 영어 소통을 원하는 분들에게 특히 효과적입니다.

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