쉐도잉 연습: Subtracting Fractions - 영상으로 영어 말하기 배우기

In this lesson, we're going to focus on how to subtract two or three fractions.

So let's start with this example.

3 over 5 minus 1 over 2.

How can we subtract those two fractions?

The first thing we need to do is multiply the two denominators of the fractions.

5 times 2 is 10.

And then we need to cross multiply.

3 times 2 is 6.

5 times negative 1 is negative 5.

So now we need to subtract 6 and 5, which will give us 1.

So the final answer is 1 over 10.

So that is the solution to this problem.

Now let's work on another one.

So let's subtract 4 over 3 by 3 over 4.

And let's use the same technique.

So first, let's multiply the two denominators of the fractions.

3 times 4 is 12. And then cross multiply.

4 times 4 is 16.

3 times negative 3 is negative 9.

Now, 16 minus 9 is 7.

So the answer is going to be 7 divided by 12.

So now it's your turn.

Go ahead and subtract these two fractions.

3 over 8 minus 1 over 7 and also 5 over 7 minus 2 over 5.

So starting with the first example, let's multiply 8 by 7.

So 8 times 7 is 56.

and then let's cross multiply.

3 times 7 is 21 and 8 times negative 1 is negative 8.

So now we need to subtract.

21 minus 8 is 13.

So the answer to the first problem is going to be 13 over 56.

Now for the next example let's multiply 5, I mean 7 and 5.

7 times 5 is 35 5 times 5 is 25 and then we have 7 times 2 which is 14

so now let's subtract 25 and 14 25 minus 14 is 11

and so this is going to be 11 over 35 by the way I'm going to post some links

in the description section of this video where you can find more of my videos on fractions, like how to multiply fractions and how to divide them as well and some other stuff too.

But before we go into subtracting three fractions, let's talk about another method in which we can subtract two fractions.

So in the previous method we would multiply 9 and 4

and that will give us 36 and then we would cross multiply.

5 times 4 is 20 and then 9 times 1 is 9

but 9 times 1 is negative 9 so it's gonna be 20 minus 9

which is 11 and so this will give us 11 over 36 now another way in

which you can do the same problem

and get the same results is to get the common denominators first before combining the two fractions 9 times 4 is 36.

So to get a common denominator of 36, we need to multiply the first fraction by 4 over 4, and the second one by 9 over 9.

4 times 5 is 20, 4 times 9 is 36.

And so we're going to get this.

So now that these two are the same, we can combine the numerators of the two fractions.

So 20 minus 9 is 11.

And so we're going to get the same answer, 11 over 36.

Now, this technique is useful if you have multiple fractions.

Let's say if you want to subtract 3 or 4 fractions, you could do that.

So let's say if we have 8 over 9 minus 1 over 3 minus 2 over 5.

So we'll need to find a common denominator of those three fractions So what is the least common multiple of 9, 3, and 5?

3 already goes into 9 So any multiple of 9 is a multiple of 3

So we don't really need to worry about this So what is the common multiple between 9 and 5?

Well, 9 times 5 is 45 So 45 is the lowest number that can go into 9,

3, and 5 Now 45 divided by 9 is 5 So I'm going to multiply this fraction by 5 over 5

Now 45 divided by 3 is 15 So I'm going to multiply the second fraction by 15 over 15.

And 45 divided by 5 is 9.

So I'm going to multiply the last fraction by 9 over 9.

5 times 8 is 40.

5 times 9 is 45.

15 times 1 is 15, 15 times 3 is 45, 2 times 9 is 18, 5 times 9 is 45.

And now we need to subtract.

So 40 minus 15 is 25, and 25 minus 18 is 7.

So this is going to be 7 over 45. And that's the answer.

Let's try another example.

9 over 10 minus 1 over 5 minus 2 over 7.

Feel free to pause the video and work on that example.

So let's get a common denominator between 10, 5, and 7.

So 5 goes into 10, so we don't have to worry about the 5.

Any multiple of 10 is going to be a multiple of 5.

So multiples of 10 are 10, 20, 30, 40, all the way to 70.

Multiples of 7 are 7, 14, 21, 28, all the way to 70.

If you multiply 10 and 7, you're going to get a common multiple between 10 and 7, which is 70.

So it turns out that 70 is the common denominator that we want to get to.

70 divided by 10 is 7.

So let's multiply the first fraction by 7 over 7.

70 divided by 5.

Let's see what that is.

So let's use long division.

5 goes into 7 one time.

5 times 1 is 5.

And then subtract.

7 minus 5 is 2.

Bring that into 0.

5 goes into 24 times.

So 70 divided by 5 is 14.

So we need to multiply this fraction by 14 over 14.

70 divided by 7 is 10.

So we're going to multiply the last fraction by 10 over 10.

7 times 9 is 63.

And we know 7 times 10 is 70.

And 5 times 14 is 70.

And 2 times 10 is 20. So now let's subtract.

63 minus 14.

That's 49.

And 49 minus 20 is 29.

100

So the final answer for this problem is 29 divided by 70.

101

Let's work on one last example.

102

3 over 4 minus 1 over 2 plus 5 over 3 minus 2 over 5.

103

Go ahead and try that example.

104

So what is a common multiple between 2, 3, 4, and 5?

105

Well, we don't have to worry about the 2 because 2 goes into 4.

106

So all we need to do is multiply 4 times 3 times 5, which is 60.

107

And so 60 is going to be the common denominator that we need to get to.

108

60 divided by 4 is 15.

109

So we're going to multiply this fraction by 15 over 15.

110

60 divided by 2 is 30, so we're going to multiply the second fraction by 30 over 30.

111

And 60 divided by 3 is 20, so let's multiply this fraction by 20 over 20.

112

And finally, 60 divided by 5 is 12.

113

Now let's multiply.

114

15 times 3 is 45, and we know 15 times 4 is 60.

115

1 times 30 is 30, and 2 times 30 is 60.

116

5 times 20 is 100.

117

320 is 60.

118

2 times 12 is 24, and 5 times 12 is 60.

119

So now we'll need to subtract So first let's subtract these two numbers 45 minus 30 is 15

120

So we have 15 over 60 And then let's subtract these two 100 minus 24

121

100 minus 20 is 80 80 minus 4 is 76 So now we need to add 15 and 76

122

15 plus 76 is going to be 91 and so

123

that is the final answer it's a 91 over 60

124

so that's all i got for this video be sure to

125

check out my next video on multiplying fractions thanks for watching

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✨ 추천 영상

62 문장

이 레슨의 어휘와 말하기 포인트

이 B1 수준 말하기 레슨은 영상 “Subtracting Fractions”을(를) 바탕으로 합니다. 가장 자주 반복되는 단어는 다음과 같습니다: fraction, multiply, minus, subtract, divided. 이 영상에는 섀도잉할 문장 125개와 단어 1005개가 있습니다. 말하는 구간의 길이는 10:58입니다. 화자는 분당 약 92단어로 천천히 말해서 소리 하나하나를 따라 하기에 여유가 있습니다. 단어의 87%가 영어에서 가장 많이 쓰이는 3,000단어에 속해 어휘가 쉬운 편입니다.

이 영상의 핵심 어휘

영상에서 가장 어려운 단어 15개를 발음, 뜻과 함께 정리했습니다.

단어	발음	뜻
fraction 명사	/ˈfɹæk.ʃən/	분수
minus	/ˈmaɪ.nəs/	빼기
divide 동사	/dɪˈvaɪd/	나누다, 가르다
technique 명사	/tɛkˈniːk/	기술
combine 동사	/kəmˈbaɪn/	조합하다, 결합하다
lesson 명사	/ˈlɛs.ən/	수업, 과
pause 명사	/pɔːz/	멈춤, 휴지
multiply 동사	/ˈmʌltɪplaɪ/	곱하다
subtract 동사	/səbˈtɹækt/	빼다
denominator 명사	/dɪˈnɒmɪneɪtə(ɹ)/	분모
numerator 명사	/ˈnuː.məɹˌeɪ̯.təɹ/	분자
negative 형용사	/ˈnɛɡ.ə.tɪv/	소극적인
cross 명사	/kɹɑs/	십자
worry 동사	/ˈwʌ.ɹi/	걱정하다
plus	/ˈplʌs/	더하기

따라 말해 볼 만한 문장

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

How can we subtract those two fractions?
Let's see what that is.
Let's work on one last example.

이 영상의 문법

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

문형	영상 속 표현
최상급 the -est / the most … — 집단에서 가장 높거나 낮은 것	the least common · the lowest
“going to” 미래 be going to + 동사 — 계획이나 곧 일어날 것이 분명한 일	we're going to focus · is going to be · gonna be
의무: must / have to / need to 어떤 일이 필요하다고 말할 때	need to do · need to cross · need to subtract
“will” 미래 will + 동사 — 결정, 약속 또는 예측	will give · we'll need

주의할 발음

화자는 we're, I'm, don't 같은 축약형과 약화된 형태를 17번 사용합니다. 들리는 대로 짧게 발음하세요.

“sh”와 “zh” 소리: fraction /ˈfɹæk.ʃən/, section /ˈsɛkʃən/, division /dɪˈvɪʒn̩/, solution /səˈl(j)uːʃən/, description /dɪˈskɹɪpʃən/
긴 단어 — 강세 위치에 주의: denominator /dɪˈnɒmɪneɪtə(ɹ)/, numerator /ˈnuː.məɹˌeɪ̯.təɹ/

한국어 화자가 어려워하는 소리:

/f/ — ㅍ(/p/)으로 바꾸지 말고 윗니를 아랫입술에 대기: fraction /ˈfɹæk.ʃən/, focus /ˈfoʊ̯.kəs/, useful /ˈjuːsfəl/
/v/ — ㅂ(/b/)과 구별하기: divide /dɪˈvaɪd/, negative /ˈnɛɡ.ə.tɪv/, previous /ˈpɹi.vi.əs/, division /dɪˈvɪʒn̩/

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, fraction, minus, divide 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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