쉐도잉 연습: Math Antics - Percents And Equivalent Fractions - 영상으로 영어 말하기 배우기
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Hi! Welcome to Math Antics.
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In our first video about percents, we learned that a percent is just a special fraction that always has 100 as the bottom number.
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So that’s simple enough, but it brings up a very important question.
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If a percent always has 100 as the bottom number, then how can we use percents in situations that don’t involve 100 things?
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Like if you score a 90% on a test, but the test only had 50 questions on it.
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90% means 90 out of 100, but how can you get 90 questions right if there's only 50 on the test?
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Or what if your friend says that he’ll give you 50% of his candy bar.
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50% means 50 out of 100. But how can he give you 50% if does’t have 100 candy bars? He’s only got 1.
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Or, how about when your talking about things bigger than 100?
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…like if you hear on the news that 65% of Americans like watching football.
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65% is 65 out of 100, but I’m pretty sure there’s more than 100 Americans!
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The fact is that percents are used all the time to describe situation where the total involved is either more or less than 100, so how does that all work?
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Well, the key to understanding how percents can be used in all these situations is to realize that percents are equivalent fractions.
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You might already know that equivalent fractions are fractions that represent the same amount or value, but they do it with different top and bottom numbers.
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A simple example of equivalent fractions is 1 over 2 and 2 over 4.
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These fractions both represent the same value but they use different numbers to do it.
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And that’s how percents can be used even if the total isn’t 100.
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A percent is an equivalent fraction that tells you how much you’d have IF the total WAS 100.
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In the case of one-half, another equivalent fraction would be 50 over 100 because 50 is half of 100.
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But as you learned in the last video, 50 over 100 is a percent, and that’s why 50% of a candy bar is the same as half of the candy bar.
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To see this even more clearly, let’s think about that test I mentioned where you got a score of 90%.
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90% is the same as the fraction 90 over 100. But since the test really only had 50 questions, the actual score must be an equivalent fraction with 50 as the bottom number.
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And even though we don’t know what the top number would be, we can figure it out because we know that our actual score is equivalent to 90 over 100.
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To show you how, let’s review one of the easiest ways to get a fraction that is equivalent to another fraction.
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If you multiply the top and bottom numbers of a fraction by the same number, the result we be equivalent to the original fraction.
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For example, if you have the fraction 2 over 3, you could make an equivalent fraction by multiplying the top by 4, AND the bottom by 4.
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You have to do the same thing to both the top and bottom numbers or the result won’t be equivalent.
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On the top, 2 × 4 = 8 and on the bottom, 3 × 4 = 12.
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So the fractions 2 over 3, and 8 over 12 are equivalent fractions.
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And, you can also make an equivalent fraction by dividing both the top and bottom numbers by the same number.
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This is really what we’re doing when we simplify a fraction.
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For example, if you have the fraction 6 over 20, you could divide the top and bottom numbers by 2, since they're both even numbers.
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On the top you’d have 6 divided by 2 which is 3, and on the bottom you’d have 20 divided by 2 which is 10.
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So 6 over 20, and 3 over 10 are equivalent fraction.
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And now that we know how to do that, we can figure out what our actual test score was.
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Notice the relationship between our fractions’ bottom numbers, 50 is exactly half of 100 so we could go from 100 to 50 by dividing by 2.
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And that means, if we do the same thing to the top number we’ll get the top number of the equivalent fraction.
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And since 90 divided by 2 is 45, 45 over 50 is equivalent to 90 over 100.
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And now we know that our actual test score must have been 45 out of 50.
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Okay, now I know what you're thinking.
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If our actual score was 45 out of 50, why not just leave it like that? Why did our teacher convert it into a percentage?
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Well, one important reason is that converting things into percents makes them easier to compare.
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For example, suppose a student took five different tests during the school year and each test had a different number of questions.
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Here’s the scores they got on those 5 tests: 40 out of 80, 18 out of 30, 12 out of 16, 96 out of 120, and 19 out of 20.
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Since each test score looks really different, it’s not so easy to tell how well the student did or to see how the scores changed over time.
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But what if we convert each of these scores into an equivalent fraction with 100 as the bottom number?
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…in other words …their equivalent percent form.
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Wow! Now it’s much easier to compare the scores.
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On the first test, the student only got 50% or half correct, but they did better on each test they took during the year… 60%, 75, 80, and finally 95% on the last test.
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The reason percents can help us easily compare things is because they’re alway on the same scale that ranges from 0 to 100.
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In fact, percents are very similar to that ‘scale of 1 to 10’ that you’re always hearing about: come on… come on… yeah… go…go…go… Catch It!
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YES!! YES!!
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Oh Man!!… Did you see that?
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Oh my gosh… oh my… On a scale of 1 to 10, how awesome was that play?!
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So just like a scale of 1 to 10, percents give us a way to quantify things on a common scale using numbers that are easier for us to relate to.
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And that’s especially helpful when we're dealing with complicated numbers; like numbers that are either really small or really big.
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Remember our example about Americans and football?
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We used 65% to to describe how many like watching it.
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Well the actual numbers might look something like this: 205,636,600 over 316,364,000.
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That’s a LOT of people and that fraction is not very easy to imagine.
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But, the equivalent fraction, 65 over 100 is much easier to imagine.
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And it tells you that for every 100 Americans, 65 of them like watching football.
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Okay, now that you know that percents are really just a special kind of equivalent fraction that always has 100 as the bottom number, let’s see a few examples that are so common you should probably memorize them.
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We already saw that 1/2 is the same as 50%, because 1/2 and 50/100 are equivalent factions.
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One-fourth is the same as 25% because 1/4 and 25/100 are equivalent fractions.
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And three-fourths is the same as 75% because 3/4 and 75/100 are equivalent fractions.
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The fractions 1/3 and 2/3 are also really common, but their equivalent percents are a little different.
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That’s because the those fractions have repeating decimal values which means that the percents are also repeating: 1/3 is 33.33333% and 2/3 is 66.66666% But you can usually just round them off to 33% and 67% Alright, that’s all for this video.
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But knowing that percents are equivalent fractions will really help you understand all kinds of math problems that involve percentages.
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As always, be sure to practice what you’ve learned by doing the exercises for this section.
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Thanks for watching Math Antics, and I’ll see ya next time.
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Learn more at www.mathantics.com
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이번 수업에 대하여
이번 수업에서는 백분율과 그것의 동등한 분수에 대해 배울 것입니다. 백분율은 항상 100을 분모로 가진 특별한 분수라는 것을 이해하고, 다양한 상황에서 백분율을 어떻게 사용할 수 있는지를 배우게 됩니다. 예를 들어, 시험 점수나 친구가 줄 수 있는 사탕의 양을 백분율로 표현하는 방법을 생각해 볼 것입니다. 이를 통해 여러분은 백분율이 어떻게 다른 숫자에서도 적용될 수 있는지, 그리고 그것이 어떻게 그 상황을 설명하는 데 유용한지를 알게 됩니다.
주요 어휘 및 구문
- 백분율 (percent): 100을 분모로 가진 특별한 분수.
- 동등한 분수 (equivalent fraction): 같은 양을 나타내는 분수.
- 시험 점수 (test score): 시험에서 얻은 점수.
- 비교하다 (compare): 두 가지를 비교하기 위해 살펴보는 것.
- 정확한 점수 (actual score): 실제로 얻은 점수.
- 분수 (fraction): 전체를 나누는 방식으로 나타낸 수치.
- 변환하다 (convert): 한 형태를 다른 형태로 바꾸는 것.
- 스케일 (scale): 양의 상대적인 크기를 보여주는 기준.
연습 팁
이 비디오에서 제시된 내용을 연습하는 가장 좋은 방법은 shadow speak 기법을 사용하는 것입니다. 비디오의 속도와 음조를 잘 듣고 따라 말해보세요. 처음에는 조금 느리게 따라하면서 발음과 억양에 집중해 보세요. 영어 발음 교정을 위해 중요한 것은 소리 내어 말하는 것입니다. 또한, IELTS 스피킹과 같은 시험 준비에도 도움이 됩니다. 자신의 목소리를 녹음하여 나중에 들어보는 것도 좋은 방법입니다. 이를 통해 자신의 발음과 억양에서 개선이 필요한 부분을 파악할 수 있습니다. 계속해서 반복적으로 연습하며 자신감을 쌓아보세요.
이 영상의 문법
화자가 가장 많이 쓰는 문형을 영상 속 실제 표현과 함께 정리했습니다.
| 문형 | 영상 속 표현 |
|---|---|
| “might / may” 가능성 might/may + 동사 — 가능하지만 확실하지 않은 일 | might already know · might look |
| 현재진행 am/is/are + -ing — 지금 또는 요즘 일어나고 있는 일 | we're doing · you're thinking · you're always hearing |
| “will” 미래 will + 동사 — 결정, 약속 또는 예측 | he'll give · won't be · we'll get |
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.