쉐도잉 연습: Math Antics - What Percent Is It? - 영상으로 영어 말하기 배우기
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Hi! Welcome to Math Antics.
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In this video, we’re gonna learn how to do another common type of problem involving percents.
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We’re gonna learn how to figure out, “What percent is it?” In our last video, we learned how to do a really common percent problem which was finding a percent of a number.
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For example, we learned how you could solve a problem like, “What is 20% of 50?” And the answer to that problem is 10.
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So we could say that, “10 is 20% of 50” Let’s look closely at that statement for a minute.
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Notice that there’s three different numbers in it: 10, 20 and 50.
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That’s because a percentage is really a relationship between 3 numbers.
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Well, actually it’s a relationship between 4 numbers, but the forth number is always 100, so you always know it.
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To see what I mean, think back to our video about percents and equivalent fractions.
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In that video, we learned that a percent is really an equivalent fraction that has 100 as the bottom number.
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So we could rewrite our statement like this: 10 over 50 equals 20 over 100.
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This is exactly the same as saying that 10 is 20 PER-CENT of 50.
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So these are the four components of a percent problem.
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But since we know that 100 is always gonna be the bottom number of this equivalent fraction (the percent) we can just rewrite it using the percent symbol.
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That way we can focus on the other three numbers that can change.
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And we’re gonna give each one of these three numbers a name so that we don’t get confused.
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We’re gonna call the top number of the fraction, “the part we have’” or just the “part” for short.
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And we’re gonna call the bottom number the “total”, and we’re gonna call the number in front of the percent sign the “percent’” (or percentage).
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And since there’s three different numbers that can change in a percentage problem, that means there’s three different questions that you can ask.
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To see these three questions let’s rewrite our original statement (10 is 20% of 50) three different times.
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But in the first statement, we replace the ‘10’ with ‘what’ and it becomes, “what is 20% of 50” In the second statement, we replace the ’20’ with ‘what’ and it becomes, “10 is what % of 50”.
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And in the third statement, we replace the ’50’ with ‘what’ and it becomes, “10 is 20% of what?” Doing this is helpful because, whenever you're given a problem involving percents, the first thing you need to figure out is WHAT the problem is asking you to find.
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...ya know… which number is missing?
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In the first statement, the ‘part we have’ is missing.
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In the second statement, the ‘percent’ is missing.
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And in the third statement, the ‘total’ is missing.
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And these three statements represent the three most common types of percentage problems.
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The first type is what we learned in the last video, “Finding a Percent of a Number”.
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In this type of problem, we know the percent and we know the total, but we don’t know what part of that total we have.
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The second type of problem is what we’re gonna learn in this video.
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In this type of problem, we know both the total, and we know what part of that total we have.
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But we need to figure out what percentage of the total that part is.
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We need to find, “What percent is it?” And the third type of problem is what we’ll learn in the next video.
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For that type of problem, we know what part we have and we know what percent of the total it is.
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We just don’t know the total itself.
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Have I lost you yet?
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Don’t worry - it’ll make a lot more sense after we look at a few examples.
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So, let’s look at an example of a “type 2” problem, where we know the part we have and we know the total, but we don’t know what the percent is.
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This example is a word problem and it says: Your uncle, who really likes to travel, has visited 35 of the 50 U.S. states.
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What percent of the states has he visited?
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The key words in this problem are, “what percent” because they let us know that it’s the percent that’s missing.
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So the two numbers that it gives us must be the ‘total’, and the ‘part we have’.
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Well… in this case, it’s not really the part we have… it’s the part that our uncle has visited, but you get the idea.
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And sometimes it can be hard to tell which number the total is.
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Often it’s the bigger number, but not always.
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And that’s where the word ‘“of” can help us out.
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The word “of” usually goes in front of the number that’s the total.
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So when you see “…OF the 50 US states”, it’s a clue that 50 is the total.
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Alright then, so we put 50 on the bottom of the fraction and 35 on top.
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Now we’re ready to figure out the part we don’t know; the percent.
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To find the percent, all we need to do is convert the fraction into its percent form.
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That means we need to convert it into an equivalent fraction that has 100 as the bottom number.
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Well, one way we could do that would be to look for a number that we could multiply both the top and bottom numbers by that would change the bottom number into 100.
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Well the number 2 looks like it would work.
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If we multiply the bottom by 2 (2 × 50 gives us 100) and then we also need to multiply the top by 2 (and 2 × 35 = 70).
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So now we can see that 70 over 100 is equivalent to 35 over 50, and since 70 over 100 is just 70% it means our uncle has visited 70% of the states.
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And all I got was this lousy tee-shirt.
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Alright, that way of finding a percent seems pretty easy.
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You just write the numbers that you know as a fraction, and then convert that fraction into an equivalent fraction with 100 as the bottom number.
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And that tells you what percent it is.
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The trouble is, that way is only easy if it’s easy to change the bottom number into 100.
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For example, what if instead of 50, you had 80 as the bottom number?
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What could you multiply 80 by to get 100? Well, that’s not as easy to figure out.
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So, even though finding an equivalent fraction is sometimes a good way to convert a fraction into a percent form, I’m gonna show you another way that I think is even better.
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This second way is based on the fact that a fraction is just a division problem where the top number is divided by the bottom number.
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If you do the division, you’ll end up with the decimal value of the fraction.
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And as we saw in our first video about percents, it’s easy to convert from a decimal value into a percent.
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You just move the decimal point two places to the right, which is the same as multiplying by 100.
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The only drawback to finding the percent this way is that it involves division, and division can sometimes be tricky if you don’t have a calculator.
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But if you do have a calculator, or if you’re really good at long division, then this way works best.
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To see this way in action, let’s try this word problem: Your Aunt has baked 80 cookies, and (because she’s a very nice Aunt) she gave you 28 to take home with you.
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What percent of the cookies did she give you?
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Okay, so we know that the total is 80, and that the part we got was 28.
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That means that our fraction will be 28 over 80.
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Using our calculator, we enter 28 divided by 80 and we get 0.35 That’s the decimal form of the fraction.
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And now, to go from the decimal form to a percent, we just move the decimal two places to the right. That gives us 35.
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So, when our Aunt gave us 28 out of the 80 cookies, she gave us 35% of the cookies that she baked.
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Mmmm… mmm….. Oh!
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Alright, so… That’s how you find out “What percent is it?” You make a fraction from the part you have and from the total, and then you convert that fraction into its percent form, either by figuring out what the equivalent fraction would be or by just dividing to get the decimal value and turning that into a percent.
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Now, this was kind of a complicated lesson, so don’t worry if you're still a little confused.
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There’s two things that you can do that will help make it clearer.
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First, you can re-watch the video to catch anything you might have missed the first time through.
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And second, you can practice using the procedures on your own, which will really help you understand them better.
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Good luck, and as always, 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 비율 문제를 해결하는 방법을 배우게 됩니다. 특히, 비율이 무엇인지, 그리고 특정 부분을 알고 있을 때 전체와의 관계를 통해 비율을 찾는 방법을 집중적으로 다룰 것입니다. 예를 들어, "50개 주 중에서 35개 주를 방문한 경우, 몇 퍼센트인가?"와 같은 문제를 해결하는 데 필요한 기초를 마련할 수 있습니다. 이 수업을 통해 비율을 구하는 세 가지 기본 질문을 이해하고, 각 질문에 따른 해결 방법을 학습할 것입니다.
주요 어휘 및 구문
- 퍼센트 (percent): 비율을 나타내는 수치
- 전체 (total): 비율을 계산할 때의 전체 수치
- 부분 (part): 주어진 전체 중의 특정 수치
- 무엇 (what): 문제가 요구하는 숫자
- 방문하다 (visited): 어떤 장소나 사물을 경험하다
- 주 (states): 미국의 주를 의미
- 의 (of): 특정한 관계를 나타내는 전치사
연습 팁
이번 비디오에서 다루는 내용은 조금 빠를 수 있지만, 영어 쉐도잉 기법을 활용하면 많은 도움이 될 것입니다. 비디오의 특정 구간을 반복해서 시청하면서, 강사의 발음을 따라 해보세요. 쉬운 문장부터 시작하여 점차 긴 문장으로 나아가며 연습하는 것이 좋습니다. shadowspeaks 기법을 적용해 보세요. 강사의 톤과 리듬을 맞추면, 자연스럽게 영어 회화 연습이 가능합니다. 특히 비율 문제와 같은 수학적인 개념을 설명하는 경우, 이해를 돕기 위해 다양한 예시를 함께 듣는 것이 중요합니다. 이런 방법을 통해 IELTS 스피킹에서 발생할 수 있는 수학 관련 질문에 자신감을 가질 수 있게 될 것입니다.
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.