跟读练习: Math Antics - What Percent Is It? - 通过视频学习英语口语
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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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为什么要通过这个视频练习口语？
这个视频提供了一个很好的机会，让学习者在实际语境中练习英语口语。通过与视频内容进行互动，你可以提高自己的听力理解能力，并帮助你更流利地表达自己的想法。视频中涉及的百分比问题可以很容易地转化为日常生活中的实际应用场景，练习这些内容能增强你的自信心，尤其是在雅思口语练习中，这一点尤为重要。同时，通过英语影子跟读，你可以更好地模仿发音和语调，从而提升你的发音能力。
语法和表达的实际应用
视频中使用了几个关键的语法结构，有助于学习者理解和实践：
- What is ...? - 用于提出问题，例如 “What percent is it?”，这种结构在日常对话中非常常见。
- ... is ... of ... - 用于描述部分与整体的关系，例如 “10 is 20% of 50”。这是表达部分与整体之间关系的重要句型。
- ... is what % of ...? - 这是一种常用的提问方式，可以有效帮助你厘清问题的关键。
学习并使用这些结构，能让你的交流显得更加精准和自然，帮助你在雅思口语练习中更有条理地表达。
常见的发音陷阱
在视频中，一些词汇和表达可能会给学习者带来发音上的挑战。比如：
- percent - 这个词的发音可能较为困难，尤其是在快速交流中，容易被忽视。
- total - 此词的音节分开发音时，注意连音的标准发音，否则可能会导致理解困惑。
- what - 快速说时，基于口音的不同可能导致发音变得模糊。
在练习中，利用shadowspeak来改善这些发音问题是非常有效的。通过模仿视频中讲解者的语调和节奏，你可以提高英语发音的准确性，使交流更加流畅。
视频中的语法
说话人最常用的结构，并附上视频中的原话：
| 结构 | 视频中的用法 |
|---|---|
| 现在完成时 have/has + 过去分词 — 过去发生但与现在仍有关联的事 | has visited · has baked |
| 定语从句 who / which + 从句 — 补充说明人或事物 | problem which was · right, which is · own, which will |
| “going to” 表将来 be going to + 动词 — 计划或明显即将发生的事 | gonna learn · gonna be · gonna give |
| “will” 表将来 will + 动词 — 决定、承诺或预测 | we'll learn · it'll make · you'll end |
什么是跟读法？
跟读法 (Shadowing) 是一种有科学依据的语言学习技巧，最初开发用于专业口译员的培训，并由多语言者Alexander Arguelles博士普及。这个方法简单而强大：您在听英语母语原声的同时立即大声重复——就像是一个延迟1-2秒紧跟说话者的影子。与被动听力或语法练习不同，跟读法强迫您的大脑和口腔肌肉同时处理并模仿真实的讲话模式。研究表明它能显着提高发音准确性，语调，节奏，连读，听力理解和口语流利度——使其成为雅思口语备考和真实英语交流最有效的方法之一。