跟讀練習: Math Antics - Percents And Equivalent Fractions - 通過影片學習英語口語
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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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背景與背景
在這段影片中，講者通過簡單易懂的方式介紹了百分比和等值分數的概念。通過數學應用，他揭示瞭如何在不同的情境中使用百分比，儘管這些情境中的總量可能並不總是100。對此，講者用了多個例項，使得觀眾能夠更好地理解如何將這些數學概念應用於實際生活中。這種講解不僅讓數學變得生動，也為學習者提供了一個提高英語口語和數學邏輯思維的機會，非常適合那些希望通過看YouTube學英語的人群。
日常交流的五個常用短語
- 百分比是特殊的分數。
- 如何使用百分比來描述情況。
- 等值分數代表相同的數量或價值。
- 分數簡化的基本方法。
- 將分數轉換為百分比以便比較。
逐步練習指導
掌握這段影片中的數學概念，尤其是百分比和等值分數，對於學習者來說可能有一定的挑戰。以下是一些 英語影子跟讀 的步驟，幫助您更好地理解內容：
- 先觀看影片：觀看影片的第一遍，關注講者的演講風格和內容，儘量理解整個概念。
- 逐句跟讀：之後，選擇影片中的一句話，暫停影片並模仿講者的發音和語調。這可以幫助您在英語口語練習中建立信心。
- 分析關鍵點：對照影片內容，思考其中的關鍵概念，比如如何從50個問題中得出90%的得分。理解這些關鍵點是提高英語聽說能力的基礎。
- 反覆練習：不斷重複這個過程，直到您可以流利地說出相應的句子。這也是雅思口語練習中常用的方法。
- 自我測試：最後，可以嘗試用自己的話解釋這些概念，看看能否用不同的表述方式傳達相同的意思。
通過以上的練習，學習者們能在掌握數學知識的同時，自然提高他們的英語口語能力，為日常交流打下堅實的基礎。嘗試堅持不懈地進行shadow speech和影子跟讀，相信您會看到顯著的進步！
影片中的語法
說話人最常用的結構，並附上影片中的原話：
| 結構 | 影片中的用法 |
|---|---|
| 用 “might / may” 表可能 might/may + 動詞 — 有可能但不確定的事 | might already know · might look |
| 現在進行時 am/is/are + -ing — 此刻或近期正在發生的事 | we're doing · you're thinking · you're always hearing |
| “will” 表將來 will + 動詞 — 決定、承諾或預測 | he'll give · won't be · we'll get |
什麼是跟讀法？
跟讀法 (Shadowing) 是一種有科學依據的語言學習技巧，最初開發用於專業口譯員的培訓，並由多語言者Alexander Arguelles博士普及。這個方法簡單而強大：您在聽英語母語原聲的同時立即大聲重複——就像是一個延遲1-2秒緊跟說話者的影子。與被動聽力或語法練習不同，跟讀法強迫您的大腦和口腔肌肉同時處理並模模擬實的講話模式。研究表明它能顯著提高發音準確性，語調，節奏，連讀，聽力理解和口語流利度——使其成為雅思口語備考和真實英語交流最有效的方法之一。