跟讀練習: Math Antics - Finding A Percent Of A Number - 通過影片學習英語口語
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Hi and welcome to Math Antics.
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In today’s video, we’re gonna learn how to do one of the most common calculations with percentages.
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We’re gonna learn how to find a percent of a number.
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But what does that even mean?
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Do numbers have percents that they hide somewhere and then we have to go looking for them like a game of hide and seek?
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Gottch ya! Umm - not exactly.
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Finding a percent of a number makes more sense if you remember that a number just represents an amount and that a percent is really just a fraction.
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So finding a percent of a number really means finding a fraction of an amount.
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Think about it this way… Let’s say the number 20 represents an amount, like the amount of lady bugs that you found at the park one day.
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And let’s also imagine that you agreed to give 25% of all the lady bugs you found to your little sister.
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Okay then, so how many is that?
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If you have 20 lady bugs, how many is 25% of that amount?
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That’s what it means to find a percent of a number.
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You’re finding out how much that percent (or fraction) of the total is.
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In this case, since our total is 20, we need to know what 25% of 20 is.
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So how do we figure that out?
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Well, it’s really easy if you remember back to one of our fractions videos; the one about multiplying fractions.
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In that video, we learned that when dealing with fractions, sometimes the word “of” is used instead of the multiplication symbol.
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When they say find 1/2 of 16, they really mean find 1/2 times 16.
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Well guess what… Since a percent is just a special fraction… “of” means the exact same thing with percents that it did with fractions.
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When we have 25% of 20, that means the same as 25% times 20.
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Great! So all we have to do to find a percent of a number is to multiply.
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But how do we multiply a percent and a number together?
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Do we just forget about the percent sign and multiply the numbers together?
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No! If we did it that way, our answer would be WAY too big.
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25% should be a smaller part (or fraction) of 20 lady bugs.
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But if we did 25 times 20, we’d get 500 lady bugs!! Clearly that’s not the right answer!
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Here’s what we have to do instead...
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Remember that when you see a percent written like this with the percent sign, it’s an abbreviation for a fraction; in this case, 25 over 100.
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So we need to use that fraction form when we multiply since we’re really multiplying by a fraction.
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Now some of you may also remember that percents have a decimal form. We’ll get to that in just a minute.
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Okay then, if we use the fraction form of our percent, then our problem becomes: 25/100 times 20.
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Now that’s a problem we know how to do.
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To multiply fractions, we just multiply the top numbers, and then we multiply the bottom numbers to get the answer.
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And we can just write 20 as a fraction by putting a 1 as the bottom number, because 20 over 1 is the exact same value as 20.
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So, let’s go ahead and multiply.
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On the top, we have 25 × 20 which gives us 500.
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And on the bottom, we have 100 × 1 which is just 100.
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So our answer is 500 over 100.
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Now 500 over 100 might seem like a strange answer, but that’s just because we still need to simplify it.
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500 over 100 simplifies to 5 over 1, and 5 over 1 is just 5.
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That’s much better. So, 25% of 20 is 5.
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Alright, so to find a percent of a number, we just need to multiply the fraction form of the percent by the number and we have our answer.
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But, there’s another slightly different method that you can use that works especially well if you’re allowed to use a calculator.
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In our first percentages video, we learned that percents have both a fraction form and a decimal form.
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We’ve already seen how we can use the fraction form to find a percent of a number, but we can also use the decimal form if we want to instead.
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The procedure starts the same. If you need to find 25% of 20, you first replace the word “of” with the multiplication symbol.
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Next, we’ll replace the percent, but with its decimal form this time. 25% is the same as the decimal 0.25 Then, all we have to do is multiply.
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And although I could easily do the decimal multiplication by hand, I happen to have a calculator, so I’m gonna use it.
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I just enter 0.25 × 20, hit equals, and I get 5.
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Yep - That’s the same answer we got when we used the fraction form of 25%. Oh Yeah!
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So that’s how you find a percent of a number. You just multiply the number by either the fraction form OR the decimal form of the percent.
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Either way will give you the right answer, so you can choose whichever will be easier for you to do.
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Let’s see a couple more examples before you practice on your own.
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This next one involves money.
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Pretend that your best friend has a job walking dogs and offers to give you 35% of whatever he earns if you help walk some of the dogs.
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If your friend earns $80 that week, how much of the money will you get?
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In other words, you need to figure out what 35% of 80 is.
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Okay then, let’s start by replacing the “of” with the times symbol.
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And next we have to decide if we want to replace the percent with its fraction form or its decimal form.
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I think I’ll use the decimal form for this one which means I'll replace the 35% with 0.35 Now, all we have to do is multiply 0.35 times 80, and that’s 28.
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That means you’ll get 28 dollars if you help your friend walk those dog.
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Cha-ching! Okay then… In the last two problems, we found a percent of a number, which, like we learned at the beginning of the video, just means finding a fraction of an amount.
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And like you’d expect when finding a fraction of something, the answer was smaller than the amount we started with.
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But remember, fractions can be ‘improper’ too which means that their value is greater than 1.
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And in the same way, percents can be greater than 100%. So you might come across situations like this… Suppose that last year, your school had 400 students, but this year it has 120% of that amount.
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Well, 100% would mean the exact same number of students as last year, so 120% must mean that there’s more students now, but how many students?
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To find out, we need to calculate what 120% of 400 is.
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Great, we know just how to do that.
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We just multiply 400 by the fraction form OR the decimal form of 120%.
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Let’s use the decimal form again.
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To get the decimal form of 120%, we move the decimal point over 2 places to the left, and we get 1.20 So we multiply 1.20 times 400 which gives us 480.
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So this year there’s 480 students at school.
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Alright then, that’s how you find the percent of a number.
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And it’s a really useful math skill that has a LOT of real-life applications so it’s important to learn how to do it right.
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As always, the best way to learn math is to practice on your own.
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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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背景與脈絡
在這段影片中，講解者以輕鬆幽默的方式介紹瞭如何找出一個數字的百分比。通過生動的例子，講解者讓觀眾明白百分比不僅僅是數字背後的簡單抽象，而是可以通過具體的計算理解的實際數量。學習這種計算方法對日常生活中的交流、購物或決策判斷非常有幫助。使用本網站的shadowing site，能讓你更好地理解和應用這些概念。
日常交流中的五個重要短語
- 找到數字的百分比 - 解釋如何計算一個數值的特定百分比。
- 把“的”換成乘法符號 - 強調在解決百分比時需要進行乘法的步驟。
- 使用分數形式 - 根據講解，將百分比用分數表達，幫助理解乘法過程。
- 簡化結果 - 計算完成後，不要忘記簡化分數，以得出更易讀的結果。
- 選擇數字形式 - 當處理百分比計算時，可以選擇使用小數形式，特別是使用計算器時。
逐步跟讀指南
為了幫助你在理解這段影片內容的過程中提高英語口語技巧，以下是逐步操作的方法：
- 第一步：仔細觀看影片，理解講解者的表達和語調。儘量模仿講解者的口音和語速。
- 第二步：使用shadowspeak或shadow speech技術，試圖同時重複講解者的每個句子。專注於語音的音調和節奏。
- 第三步：記錄下來自己的聲音，與原影片進行對比，找出需要改進的地方。注意語句的流利度和發音準確性。
- 第四步：選擇前面提到的五個短語進行迴圈練習，持續重複並使用不同的場景進行練習，直到在交流中能流利自如地使用它們。
- 第五步：利用社群的資源，與他人討論這些概念，分享計算百分比的實際經驗，增強學習的樂趣與實用性。
通過以上的練習，你將能夠更自信地使用與百分比相關的英語表達，同時提升你的英語口語能力。記得常常訪問我們的shadowspeaks資源，獲取更多學習啟發！
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 |
|---|---|
| 條件句 if + 從句，will/would + 動詞 — 條件及其結果 | if we did 25 times 20, we'd get |
| 定語從句 who / which + 從句 — 補充說明人或事物 | one which means · too which means |
| 用 “might / may” 表可能 might/may + 動詞 — 有可能但不確定的事 | may also remember · might seem · might come |
| 比較級 -er than / more … than — 比較兩個事物 | smaller than · greater than |
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。