跟讀練習: Math Antics - Calculating Percent Change - 通過影片學習英語口語
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So, with a customer acquisition cost of $35 ,000, and a weighted sales pipeline of $1 .2 ,000, and a monthly recurring revenue of $2 .4 million,
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we had net sales go from 4 .9 million APR to approximately 5 .1 million per capita.
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But what about the percent change?
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Ah, yes, percent change.
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It's always good to know percent change.
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I'll explain that all to you right now.
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Oh, sorry, I'm getting a phone call.
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I got to take this, but then I'll explain all that percent change to you.
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Hi, I'm Rob.
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Welcome to Math Antics.
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In this lesson, we're going to learn how to calculate percent increase and decrease, known collectively as percent change.
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If you're not very familiar with percents, I'd highly recommend watching some of our other videos about them before continuing on.
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Lots of times, when you have a change in value, you just say how much something goes up or down in absolute terms,
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like: "The population of this city increased by a thousand people." or the cost of this shirt decreased by $15.
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But you can also express those sorts of changes in relative terms using percentages.
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Unlike an absolute change, a percent change always relates the amount of change to the number 100.
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The term 'percent' literally means 'per 100'.
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So 'percent change' means 'per 100 change' or the change 'per 100'.
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So let's start by imagining that you have 100 of something.
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Like 100 bucks.
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Oh yeah!
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If you start out with 100, but then you get 20 more, that would be a 20 % increase, because the amount went up by 20 per the original 100.
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Likewise, if you start out with exactly 100 bucks but then you lose 15, that would be a 15 % decrease because it went down by 15 per the original 100.
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So as you can see, it's pretty easy to figure out the percent change when the original amount is exactly 100.
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But you don't have to start with 100 to express change as a percentage.
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Almost any original value and any amount of change can be represented as a percent change thanks to equivalent fractions.
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For example, instead of $100, suppose that you start out with $750.
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Then imagine that you get $150 more.
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What percent increase is that?
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To figure that out, let's use a simple diagram.
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This blue bar represents the original $750.
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And this green bar represents the $150 increase.
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Now let's use our imagination and ask, "What if that original amount was only $100?" what would the equivalent change in value be?
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Basically, we're asking: If you had the fraction 150 over 750,
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what would an equivalent fraction be that has 100 as the bottom number?
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Put another way, if you have 750 and get 150 more, it's equivalent to having 100 and getting 'x' more.
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We're using the letter 'x' to temporarily represent the missing value.
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The top number of the original fraction is the absolute change.
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and the top number of the equivalent fraction is the percent change.
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So let's figure out what the missing value is in two different ways.
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First, visually using our diagram, and second, using simple arithmetic.
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By definition, if you divide any amount up into 10 equal parts, then each one of those parts will be 10 % of the original amount.
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So, if you divided the original $750 up into 10 equal amounts, Each of those amounts would be $75.
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That means that a $75 increase would be equivalent to a 10 % increase.
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Of course, we had an increase of $150, not $75.
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150 is exactly 75 plus 75, so that would be another 10 % of the original amount.
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As you can see from the diagram, if you start with 750 and then you get 150 more, that's equivalent to starting with 100 and getting 20 more.
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In other words, it's a 20 % increase.
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Now let's see how we could get that same answer without using a diagram.
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Using a little basic algebra, we can solve for the unknown value x, All we need to do is multiply both sides of the equation by 100.
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Doing that gives us x all by itself on this side of the equation because the 100 over 100 cancels out.
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And on the other side, we have the change in value divided by the original value all times 100.
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Using a calculator, 150 divided by 750 equals 0 .2 and 0 .2 times 100 equals 20,
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or 20 percent, which is the exact same answer we got from our diagram.
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So the formula for calculating percent change is simple:
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All you have to do is take the absolute change and divide that by the original amount, and then multiply the result by 100.
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This formula may look even more intuitive to you if we put it back in the equivalent fraction form.
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These are just two different ways of writing the exact same relationship.
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Now that we have a formula for calculating percent change, let's try using it in a couple quick examples.
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Suppose a doggy daycare takes care of 25 dogs on Friday, but on Saturday, three more dogs join the group.
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What percent increase is that?
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Well, the original amount of dogs is 25 and the change in dogs is +3.
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According to our formula, we just need to divide the change by the original
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and multiply it by 100 to get the percent change.
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Using a calculator, we get 3 divided by 25 equals 0 .12.
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and then 0 .12 times 100 equals 12.
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That means the number of dogs at the daycare increased by 12 % from Friday to Saturday.
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That was pretty easy, but what about this example?
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Suppose you want to buy a pair of shoes that cost $65.
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but you have a discount coupon that will reduce the price by $15.
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What would the percent decrease in price be if you use your coupon?
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Well, the original price is $65 and the change in price will be -15.
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It's negative because it's a decrease.
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So let's plug those numbers into our formula.
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That gives us percent change equals negative 15 divided by 65 times 100.
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Again, using a calculator, negative 15 divided by 65 equals negative 0 .23 rounded off to two decimal places.
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And negative 0 .23 times 100 equals negative 23.
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so the coupon will decrease the price of the shoes by 23%.
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Okay, so if you're given an original amount and told how much that amount changes, it's really easy to calculate the percent change using this simple formula.
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But sometimes math problems don't tell you what the absolute change in a value is.
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Instead, they just give you an original value and a new value.
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In that case, you need to calculate the change yourself.
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Here's how you do that: Suppose you're given a problem that says last year your school had 420 students, but this year it has 441 students.
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What's the percent change in student population?
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This problem doesn't directly say what the absolute change in student population was.
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It just tells us what the value was originally and what it is now.
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We know that there was a change because of the difference in the numbers.
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And in math, what does the word "difference" make you think of?
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Yep, subtraction.
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We can figure out the absolute change just by subtracting.
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But order matters in subtraction.
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So should we subtract the original amount from the new amount or the new amount from the original amount?
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Well, the standard way of doing it is to start with the new amount and subtract the original amount from it.
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If the new amount is bigger than the original, the answer you get will be a positive number.
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which means that you have a percent increase.
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But if the new amount is smaller than the original, the answer you get will be a negative number, which means you have a percent decrease.
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So if we do that, we have 441 minus 420, which is positive 21.
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So we have an increase of 21 students.
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Positive 21 divided by the original amount, 420, equals positive 0 .05.
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and 0 .05 times 100 equals 5.
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Since that's positive, we have a 5 % increase in students.
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But what if you subtracted in the wrong order and got negative 21 instead?
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If you plug that into the formula for percent change, you'll get -21 divided by 420 which equals -0 .05.
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and then multiplying by 100 gives you -5, which suggests a 5 % decrease because the sign is negative.
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But, since you're paying attention, you'll realize that you couldn't possibly have a 5 % decrease in students since the number got bigger over time.
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The problem tells us that it was 420 last year and this year it's 441.
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So you must really have a 5 % increase.
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The point here is that in math, it's always important to use your intuition and ask yourself if an answer makes sense,
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rather than simply trying to memorize a formula without thinking about what it really means.
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And speaking of intuition, before we wrap up, I want to explore just a few more situations that will hopefully give you a better intuition about percent increase and decrease.
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First, let's consider the case where you start with 1 of something and end up with 2.
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What would the percent increase be?
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Well, the original amount is 1, and the change is also 1.
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Plugging those numbers into the formula gives 1 over 1 times 100, which simplifies to 100.
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So the percent increase is 100%.
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That may seem kind of odd, but it makes total sense if you think about it.
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If you have 1 and then you get 1 more, you're gaining 100 % of what you started with.
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And that's true any time the original amount doubles.
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If you start with 2 and get 2 more, for a total of 4, the increase is 100 % because 2 divided by 2 times 100 is 100.
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And if you start with 5 and then get 5 more, for a total of 10, The increase is 100%.
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because 5 divided by 5 times 100 is also 100.
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So anytime the original amount you have doubles, it's an increase of 100%.
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But what if you start with 2 and then end up with 1?
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Considering what we just learned, you might be tempted to think that that's a decrease of 100%.
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But if we use our formula, we'll see that that's not the case.
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Since the original amount is 2, we put a 2 on the bottom of the fraction.
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and the change is -1 since we decreased from 2 to 1.
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So a negative 1 goes up on top.
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Now, if we simplify, we get negative 1 divided by 2, which is negative 0 .5.
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and negative 0 .5 times 100 is negative 50 or a 50 % decrease.
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The reason that the percent changes are different in these two cases, doubling the amount versus cutting it in half, is that the percent change always compares the change to the original amounts,
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which are different in these two cases.
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Finally, let's determine what the percent increase would be if you start with 1 and end up with 3.
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And conversely, what would the percent decrease be if you start with 3 and end up with 1?
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In the first case, the change is positive 2 and in the second case, it's negative 2.
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Let's plug those values into our formula for percent change, along with the original values in each case, and see what answers we get.
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Going from 1 to 3, positive 2 divided by 1 times 100 equals 200, or a 200 % increase.
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And, going from 3 to 1, -2 divided by 3 times 100 equals -67, rounded to the nearest whole number,
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or a 67 % decrease.
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Again, even though the magnitude of the change was the same, the percent changes are different because we started out with different original amounts.
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And this example also shows that you can get a percent change that's greater than 100%.
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Alright, so now you know what percent change is and how to calculate it.
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The formula for calculating it is pretty simple, so you should be able to remember it after you've used it on several problems.
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And that's the key to learning math.
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You can't just watch videos about it.
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You need to actually use it to solve problems.
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So, be sure to practice what you've learned in this video!
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As always, thanks for watching Math Antics, and I'll see you next time!
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That's what my calculator says.
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Learn more at MathAntics .com.
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背景與上下文
在這段影片中，主持人Rob以幽默的方式介紹瞭如何計算規模變化（percent change），這在我們的日常生活中非常重要，無論是商業、經濟還是個人財務。Rob以簡單的示例開始，講解了如何使用百分比來表達增加或減少的量。這種能力將幫助你有效地進行日常溝通和專業討論。為了更好地理解和掌握這些知識，建議您通過跟隨該影片進行跟讀練習，提升您的英語發音和流利度。
日常交流的五個常用短語
- 增加了多少？（How much did it increase?）
- 減少了多少？（How much did it decrease?）
- 我最開始有100。（I originally had 100.）
- 這相當於哪些變化？（What does that equate to?）
- 我們來計算一下。（Let’s calculate it.）
逐步影子跟讀指南
要更有效地掌握影片中的內容和表達方式，您可以採用以下逐步影子跟讀方法：
- 步驟一：觀看影片前，請先調節音量，確保您能清晰聽到Rob的講解。
- 步驟二：首次觀看時，專注於理解語速和發音。可以適當暫停影片以便跟上內容。
- 步驟三：在觀看的同時，嘗試重複Rob的每一句話，模仿他的語音語調，以提高您的英語發音。
- 步驟四：可使用英語影子跟讀技術，即逐句跟讀並儘量同步說出，幫助您的口語流利度。
- 步驟五：反覆觀看影片，特別關注其中的短語和句子。這將有助於您擴大詞彙量，實現跟讀效果的最大化。
通過利用這樣的影子跟讀技巧，結合多次觀看看YouTube學英語的內容，您不僅可以提高英語發音，還能夠在實際交流中更自信地使用這些表達。
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 use our formula, we'll see |
| 被動語態 be + 過去分詞 — 強調發生了什麼，而不是誰做的 | can be represented · might be tempted |
| 定語從句 who / which + 從句 — 補充說明人或事物 | percent, which is · number, which means |
| 用 “might / may” 表可能 might/may + 動詞 — 有可能但不確定的事 | may look · may seem · might be |
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。