跟讀練習: Adding Fractions With Unlike Denominators - 通過影片學習英語口語

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In this video, we're going to talk about how to add two fractions.

So let's start with this example.

2 over 3 plus 3 over 4.

So how can we add these two fractions?

The first thing you can do is multiply the denominators of the fractions.

3 times 4 is 12. And then cross multiply.

2 times 4 is 8, and then multiply 3 times 3, and that will give you 9.

And then you could add 8 and 9.

8 plus 9 is 17.

So we get the answer 17 over 12.

And so this is our answer as an improper fraction.

Now, let's try another example.

So let's add 5 over 3 plus 1 over 2.

So let's follow the same technique.

3 times 2 is 6. And then cross multiply.

5 times 2 is 10.

3 times 1 is 3.

And then we're going to add 10 plus 3.

So 10 plus 3 is 13.

So the answer is 13 over 6. by the way

if you want more videos on fractions let's say how to subtract fractions how to multiply

or divide fractions check out the description section of this video i'm going to post some links there

that you might find useful

but now let's get back to this video let's work on another problem

so now it's your turn go ahead and add the following fractions 2 over 5 plus 1 over 4

And also try this example, 3 over 7 plus 5 over 9.

Feel free to pause the video and try those examples.

So let's start with the first one.

So first we're going to multiply 5 and 4.

5 times 4 is 20. And then cross multiply.

2 times 4 is 8.

5 times 1 is 5.

And now we can add 8 plus 5 is 13.

So the answer is 13 over 20.

Now let's try the example below.

So let's multiply 7 by 9.

7 times 9 is 63. And then cross multiply.

3 times 9 is 27.

And 7 times 5 is 35.

So now we'll need to add 27 and 35.

So you can use a calculator or you can do it the old-fashioned way.

Let's do it the old-fashioned way.

5 plus 7 is 12, so we need to write the 2, carry over the 1.

And then 3 plus 2 plus 1 is 6.

So 27 plus 35 is 62.

So the final answer for that example is 62 divided by 63.

So at this point, you know how to add 2 fractions.

But what if you need to add, let's say, 3 fractions?

What should you do?

So before we go into this example, I want to show you another example of adding 2 fractions but using a different method.

So let's start with this problem, 3 over 8 plus 5 over 7.

So let's begin by using the method that you're familiar with

and then we'll use a new method to get the same answer.

So what we did before is multiply the two denominators of the fractions.

8 times 7 is 56.

And then we would cross multiply.

3 times 7 is 21.

And 8 times 5 is 40.

And then we would add 21 plus 40 is 61.

So our answer for this example would be 61 over 56.

Now here's another method which is useful if you're adding multiple fractions.

So what you want to do is get a common denominator of 56.

In order to do so, the fraction on the left you need to multiply the top and the bottom by 7.

And for the fraction on the right, multiply the top and the bottom by 8.

So this would give you a common denominator of 56.

So 3 times 7 is 21, and 7 times 8 is 56.

5 times 8 is 40, and on the bottom, 7 times 8 is 56.

Now whenever you're adding two fractions, if the denominator is the same, then you're allowed to add the numerators of the two fractions.

So 21 plus 40 is 61.

And thus, we're going to get the same answer of 61 over 56.

This technique works if you're adding, let's say, three fractions or even four fractions.

Now, let's try this example.

2 over 5 plus 3 over 4 plus 1 over 3.

So the first thing we need to do is identify a common denominator that we need to get to.

So we need to find the least common multiple of 5, 4, and 3.

How can we do so?

Well, a simple way is to multiply 5 times 4 times 3.

You could use any common multiple.

It doesn't really have to be the least common multiple.

But if you could find the least common multiple, then it's going to be easier.

But let's keep it simple.

so 5 times 4 times 3

5 times 4 is 20 20 times 3 is 60 so 60 is a common multiple of 5, 4, and 3 it might even be the least common multiple

and I think it is so what I'm going to do now is take 60 and divide it by 5

60 divided by 5 is 12 so therefore I'm going to multiply the second fraction, I mean the first fraction, by 12.

So that will give me a common denominator of 60.

Now 60 divided by 4 is 15.

So I need to multiply the second fraction, the top and the bottom, by 15.

Whatever you multiply the bottom of a fraction by, you need to do so also to the top.

Now 60 divided by 3 is 20.

So I'm going to multiply the third fraction by 20 over 20.

12 times 2 is 24 and we know that 12 times 5 is 60.

15 times 3 is 45 and 15 times 4 is 60.

20 times 1 is 20.

20 times 3 is 60.

So notice that we have a common denominator of 60.

So now all we need to do is add up the three numerators.

So let's find a sum of 45, 24, and 20.

5 plus 4 is 9.

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4 plus 2 plus 2 is 8.

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So 24 plus 45 plus 20 is 89.

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So our answer for this problem is 89 over 60.

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So that's how you can add three fractions together.

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Now let's try another example.

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So now it's your turn.

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Go ahead and add 1 over 4 plus 5 over 6 plus 1 over 2.

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So let's identify the least common multiple of 4, 6, and 2.

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Multiples of 6 are 6, 12, 18, 24, and so forth.

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Multiples of 4 are 4, 8, 12, 16, 20.

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Multiples of 2 are 2, 4, 6, 8, 10, 12, 14.

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So which of these are the least common multiple of 2, 4, and 6?

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Notice that 12 is the lowest common number or lowest common multiple of 2, 4, and 6.

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So therefore, 12 is the least common multiple.

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Now, 12 divided by 4 is 3.

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So I'm going to multiply this fraction by 3 over 3.

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And 12 divided by 6 is 2.

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So I'm going to multiply this second fraction by 2 over 2.

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And 12 divided by 2 is 6.

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So I'm going to multiply this fraction.

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Let's change that color. By 6 over 6.

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So I'm going to get 3 over 12 plus 2 times 5 is 10.

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2 times 6 is 12.

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and then 6 times 1 is 6, 6 times 2 is 12.

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So now we need to add.

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3 plus 10 is 13.

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13 plus 6 is 19.

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So the final answer is 19 over 12.

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So that is it for this video.

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Be sure to check out my next video on subtracting fractions.

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I'm going to post some links in the description section of this video, so feel free to take a look at that.

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Thank you.

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本節課你將練習什麼？

這節課我們通過學習“異分母分數相加”的方法，同時提升英語聽力和口語能力。你會跟著影片中的講解，一邊理解數學知識，一邊練習英語表達，尤其是如何清晰描述計算步驟。通過影子跟讀（shadow speech），你能逐漸跟上影片的語速，提高英語發音的準確性，還能學會用英語講解數學問題呢！

核心詞彙與表達

fractions：分數
denominators：分母
cross multiply：交叉相乘
improper fraction：假分數
carry over：進位
shadow speech：影子跟讀

影子跟讀練習技巧

影片中的講解語速適中，語氣清晰，非常適合進行英語影子跟讀（英語影子跟讀）練習。建議你先完整聽一遍，熟悉內容後，嘗試滯後1-2秒跟讀。注意模仿說話人的語調，比如講解計算步驟時的停頓和重音（如“cross multiply”中的重音在“cross”）。練習時可以把重點放在“如何用英語描述分數加法”上，比如“3 times 4 is 12”“add 8 and 9”這樣的表達。堅持用shadow peaks方法練習，不僅能提高英語發音，還能讓你更自信地用英語表達數學思維。別擔心出錯，慢慢來，你會越練越好的！

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
最高階 the -est / the most … — 一組中最高或最低的	the least common · the lowest
用 “might / may” 表可能 might/may + 動詞 — 有可能但不確定的事	might find · might even be
“going to” 表將來 be going to + 動詞 — 計劃或明顯即將發生的事	we're going to talk · we're going to add · i'm going to post
義務：must / have to / need to 表示某事是必要的	need to add · need to write · need to multiply

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。

影子跟讀法: 閱讀完整分步指南 →

跟讀練習: Adding Fractions With Unlike Denominators - 通過影片學習英語口語

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本節課你將練習什麼？

核心詞彙與表達

影子跟讀練習技巧

影片中的語法

什麼是跟讀法？