跟讀練習: Multiplying Fractions - The Easy Way! - 通過影片學習英語口語

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In this video we're going to focus on multiplying fractions.

So let's start with a simple example.

Let's multiply 3 over 5 by 4 over 7.

Now for each of these examples feel free to pause the video and try these problems yourself.

See if you can get the answer.

So what do we need to do in this problem?

How can we multiply these two fractions?

When multiplying fractions you need to multiply across.

So we're going to multiply 3 and 4 together.

3 times 4 is 12.

Next, we need to multiply the two denominators together.

5 times 7 is 35.

And so that's it for this problem.

That's all we need to do.

And the answer is 12 over 35.

Now, it's important to check and see if you could reduce the fraction.

And for this example, we can't simplify the fraction.

So the final answer is 12 over 35.

Now let's try another example.

Go ahead and multiply these two fractions.

2 over 5 times 3 over 11.

So once again, we're going to multiply across.

2 times 3 is 6.

And then we're going to multiply 5 and 11.

5 times 11 is 55.

And so this is the answer.

We can't simplify this answer.

Now let's try some examples where we have to simplify the final answer.

So let's multiply 3 over 2 by 4 over 9.

Go ahead and try this.

3 times 4 is 12.

And 2 times 9 is 18.

So we get 12 over 18.

How can we reduce that fraction?

Now, both of these numbers are even, so we can divide 12 and 18 by 2.

12 divided by 2 is 6.

18 divided by 2 is 9.

Now, can we reduce this fraction, or is that the final answer?

6 and 9 are both divisible by 3, so we could divide both numbers by 3.

6 divided by 3 is 2, 9 divided by 3 is 3.

So our final answer is 2 over 3.

Now there's another way in which you can get the same answer.

So once you got to, let's say this part, you could do it this way.

You could say 12 is 6 times 2, and 18 is 6 times 3.

So at this point, you can cancel the 6, and this will give you the final answer of 2 over 3.

So that's another way in which you could reduce a fraction.

Now let's work on another example that's similar to the last one.

4 over 3 times 9 over 8.

So pause the video and work on this example.

So let's multiply across.

What is 4 times 9?

4 times 9 is 36.

And what's 3 times 8?

3 times 8 is going to be 24.

So how can we reduce 36 over 24?

24 and 36 are multiples of 12.

12 times 3 is 36, and 12 times 2 is 24.

So it really helps to know your multiplication tables.

So at this point, we can cancel our 12.

And so the final answer is going to be 3 over 2.

Now let's talk about what to do when multiplying two fractions

that contain large numbers such as this one now what I

don't recommend is multiplying across 24 times 45 it's gonna be a big number let's see what

that number is gonna be if you multiply across that's gonna give you a thousand

and eighty and then if you multiply 27 by 32 that's gonna give you a large number as well.

That's going to be 864.

So what are you going to do to reduce this fraction?

That's not going to be fun and it's going to take a long time.

So there has to be an easier way of getting the answer for this problem.

And the key is to simplify before you multiply.

So, for instance, 28, we can write that as 8 times 3.

27, we can write it as 9 times 3, because 9 times 3 is 27.

Now, 45, you want to break it down into a number with a 9, so you can cancel this 9.

It turns out that 9 times 5 is 45.

And 32, we can represent it as 8 times 4.

So you want to break down these large numbers into smaller numbers in such a way

that you can cancel some of those smaller numbers.

So we can cancel an 8, we can cancel a 9, and we can cancel a 3.

And our final answer is just going to be 5 over 4.

we don't have to simplify any further than this as you

can see this second method is a lot easier than the first so

if you have large numbers I would avoid multiplying them to get even bigger numbers instead simplify before you multiply

so now it's your turn try this 56 over 44 times 55 over 40

go ahead and multiply these two fractions.

So let's not multiply 56 by 55.

Let's avoid that.

56, we can write that as 8 times 7.

44 is 11 times 4.

And 55 is 11 times 5.

40 is 8 times 5.

So we can cancel an 8.

We can cancel an 11.

And we can cancel a 5.

So the final answer is 7 over 4, and that's it.

Now, what if you get a problem that looks like this?

What is 8 multiplied by 5 over 3?

How can you take a whole number and multiply it by a fraction?

The key is to convert the whole number into a fraction.

8 is the same as 8 over 1.

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In this case, 8 and 5, they're not large numbers, so we can multiply across.

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And we can't really simplify before we multiply in this case.

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So 8 times 5, that's going to be 40.

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And then if we multiply 1 and 3, it's going to give us 3.

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So our answer is 40 over 3 as an improper fraction.

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Try this one.

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7 over 6 multiplied by 9.

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Go ahead and work on that example.

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So let's rewrite 9 as 9 over 1.

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Now this one we could simplify before we multiply if we want to.

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6, we can write that as 3 times 2.

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And 9 is 3 times 3.

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So we can cancel a 3.

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And so we're left with 7 times 3, which is 21 and 2 times 1 which is 2.

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So the answer is 21 over 2.

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By the way, if you want more videos on fractions, feel free to check out my next video on dividing fractions.

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Which I'm going to post a link to that video in the description section of this video that you're currently watching.

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But now let's get back to our next problem.

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So let's say if we have 12 over 28 times 18 over 30 times 35 over 27.

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How can we multiply these three fractions?

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So go ahead and try this problem.

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12 we can write

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that as 6 times 2 28 we could say it's 7 times 4 18 we can write

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that as 6 times 3

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but yeah i'm gonna make that 9 times 2 because there's 27 and 27 is divisible by 9

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30 is 6 times 5, 35 is 7 times 5, and 27 is 9 times 3.

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So we can cancel a 9, we can cancel a 7,

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we can cancel a 5, we can cancel a 6,

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and notice that we can also cancel 4.

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2 times 2 is 4.

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So these 2s can cancel the 4 on the bottom.

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So what's our final answer here?

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Notice that every number in the numerators of the 3 fractions have been cancelled.

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So what numbers should we put on top then if there's nothing to write?

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Well, if we think about this, 9 divided by 9.

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The reason why that cancels is because 9 over 9 is 1.

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7 divided by 7 is 1 So when everything cancels, the number to right is a 1 Now we do have a 3 on the bottom,

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so our final answer for this problem is 1 over 3 So this is the solution

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本課的詞彙與口語要點

這節 B1 級別的口語課以影片“Multiplying Fractions - The Easy Way!”為素材。影片中反覆出現的詞有：multiply, fraction, cancel, answer, simplify。這段影片共有 137 個句子、1137 個單詞可供跟讀。講話部分時長為 10:15。說話人語速平穩，每分鐘約 111 個詞，很適合跟讀。 89% 的單詞屬於英語最常用的 3,000 詞，詞彙容易理解。

影片中的重點詞彙

影片中最難的 10 個單詞，附發音和釋義：

單詞	發音	釋義
multiply 動詞	/ˈmʌltɪplaɪ/	增長 /增長
cancel 動詞	/ˈkæn.sl̩/	劃, 勾
fraction 名詞	/ˈfɹæk.ʃən/	部分
divide 動詞	/dɪˈvaɪd/	分, 分裂
simplify 動詞	/ˈsɪmplɪfaɪ/	簡化 /簡化
pause 名詞	/pɔːz/	停頓 /停頓, 暫停 /暫停
denominator 名詞	/dɪˈnɒmɪneɪtə(ɹ)/	分母
multiplication 名詞	/ˌmʌltɪplɪˈkeɪʃən/	乘法
numerator 名詞	/ˈnuː.məɹˌeɪ̯.təɹ/	分子
rewrite 動詞	/ɹiˈɹaɪt/	重寫 /重寫

影片中出現的短語動詞

單詞	發音	釋義
go ahead 動詞	/ˌɡoʊ əˈhɛd/	請便 /請便
break down 動詞		壞了 /壞了, 出故障
check out 動詞		退房
turn out 動詞		原來 /原來

值得反覆跟讀的句子

影片中簡短而完整的句子，可以直接用在日常對話裡：

How can we multiply these two fractions?
That's all we need to do.
We can't simplify this answer.
How can we reduce that fraction?
How can we multiply these three fractions?

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
比較級 -er than / more … than — 比較兩個事物	further than · easier than
“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 focus · we're going to multiply · is going to be
義務：must / have to / need to 表示某事是必要的	need to multiply · have to simplify · has to be

需要注意的發音

說話人用了 19 次縮略和弱讀形式，例如 gonna, we're, can't。請按聽到的簡短形式來說。

“sh” 和 “zh” 音: fraction /ˈfɹæk.ʃən/, multiplication /ˌmʌltɪplɪˈkeɪʃən/
長單詞——注意重音位置: divisible [dɪˈvɪzɪbəɫ], denominator /dɪˈnɒmɪneɪtə(ɹ)/, multiplication /ˌmʌltɪplɪˈkeɪʃən/, numerator /ˈnuː.məɹˌeɪ̯.təɹ/

中文母語者容易讀錯的音：

/v/ — 不要讀成 /w/，上齒輕觸下唇: divide /dɪˈvaɪd/, divisible [dɪˈvɪzɪbəɫ], convert /kənˈvɝt/
詞尾子音 — 要讀清楚，後面不要加母音: divide /dɪˈvaɪd/, pause /pɔːz/, rewrite /ɹiˈɹaɪt/, convert /kənˈvɝt/
/æ/ — 嘴張大，不要讀成 /e/: cancel /ˈkæn.sl̩/, fraction /ˈfɹæk.ʃən/

如何用這段影片練習

先完整聽一遍影片，不要開口，記下不認識的單詞。
用正常速度逐句跟讀，每句重複到你的節奏與說話人一致為止。
錄下自己的聲音並與原聲對比，特別注意 multiply, cancel, fraction 這類單詞。

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: Multiplying Fractions - The Easy Way! - 通過影片學習英語口語

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