跟读练习: Multiplying Fractions - The Easy Way! - 通过视频学习英语口语
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In this video we're going to focus on multiplying fractions.
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So let's start with a simple example.
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Let's multiply 3 over 5 by 4 over 7.
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Now for each of these examples feel free to pause the video and try these problems yourself.
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See if you can get the answer.
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So what do we need to do in this problem?
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How can we multiply these two fractions?
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When multiplying fractions you need to multiply across.
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So we're going to multiply 3 and 4 together.
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3 times 4 is 12.
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Next, we need to multiply the two denominators together.
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5 times 7 is 35.
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And so that's it for this problem.
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That's all we need to do.
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And the answer is 12 over 35.
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Now, it's important to check and see if you could reduce the fraction.
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And for this example, we can't simplify the fraction.
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So the final answer is 12 over 35.
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Now let's try another example.
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Go ahead and multiply these two fractions.
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2 over 5 times 3 over 11.
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So once again, we're going to multiply across.
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2 times 3 is 6.
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And then we're going to multiply 5 and 11.
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5 times 11 is 55.
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And so this is the answer.
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We can't simplify this answer.
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Now let's try some examples where we have to simplify the final answer.
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So let's multiply 3 over 2 by 4 over 9.
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Go ahead and try this.
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3 times 4 is 12.
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And 2 times 9 is 18.
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So we get 12 over 18.
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How can we reduce that fraction?
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Now, both of these numbers are even, so we can divide 12 and 18 by 2.
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12 divided by 2 is 6.
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18 divided by 2 is 9.
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Now, can we reduce this fraction, or is that the final answer?
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6 and 9 are both divisible by 3, so we could divide both numbers by 3.
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6 divided by 3 is 2, 9 divided by 3 is 3.
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So our final answer is 2 over 3.
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Now there's another way in which you can get the same answer.
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So once you got to, let's say this part, you could do it this way.
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You could say 12 is 6 times 2, and 18 is 6 times 3.
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So at this point, you can cancel the 6, and this will give you the final answer of 2 over 3.
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So that's another way in which you could reduce a fraction.
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Now let's work on another example that's similar to the last one.
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4 over 3 times 9 over 8.
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So pause the video and work on this example.
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So let's multiply across.
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What is 4 times 9?
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4 times 9 is 36.
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And what's 3 times 8?
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3 times 8 is going to be 24.
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So how can we reduce 36 over 24?
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24 and 36 are multiples of 12.
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12 times 3 is 36, and 12 times 2 is 24.
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So it really helps to know your multiplication tables.
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So at this point, we can cancel our 12.
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And so the final answer is going to be 3 over 2.
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Now let's talk about what to do when multiplying two fractions
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that contain large numbers such as this one now what I
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don't recommend is multiplying across 24 times 45 it's gonna be a big number let's see what
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that number is gonna be if you multiply across that's gonna give you a thousand
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and eighty and then if you multiply 27 by 32 that's gonna give you a large number as well.
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That's going to be 864.
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So what are you going to do to reduce this fraction?
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That's not going to be fun and it's going to take a long time.
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So there has to be an easier way of getting the answer for this problem.
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And the key is to simplify before you multiply.
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So, for instance, 28, we can write that as 8 times 3.
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27, we can write it as 9 times 3, because 9 times 3 is 27.
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Now, 45, you want to break it down into a number with a 9, so you can cancel this 9.
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It turns out that 9 times 5 is 45.
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And 32, we can represent it as 8 times 4.
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So you want to break down these large numbers into smaller numbers in such a way
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that you can cancel some of those smaller numbers.
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So we can cancel an 8, we can cancel a 9, and we can cancel a 3.
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And our final answer is just going to be 5 over 4.
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we don't have to simplify any further than this as you
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can see this second method is a lot easier than the first so
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if you have large numbers I would avoid multiplying them to get even bigger numbers instead simplify before you multiply
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so now it's your turn try this 56 over 44 times 55 over 40
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go ahead and multiply these two fractions.
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So let's not multiply 56 by 55.
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Let's avoid that.
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56, we can write that as 8 times 7.
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44 is 11 times 4.
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And 55 is 11 times 5.
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40 is 8 times 5.
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So we can cancel an 8.
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We can cancel an 11.
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And we can cancel a 5.
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So the final answer is 7 over 4, and that's it.
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Now, what if you get a problem that looks like this?
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What is 8 multiplied by 5 over 3?
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How can you take a whole number and multiply it by a fraction?
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The key is to convert the whole number into a fraction.
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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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本课的词汇与口语要点
这节 B1 级别的口语课以视频“Multiplying Fractions - The Easy Way!”为素材。 视频中反复出现的词有：multiply, fraction, cancel, answer, simplify。 这段视频共有 137 个句子、1137 个单词可供跟读。 讲话部分时长为 10:15。 说话人语速平稳，每分钟约 111 个词，很适合跟读。 89% 的单词属于英语最常用的 3,000 词，词汇容易理解。
视频中的重点词汇
视频中最难的 10 个单词，附发音和释义：
| 单词 | 发音 | 释义 |
|---|---|---|
| multiply 动词 | /ˈmʌltɪplaɪ/ | 增長 /增长 |
| cancel 动词 | /ˈkæn.sl̩/ | 划, 勾 |
| fraction 名词 | /ˈfɹæk.ʃən/ | 部分 |
| divide 动词 | /dɪˈvaɪd/ | 分, 分裂 |
| simplify 动词 | /ˈsɪmplɪfaɪ/ | 簡化 /简化 |
| pause 名词 | /pɔːz/ | 停頓 /停顿, 暫停 /暂停 |
| denominator 名词 | /dɪˈnɒmɪneɪtə(ɹ)/ | 分母 |
| multiplication 名词 | /ˌmʌltɪplɪˈkeɪʃən/ | 乘法 |
| numerator 名词 | /ˈnuː.məɹˌeɪ̯.təɹ/ | 分子 |
| rewrite 动词 | /ɹiˈɹaɪt/ | 重寫 /重写 |
视频中出现的短语动词
| 单词 | 发音 | 释义 |
|---|---|---|
| go ahead 动词 | /ˌɡoʊ əˈhɛd/ | 請便 /请便 |
| break down 动词 | 壞了 /坏了, 出故障 | |
| check out 动词 | 退房 | |
| turn out 动词 | 原來 /原来 |
值得反复跟读的句子
视频中简短而完整的句子，可以直接用在日常对话里：
- 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?
视频中的语法
说话人最常用的结构，并附上视频中的原话：
| 结构 | 视频中的用法 |
|---|---|
| 比较级 -er than / more … than — 比较两个事物 | further than · easier than |
| “going to” 表将来 be going to + 动词 — 计划或明显即将发生的事 | we're going to focus · we're going to multiply · is going to be |
| 义务：must / have to / need to 表示某事是必要的 | need to do · need to multiply · have to simplify |
需要注意的发音
说话人用了 19 次缩略和弱读形式，例如 gonna, we're, can't。请按听到的简短形式来说。
- “sh” 和 “zh” 音: fraction /ˈfɹæk.ʃən/, multiplication /ˌmʌltɪplɪˈkeɪʃən/
- 长单词——注意重音位置: divisible [dɪˈvɪzɪbəɫ], denominator /dɪˈnɒmɪneɪtə(ɹ)/, multiplication /ˌmʌltɪplɪˈkeɪʃən/, numerator /ˈnuː.məɹˌeɪ̯.təɹ/
中文母语者容易读错的音：
- /v/ — 不要读成 /w/，上齿轻触下唇: divide /dɪˈvaɪd/, divisible [dɪˈvɪzɪbəɫ], convert /kənˈvɝt/
- 词尾辅音 — 要读清楚，后面不要加元音: divide /dɪˈvaɪd/, pause /pɔːz/, rewrite /ɹiˈɹaɪt/, convert /kənˈvɝt/
- /æ/ — 嘴张大，不要读成 /e/: cancel /ˈkæn.sl̩/, fraction /ˈfɹæk.ʃən/
如何用这段视频练习
- 先完整听一遍视频，不要开口，记下不认识的单词。
- 用正常速度逐句跟读，每句重复到你的节奏与说话人一致为止。
- 录下自己的声音并与原声对比，特别注意 multiply, cancel, fraction 这类单词。
什么是跟读法？
跟读法 (Shadowing) 是一种有科学依据的语言学习技巧，最初开发用于专业口译员的培训，并由多语言者Alexander Arguelles博士普及。这个方法简单而强大：您在听英语母语原声的同时立即大声重复——就像是一个延迟1-2秒紧跟说话者的影子。与被动听力或语法练习不同，跟读法强迫您的大脑和口腔肌肉同时处理并模仿真实的讲话模式。研究表明它能显着提高发音准确性，语调，节奏，连读，听力理解和口语流利度——使其成为雅思口语备考和真实英语交流最有效的方法之一。