跟读练习: Subtracting Fractions - 通过视频学习英语口语

In this lesson, we're going to focus on how to subtract two or three fractions.

So let's start with this example.

3 over 5 minus 1 over 2.

How can we subtract those two fractions?

The first thing we need to do is multiply the two denominators of the fractions.

5 times 2 is 10.

And then we need to cross multiply.

3 times 2 is 6.

5 times negative 1 is negative 5.

So now we need to subtract 6 and 5, which will give us 1.

So the final answer is 1 over 10.

So that is the solution to this problem.

Now let's work on another one.

So let's subtract 4 over 3 by 3 over 4.

And let's use the same technique.

So first, let's multiply the two denominators of the fractions.

3 times 4 is 12. And then cross multiply.

4 times 4 is 16.

3 times negative 3 is negative 9.

Now, 16 minus 9 is 7.

So the answer is going to be 7 divided by 12.

So now it's your turn.

Go ahead and subtract these two fractions.

3 over 8 minus 1 over 7 and also 5 over 7 minus 2 over 5.

So starting with the first example, let's multiply 8 by 7.

So 8 times 7 is 56.

and then let's cross multiply.

3 times 7 is 21 and 8 times negative 1 is negative 8.

So now we need to subtract.

21 minus 8 is 13.

So the answer to the first problem is going to be 13 over 56.

Now for the next example let's multiply 5, I mean 7 and 5.

7 times 5 is 35 5 times 5 is 25 and then we have 7 times 2 which is 14

so now let's subtract 25 and 14 25 minus 14 is 11

and so this is going to be 11 over 35 by the way I'm going to post some links

in the description section of this video where you can find more of my videos on fractions, like how to multiply fractions and how to divide them as well and some other stuff too.

But before we go into subtracting three fractions, let's talk about another method in which we can subtract two fractions.

So in the previous method we would multiply 9 and 4

and that will give us 36 and then we would cross multiply.

5 times 4 is 20 and then 9 times 1 is 9

but 9 times 1 is negative 9 so it's gonna be 20 minus 9

which is 11 and so this will give us 11 over 36 now another way in

which you can do the same problem

and get the same results is to get the common denominators first before combining the two fractions 9 times 4 is 36.

So to get a common denominator of 36, we need to multiply the first fraction by 4 over 4, and the second one by 9 over 9.

4 times 5 is 20, 4 times 9 is 36.

And so we're going to get this.

So now that these two are the same, we can combine the numerators of the two fractions.

So 20 minus 9 is 11.

And so we're going to get the same answer, 11 over 36.

Now, this technique is useful if you have multiple fractions.

Let's say if you want to subtract 3 or 4 fractions, you could do that.

So let's say if we have 8 over 9 minus 1 over 3 minus 2 over 5.

So we'll need to find a common denominator of those three fractions So what is the least common multiple of 9, 3, and 5?

3 already goes into 9 So any multiple of 9 is a multiple of 3

So we don't really need to worry about this So what is the common multiple between 9 and 5?

Well, 9 times 5 is 45 So 45 is the lowest number that can go into 9,

3, and 5 Now 45 divided by 9 is 5 So I'm going to multiply this fraction by 5 over 5

Now 45 divided by 3 is 15 So I'm going to multiply the second fraction by 15 over 15.

And 45 divided by 5 is 9.

So I'm going to multiply the last fraction by 9 over 9.

5 times 8 is 40.

5 times 9 is 45.

15 times 1 is 15, 15 times 3 is 45, 2 times 9 is 18, 5 times 9 is 45.

And now we need to subtract.

So 40 minus 15 is 25, and 25 minus 18 is 7.

So this is going to be 7 over 45. And that's the answer.

Let's try another example.

9 over 10 minus 1 over 5 minus 2 over 7.

Feel free to pause the video and work on that example.

So let's get a common denominator between 10, 5, and 7.

So 5 goes into 10, so we don't have to worry about the 5.

Any multiple of 10 is going to be a multiple of 5.

So multiples of 10 are 10, 20, 30, 40, all the way to 70.

Multiples of 7 are 7, 14, 21, 28, all the way to 70.

If you multiply 10 and 7, you're going to get a common multiple between 10 and 7, which is 70.

So it turns out that 70 is the common denominator that we want to get to.

70 divided by 10 is 7.

So let's multiply the first fraction by 7 over 7.

70 divided by 5.

Let's see what that is.

So let's use long division.

5 goes into 7 one time.

5 times 1 is 5.

And then subtract.

7 minus 5 is 2.

Bring that into 0.

5 goes into 24 times.

So 70 divided by 5 is 14.

So we need to multiply this fraction by 14 over 14.

70 divided by 7 is 10.

So we're going to multiply the last fraction by 10 over 10.

7 times 9 is 63.

And we know 7 times 10 is 70.

And 5 times 14 is 70.

And 2 times 10 is 20. So now let's subtract.

63 minus 14.

That's 49.

And 49 minus 20 is 29.

100

So the final answer for this problem is 29 divided by 70.

101

Let's work on one last example.

102

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

103

Go ahead and try that example.

104

So what is a common multiple between 2, 3, 4, and 5?

105

Well, we don't have to worry about the 2 because 2 goes into 4.

106

So all we need to do is multiply 4 times 3 times 5, which is 60.

107

And so 60 is going to be the common denominator that we need to get to.

108

60 divided by 4 is 15.

109

So we're going to multiply this fraction by 15 over 15.

110

60 divided by 2 is 30, so we're going to multiply the second fraction by 30 over 30.

111

And 60 divided by 3 is 20, so let's multiply this fraction by 20 over 20.

112

And finally, 60 divided by 5 is 12.

113

Now let's multiply.

114

15 times 3 is 45, and we know 15 times 4 is 60.

115

1 times 30 is 30, and 2 times 30 is 60.

116

5 times 20 is 100.

117

320 is 60.

118

2 times 12 is 24, and 5 times 12 is 60.

119

So now we'll need to subtract So first let's subtract these two numbers 45 minus 30 is 15

120

So we have 15 over 60 And then let's subtract these two 100 minus 24

121

100 minus 20 is 80 80 minus 4 is 76 So now we need to add 15 and 76

122

15 plus 76 is going to be 91 and so

123

that is the final answer it's a 91 over 60

124

so that's all i got for this video be sure to

125

check out my next video on multiplying fractions thanks for watching

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✨ 推荐视频

62 句

本课的词汇与口语要点

这节 B1 级别的口语课以视频“Subtracting Fractions”为素材。视频中反复出现的词有：fraction, multiply, minus, subtract, divided。这段视频共有 125 个句子、1005 个单词可供跟读。讲话部分时长为 10:58。说话人语速较慢，每分钟约 92 个词，你有足够的时间模仿每一个音。 87% 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 15 个单词，附发音和释义：

单词	发音	释义
fraction 名词	/ˈfɹæk.ʃən/	部分
minus	/ˈmaɪ.nəs/	減 /减
divide 动词	/dɪˈvaɪd/	分, 分裂
technique 名词	/tɛkˈniːk/	技術 /技术, 技巧
combine 动词	/kəmˈbaɪn/	結合 /结合, 組合 /组合
lesson 名词	/ˈlɛs.ən/	課業 /课业, -課 /-课
pause 名词	/pɔːz/	停頓 /停顿, 暫停 /暂停
multiply 动词	/ˈmʌltɪplaɪ/	增長 /增长
subtract 动词	/səbˈtɹækt/	減 /减, 減去 /减去
denominator 名词	/dɪˈnɒmɪneɪtə(ɹ)/	分母
numerator 名词	/ˈnuː.məɹˌeɪ̯.təɹ/	分子
multiple 形容词	/ˈmʌltɪpəl/	多種 /多种
negative 形容词	/ˈnɛɡ.ə.tɪv/	否定的, 消極 /消极
cross 名词	/kɹɑs/	十字, 交叉
worry 动词	/ˈwʌ.ɹi/	著急, 着急

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
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 subtract those two fractions?
Let's see what that is.
Let's work on one last example.

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
最高级 the -est / the most … — 一组中最高或最低的	the least common · the lowest
“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 · is going to be · gonna be
义务：must / have to / need to 表示某事是必要的	need to do · need to cross · need to subtract
“will” 表将来 will + 动词 — 决定、承诺或预测	will give · we'll need

需要注意的发音

说话人用了 17 次缩略和弱读形式，例如 we're, I'm, don't。请按听到的简短形式来说。

“sh” 和 “zh” 音: fraction /ˈfɹæk.ʃən/, section /ˈsɛkʃən/, division /dɪˈvɪʒn̩/, solution /səˈl(j)uːʃən/, description /dɪˈskɹɪpʃən/
长单词——注意重音位置: denominator /dɪˈnɒmɪneɪtə(ɹ)/, 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/, negative /ˈnɛɡ.ə.tɪv/, previous /ˈpɹi.vi.əs/, division /dɪˈvɪʒn̩/
词尾辅音 — 要读清楚，后面不要加元音: minus /ˈmaɪ.nəs/, divide /dɪˈvaɪd/, technique /tɛkˈniːk/, pause /pɔːz/, subtract /səbˈtɹækt/
/æ/ — 嘴张大，不要读成 /e/: fraction /ˈfɹæk.ʃən/, subtract /səbˈtɹækt/

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 fraction, minus, divide 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。

影子跟读法: 阅读完整分步指南 →

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