跟讀練習: Subtracting Fractions - 通過影片學習英語口語

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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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本課的詞彙與口語要點

這節 B1 級別的口語課以影片“Subtracting Fractions”為素材。影片中反覆出現的詞有：fraction, multiply, minus, subtract, divided。這段影片共有 125 個句子、1005 個單詞可供跟讀。講話部分時長為 10:58。說話人語速較慢，每分鐘約 92 個詞，你有足夠的時間模仿每一個音。 87% 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 15 個單詞，附發音和釋義：

單詞	發音	釋義
fraction 名詞	/ˈfɹæk.ʃən/	部分
minus	/ˈmaɪ.nəs/	減 /減
divide 動詞	/dɪˈvaɪd/	分, 分裂
technique 名詞	/tɛkˈniːk/	技術 /技術, 技巧
combine 動詞	/kəmˈbaɪn/	結合 /結合, 組合 /組合
lesson 名詞	/ˈlɛs.ən/	課業 /課業, -課 /-課
pause 名詞	/pɔːz/	停頓 /停頓, 暫停 /暫停
multiply 動詞	/ˈmʌltɪplaɪ/	增長 /增長
subtract 動詞	/səbˈtɹækt/	減 /減, 減去 /減去
denominator 名詞	/dɪˈnɒmɪneɪtə(ɹ)/	分母
numerator 名詞	/ˈnuː.məɹˌeɪ̯.təɹ/	分子
multiple 形容詞	/ˈmʌltɪpəl/	多種 /多種
negative 形容詞	/ˈnɛɡ.ə.tɪv/	否定的, 消極 /消極
cross 名詞	/kɹɑs/	十字, 交叉
worry 動詞	/ˈwʌ.ɹi/	著急, 著急

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

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
“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 · is going to be · gonna be
義務：must / have to / need to 表示某事是必要的	need to cross · need to subtract · need to multiply
“will” 表將來 will + 動詞 — 決定、承諾或預測	will give · we'll need

需要注意的發音

說話人用了 17 次縮略和弱讀形式，例如 we're, I'm, don't。請按聽到的簡短形式來說。

“sh” 和 “zh” 音: fraction /ˈfɹæk.ʃən/, section /ˈsɛkʃən/, division /dɪˈvɪʒn̩/, solution /səˈl(j)uːʃən/, description /dɪˈskɹɪpʃən/
長單詞——注意重音位置: denominator /dɪˈnɒmɪneɪtə(ɹ)/, 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/, negative /ˈnɛɡ.ə.tɪv/, previous /ˈpɹi.vi.əs/, division /dɪˈvɪʒn̩/
詞尾子音 — 要讀清楚，後面不要加母音: minus /ˈmaɪ.nəs/, divide /dɪˈvaɪd/, technique /tɛkˈniːk/, pause /pɔːz/, subtract /səbˈtɹækt/
/æ/ — 嘴張大，不要讀成 /e/: fraction /ˈfɹæk.ʃən/, subtract /səbˈtɹækt/

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 fraction, minus, divide 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: Subtracting Fractions - 通過影片學習英語口語

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