シャドーイング練習: Subtracting Fractions - 動画で英語スピーキングを学ぶ

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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✨ おすすめ動画

62 文

このレッスンの語彙とスピーキングのポイント

このB1レベルのスピーキングレッスンは、動画「Subtracting Fractions」を教材にしています。繰り返し出てくる語は次のとおりです：fraction, multiply, minus, subtract, divided。この動画には、シャドーイング用の文が125文、単語が1005語あります。音声の長さは10:58です。話す速さはゆっくりで、1分あたり約92語です。一つ一つの音をまねる余裕があります。単語の87%は英語の頻出3,000語に含まれるため、語彙は分かりやすいです。

この動画の重要語彙

動画の中で特に難しい単語15語を、発音と意味つきで紹介します。

単語	発音	意味
fraction 名詞	/ˈfɹæk.ʃən/	断片
minus	/ˈmaɪ.nəs/	引く
divide 動詞	/dɪˈvaɪd/	分割する, 分ける
technique 名詞	/tɛkˈniːk/	技術
combine 動詞	/kəmˈbaɪn/	合わせる, 結び付ける
lesson 名詞	/ˈlɛs.ən/	授業, 学科
pause 名詞	/pɔːz/	休止, 中断
multiply 動詞	/ˈmʌltɪplaɪ/	掛ける
subtract 動詞	/səbˈtɹækt/	引く, 減らす
denominator 名詞	/dɪˈnɒmɪneɪtə(ɹ)/	分母
numerator 名詞	/ˈnuː.məɹˌeɪ̯.təɹ/	分子
multiple 形容詞	/ˈmʌltɪpəl/	多重
negative 形容詞	/ˈnɛɡ.ə.tɪv/	否定の, 否定的な
cross 名詞	/kɹɑs/	十字, クロス
worry 動詞	/ˈwʌ.ɹi/	心配する, 気にする

動画に出てくる句動詞

単語	発音	意味
go ahead 動詞	/ˌɡoʊ əˈhɛd/	どうぞお先に
check out 動詞		試験する, 検査する

繰り返し練習したい文

動画に出てくる短く完結した文です。日常会話でそのまま使えます。

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

この動画の文法

話し手がよく使っている文型を、動画の実際の表現とともに紹介します。

文型	動画での表現
最上級 the -est / the most … — グループの中で一番	the least common · the lowest
「going to」の未来表現 be going to + 動詞 — 予定や、起こりそうだと分かること	we're going to focus · is going to be · gonna be
義務：must / have to / need to 何かが必要であることを伝える	need to do · need to cross · need to subtract
「will」の未来表現 will + 動詞 — その場の決定、約束、予測	will give · we'll need

注意したい発音

話し手はwe're, I'm, don'tなど、短縮形や弱形を17回使っています。聞こえたとおりの短い形で発音しましょう。

「sh」と「zh」の音: fraction /ˈfɹæk.ʃən/, section /ˈsɛkʃən/, division /dɪˈvɪʒn̩/, solution /səˈl(j)uːʃən/, description /dɪˈskɹɪpʃən/
長い単語（アクセントの位置に注意）: denominator /dɪˈnɒmɪneɪtə(ɹ)/, numerator /ˈnuː.məɹˌeɪ̯.təɹ/

日本語話者が苦手な音：

/v/ — /b/ にならないように、上の歯を下唇に当てる: divide /dɪˈvaɪd/, negative /ˈnɛɡ.ə.tɪv/, previous /ˈpɹi.vi.əs/, division /dɪˈvɪʒn̩/
/f/ — 「フ」ではなく、上の歯と下唇で出す: fraction /ˈfɹæk.ʃən/, focus /ˈfoʊ̯.kəs/, useful /ˈjuːsfəl/
子音の連続 — 間に母音を入れない: fraction /ˈfɹæk.ʃən/, subtract /səbˈtɹækt/, cross /kɹɑs/, plus /ˈplʌs/, previous /ˈpɹi.vi.əs/

この動画での練習方法

まず声を出さずに動画を最後まで聞き、知らない単語をメモします。
通常の速度で一文ずつシャドーイングし、話し手のリズムに合うまで繰り返します。
自分の声を録音して元の音声と比べます。fraction, minus, divideなどの単語に特に注意しましょう。

シャドーイングとは？英語上達に効果的な理由

シャドーイング（Shadowing）は、もともとプロの通訳者養成プログラムで開発された言語学習法で、多言語習得者として知られるDr. Alexander Arguelles によって広く普及されました。方法はシンプルですが非常に効果的：ネイティブスピーカーの英語を聞きながら、1〜2秒の遅延で声に出してすぐに繰り返す——まるで「影（shadow）」のように話者を追いかけます。文法ドリルや受動的なリスニングと異なり、シャドーイングは脳と口の筋肉が同時にリアルタイムで英語を処理・再現することを強制します。研究により、発音精度、抑揚、リズム、連音、リスニング力、そして会話の流暢さが大幅に向上することが確認されています。IELTSスピーキング対策や自然な英語コミュニケーションを目指す方に特におすすめです。

シャドーイングのやり方: ステップ別の完全ガイドを読む →

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