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

In this video, we're going to talk about how to add two fractions.

So let's start with this example.

2 over 3 plus 3 over 4.

So how can we add these two fractions?

The first thing you can do is multiply the denominators of the fractions.

3 times 4 is 12. And then cross multiply.

2 times 4 is 8, and then multiply 3 times 3, and that will give you 9.

And then you could add 8 and 9.

8 plus 9 is 17.

So we get the answer 17 over 12.

And so this is our answer as an improper fraction.

Now, let's try another example.

So let's add 5 over 3 plus 1 over 2.

So let's follow the same technique.

3 times 2 is 6. And then cross multiply.

5 times 2 is 10.

3 times 1 is 3.

And then we're going to add 10 plus 3.

So 10 plus 3 is 13.

So the answer is 13 over 6. by the way

if you want more videos on fractions let's say how to subtract fractions how to multiply

or divide fractions check out the description section of this video i'm going to post some links there

that you might find useful

but now let's get back to this video let's work on another problem

so now it's your turn go ahead and add the following fractions 2 over 5 plus 1 over 4

And also try this example, 3 over 7 plus 5 over 9.

Feel free to pause the video and try those examples.

So let's start with the first one.

So first we're going to multiply 5 and 4.

5 times 4 is 20. And then cross multiply.

2 times 4 is 8.

5 times 1 is 5.

And now we can add 8 plus 5 is 13.

So the answer is 13 over 20.

Now let's try the example below.

So let's multiply 7 by 9.

7 times 9 is 63. And then cross multiply.

3 times 9 is 27.

And 7 times 5 is 35.

So now we'll need to add 27 and 35.

So you can use a calculator or you can do it the old-fashioned way.

Let's do it the old-fashioned way.

5 plus 7 is 12, so we need to write the 2, carry over the 1.

And then 3 plus 2 plus 1 is 6.

So 27 plus 35 is 62.

So the final answer for that example is 62 divided by 63.

So at this point, you know how to add 2 fractions.

But what if you need to add, let's say, 3 fractions?

What should you do?

So before we go into this example, I want to show you another example of adding 2 fractions but using a different method.

So let's start with this problem, 3 over 8 plus 5 over 7.

So let's begin by using the method that you're familiar with

and then we'll use a new method to get the same answer.

So what we did before is multiply the two denominators of the fractions.

8 times 7 is 56.

And then we would cross multiply.

3 times 7 is 21.

And 8 times 5 is 40.

And then we would add 21 plus 40 is 61.

So our answer for this example would be 61 over 56.

Now here's another method which is useful if you're adding multiple fractions.

So what you want to do is get a common denominator of 56.

In order to do so, the fraction on the left you need to multiply the top and the bottom by 7.

And for the fraction on the right, multiply the top and the bottom by 8.

So this would give you a common denominator of 56.

So 3 times 7 is 21, and 7 times 8 is 56.

5 times 8 is 40, and on the bottom, 7 times 8 is 56.

Now whenever you're adding two fractions, if the denominator is the same, then you're allowed to add the numerators of the two fractions.

So 21 plus 40 is 61.

And thus, we're going to get the same answer of 61 over 56.

This technique works if you're adding, let's say, three fractions or even four fractions.

Now, let's try this example.

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

So the first thing we need to do is identify a common denominator that we need to get to.

So we need to find the least common multiple of 5, 4, and 3.

How can we do so?

Well, a simple way is to multiply 5 times 4 times 3.

You could use any common multiple.

It doesn't really have to be the least common multiple.

But if you could find the least common multiple, then it's going to be easier.

But let's keep it simple.

so 5 times 4 times 3

5 times 4 is 20 20 times 3 is 60 so 60 is a common multiple of 5, 4, and 3 it might even be the least common multiple

and I think it is so what I'm going to do now is take 60 and divide it by 5

60 divided by 5 is 12 so therefore I'm going to multiply the second fraction, I mean the first fraction, by 12.

So that will give me a common denominator of 60.

Now 60 divided by 4 is 15.

So I need to multiply the second fraction, the top and the bottom, by 15.

Whatever you multiply the bottom of a fraction by, you need to do so also to the top.

Now 60 divided by 3 is 20.

So I'm going to multiply the third fraction by 20 over 20.

12 times 2 is 24 and we know that 12 times 5 is 60.

15 times 3 is 45 and 15 times 4 is 60.

20 times 1 is 20.

20 times 3 is 60.

So notice that we have a common denominator of 60.

So now all we need to do is add up the three numerators.

So let's find a sum of 45, 24, and 20.

5 plus 4 is 9.

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4 plus 2 plus 2 is 8.

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So 24 plus 45 plus 20 is 89.

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So our answer for this problem is 89 over 60.

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So that's how you can add three fractions together.

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Now let's try another example.

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So now it's your turn.

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Go ahead and add 1 over 4 plus 5 over 6 plus 1 over 2.

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So let's identify the least common multiple of 4, 6, and 2.

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Multiples of 6 are 6, 12, 18, 24, and so forth.

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Multiples of 4 are 4, 8, 12, 16, 20.

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Multiples of 2 are 2, 4, 6, 8, 10, 12, 14.

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So which of these are the least common multiple of 2, 4, and 6?

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Notice that 12 is the lowest common number or lowest common multiple of 2, 4, and 6.

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So therefore, 12 is the least common multiple.

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Now, 12 divided by 4 is 3.

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So I'm going to multiply this fraction by 3 over 3.

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And 12 divided by 6 is 2.

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So I'm going to multiply this second fraction by 2 over 2.

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And 12 divided by 2 is 6.

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So I'm going to multiply this fraction.

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Let's change that color. By 6 over 6.

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So I'm going to get 3 over 12 plus 2 times 5 is 10.

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2 times 6 is 12.

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and then 6 times 1 is 6, 6 times 2 is 12.

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So now we need to add.

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3 plus 10 is 13.

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13 plus 6 is 19.

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So the final answer is 19 over 12.

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So that is it for this video.

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Be sure to check out my next video on subtracting fractions.

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I'm going to post some links in the description section of this video, so feel free to take a look at that.

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Thank you.

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分数の足し算の基本的な方法を学ぶだけでなく、英語で数学の説明を聞き取るリスニング力も鍛えられます。また、「cross multiply」「improper fraction」などの数学用語の英語表現を覚え、自然なスピーチのリズムを掴むことができます。これらはIELTSスピーキング対策にも役立つ実践的なスキルですよ！

聞き取りに注意すべき音のつながり

動画の中では、「add two fractions」の「add two」が「アドゥー」とつながって発音されたり、「multiply the denominators」の「multiply the」が「マルチプライザ」と軽くなっている部分があります。また、「cross multiply」の「cross」は「クロス」ではなく「クロス」と短く発音されることが多いので、注意して聞きましょう。これらのリンキングやリダクションを覚えると、英語の発音を良くすることができます。

ネイティブのように話すコツ

スピーカーは説明を進める際、重要な用語やステップを強調して発音しています。例えば「first thing you can do」の「first」や「cross multiply」の「cross」は音量を上げ、長めに発音されています。このリズムとストレスを真似ることで、より自然な英語を話すことができます。shadowing siteを使って、動画の音声に合わせて繰り返し話す「shadow speech」の練習をすると効果的です。shadowspeakの技術を磨くことで、スピーキングの流れが格段に向上しますよ！

さあ、今すぐ動画を見ながら練習して、分数の足し算と英語のスキルを同時に上達させましょう！

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
「might / may」による可能性 might/may + 動詞 — 起こりうるが確実ではないこと	might find · might even be
「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 talk · we're going to add · i'm going to post
義務：must / have to / need to 何かが必要であることを伝える	need to add · need to write · need to multiply

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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聞き取りに注意すべき音のつながり

ネイティブのように話すコツ

この動画の文法

シャドーイングとは？英語上達に効果的な理由