シャドーイング練習: Multiplying Fractions - The Easy Way! - 動画で英語スピーキングを学ぶ

In this video we're going to focus on multiplying fractions.

So let's start with a simple example.

Let's multiply 3 over 5 by 4 over 7.

Now for each of these examples feel free to pause the video and try these problems yourself.

See if you can get the answer.

So what do we need to do in this problem?

How can we multiply these two fractions?

When multiplying fractions you need to multiply across.

So we're going to multiply 3 and 4 together.

3 times 4 is 12.

Next, we need to multiply the two denominators together.

5 times 7 is 35.

And so that's it for this problem.

That's all we need to do.

And the answer is 12 over 35.

Now, it's important to check and see if you could reduce the fraction.

And for this example, we can't simplify the fraction.

So the final answer is 12 over 35.

Now let's try another example.

Go ahead and multiply these two fractions.

2 over 5 times 3 over 11.

So once again, we're going to multiply across.

2 times 3 is 6.

And then we're going to multiply 5 and 11.

5 times 11 is 55.

And so this is the answer.

We can't simplify this answer.

Now let's try some examples where we have to simplify the final answer.

So let's multiply 3 over 2 by 4 over 9.

Go ahead and try this.

3 times 4 is 12.

And 2 times 9 is 18.

So we get 12 over 18.

How can we reduce that fraction?

Now, both of these numbers are even, so we can divide 12 and 18 by 2.

12 divided by 2 is 6.

18 divided by 2 is 9.

Now, can we reduce this fraction, or is that the final answer?

6 and 9 are both divisible by 3, so we could divide both numbers by 3.

6 divided by 3 is 2, 9 divided by 3 is 3.

So our final answer is 2 over 3.

Now there's another way in which you can get the same answer.

So once you got to, let's say this part, you could do it this way.

You could say 12 is 6 times 2, and 18 is 6 times 3.

So at this point, you can cancel the 6, and this will give you the final answer of 2 over 3.

So that's another way in which you could reduce a fraction.

Now let's work on another example that's similar to the last one.

4 over 3 times 9 over 8.

So pause the video and work on this example.

So let's multiply across.

What is 4 times 9?

4 times 9 is 36.

And what's 3 times 8?

3 times 8 is going to be 24.

So how can we reduce 36 over 24?

24 and 36 are multiples of 12.

12 times 3 is 36, and 12 times 2 is 24.

So it really helps to know your multiplication tables.

So at this point, we can cancel our 12.

And so the final answer is going to be 3 over 2.

Now let's talk about what to do when multiplying two fractions

that contain large numbers such as this one now what I

don't recommend is multiplying across 24 times 45 it's gonna be a big number let's see what

that number is gonna be if you multiply across that's gonna give you a thousand

and eighty and then if you multiply 27 by 32 that's gonna give you a large number as well.

That's going to be 864.

So what are you going to do to reduce this fraction?

That's not going to be fun and it's going to take a long time.

So there has to be an easier way of getting the answer for this problem.

And the key is to simplify before you multiply.

So, for instance, 28, we can write that as 8 times 3.

27, we can write it as 9 times 3, because 9 times 3 is 27.

Now, 45, you want to break it down into a number with a 9, so you can cancel this 9.

It turns out that 9 times 5 is 45.

And 32, we can represent it as 8 times 4.

So you want to break down these large numbers into smaller numbers in such a way

that you can cancel some of those smaller numbers.

So we can cancel an 8, we can cancel a 9, and we can cancel a 3.

And our final answer is just going to be 5 over 4.

we don't have to simplify any further than this as you

can see this second method is a lot easier than the first so

if you have large numbers I would avoid multiplying them to get even bigger numbers instead simplify before you multiply

so now it's your turn try this 56 over 44 times 55 over 40

go ahead and multiply these two fractions.

So let's not multiply 56 by 55.

Let's avoid that.

56, we can write that as 8 times 7.

44 is 11 times 4.

And 55 is 11 times 5.

40 is 8 times 5.

So we can cancel an 8.

We can cancel an 11.

And we can cancel a 5.

So the final answer is 7 over 4, and that's it.

Now, what if you get a problem that looks like this?

What is 8 multiplied by 5 over 3?

How can you take a whole number and multiply it by a fraction?

The key is to convert the whole number into a fraction.

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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「Multiplying Fractions - The Easy Way!」を使って、シャドーイングで英語を練習しましょう。

毎日15〜30分の練習で、IELTSスピーキングへの自信と実践的な英会話力が身につきます。

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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
比較級 -er than / more … than — 二つのものを比べる	further than · easier than
「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 · we're going to multiply · is going to 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 multiply · have to simplify

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 →

シャドーイング練習: Multiplying Fractions - The Easy Way! - 動画で英語スピーキングを学ぶ

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シャドーイングとは？英語上達に効果的な理由