Pratique du Shadowing: Multiplying Fractions - The Easy Way! - Apprendre l'anglais à l'oral avec la vidéo

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.

100

In this case, 8 and 5, they're not large numbers, so we can multiply across.

101

And we can't really simplify before we multiply in this case.

102

So 8 times 5, that's going to be 40.

103

And then if we multiply 1 and 3, it's going to give us 3.

104

So our answer is 40 over 3 as an improper fraction.

105

Try this one.

106

7 over 6 multiplied by 9.

107

Go ahead and work on that example.

108

So let's rewrite 9 as 9 over 1.

109

Now this one we could simplify before we multiply if we want to.

110

6, we can write that as 3 times 2.

111

And 9 is 3 times 3.

112

So we can cancel a 3.

113

And so we're left with 7 times 3, which is 21 and 2 times 1 which is 2.

114

So the answer is 21 over 2.

115

By the way, if you want more videos on fractions, feel free to check out my next video on dividing fractions.

116

Which I'm going to post a link to that video in the description section of this video that you're currently watching.

117

But now let's get back to our next problem.

118

So let's say if we have 12 over 28 times 18 over 30 times 35 over 27.

119

How can we multiply these three fractions?

120

So go ahead and try this problem.

121

12 we can write

122

that as 6 times 2 28 we could say it's 7 times 4 18 we can write

123

that as 6 times 3

124

but yeah i'm gonna make that 9 times 2 because there's 27 and 27 is divisible by 9

125

30 is 6 times 5, 35 is 7 times 5, and 27 is 9 times 3.

126

So we can cancel a 9, we can cancel a 7,

127

we can cancel a 5, we can cancel a 6,

128

and notice that we can also cancel 4.

129

2 times 2 is 4.

130

So these 2s can cancel the 4 on the bottom.

131

So what's our final answer here?

132

Notice that every number in the numerators of the 3 fractions have been cancelled.

133

So what numbers should we put on top then if there's nothing to write?

134

Well, if we think about this, 9 divided by 9.

135

The reason why that cancels is because 9 over 9 is 1.

136

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,

137

so our final answer for this problem is 1 over 3 So this is the solution

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Vocabulaire et conseils d’expression pour cette leçon

Cette leçon d’expression orale de niveau B1 s’appuie sur la vidéo « Multiplying Fractions - The Easy Way! ». Les mots qui reviennent le plus souvent : multiply, fraction, cancel, answer, simplify. Cette vidéo contient 137 phrases et 1137 mots à répéter en shadowing. La partie parlée dure 10:15. Le locuteur parle à un rythme régulier d’environ 111 mots par minute, confortable pour le shadowing. 89 % des mots font partie des 3 000 mots les plus courants en anglais, le vocabulaire est donc facile à suivre.

Vocabulaire clé de cette vidéo

Les 13 mots les plus avancés de la vidéo, avec leur prononciation et leur sens :

Mot	Prononciation	Sens
multiply verbe	/ˈmʌltɪplaɪ/	multiplier
cancel verbe	/ˈkæn.sl̩/	annuler, résilier
fraction nom	/ˈfɹæk.ʃən/	fraction
divide verbe	/dɪˈvaɪd/	diviser, fendre
simplify verbe	/ˈsɪmplɪfaɪ/	simplifier
divisible adjectif	[dɪˈvɪzɪbəɫ]	divisible
pause nom	/pɔːz/	pause
denominator nom	/dɪˈnɒmɪneɪtə(ɹ)/	dénominateur
multiplication nom	/ˌmʌltɪplɪˈkeɪʃən/	multiplication
numerator nom	/ˈnuː.məɹˌeɪ̯.təɹ/	numérateur
rewrite verbe	/ɹiˈɹaɪt/	réécrire, récrire
improper adjectif	/ɪmˈpɹɑ.pɚ/	impropre, inapproprié
convert verbe	/kənˈvɝt/	convertir

Les verbes à particule que vous entendrez

Mot	Prononciation	Sens
go ahead verbe	/ˌɡoʊ əˈhɛd/	vas-y, allez-y
break down verbe		tomber en panne
check out verbe		mater, regarder
get over verbe		surmonter
turn out verbe		se finir, se terminer

Des phrases à répéter

Des phrases courtes et complètes de la vidéo, à réutiliser dans la conversation de tous les jours :

How can we multiply these two fractions?
That's all we need to do.
We can't simplify this answer.
How can we reduce that fraction?
How can we multiply these three fractions?

La grammaire de cette vidéo

Les structures que le locuteur utilise le plus, avec les mots exacts de la vidéo :

Structure	Dans la vidéo
Comparatifs -er than / more … than — comparer deux éléments	further than · easier than
Futur avec « going to » be going to + verbe — un projet ou ce que l’on voit venir	we're going to focus · we're going to multiply · is going to be
Obligation : must / have to / need to dire qu’une chose est nécessaire	need to do · need to multiply · have to simplify

Prononciation à surveiller

Le locuteur utilise 19 contractions et formes réduites, comme gonna, we're, can't. Prononcez-les sous leur forme courte, telles que vous les entendez.

Les sons « sh » et « zh »: fraction /ˈfɹæk.ʃən/, multiplication /ˌmʌltɪplɪˈkeɪʃən/
Mots longs — placez bien l’accent: divisible [dɪˈvɪzɪbəɫ], denominator /dɪˈnɒmɪneɪtə(ɹ)/, multiplication /ˌmʌltɪplɪˈkeɪʃən/, numerator /ˈnuː.məɹˌeɪ̯.təɹ/

Les sons difficiles pour les francophones :

/r/ anglais — langue recourbée, sans frotter la gorge: fraction /ˈfɹæk.ʃən/, denominator /dɪˈnɒmɪneɪtə(ɹ)/, numerator /ˈnuː.məɹˌeɪ̯.təɹ/, rewrite /ɹiˈɹaɪt/, improper /ɪmˈpɹɑ.pɚ/

Comment s’entraîner avec cette vidéo

Écoutez la vidéo en entier une fois sans parler et notez les mots que vous ne connaissez pas.
Répétez phrase par phrase à vitesse normale, en reprenant chacune jusqu’à ce que votre rythme corresponde à celui du locuteur.
Enregistrez-vous et comparez avec l’original, en faisant attention à des mots comme multiply, cancel, fraction.

Qu'est-ce que la technique du Shadowing ?

Le Shadowing est une technique d'apprentissage des langues fondée sur la science, développée à l'origine pour la formation des interprètes professionnels. Le principe est simple mais puissant : vous écoutez de l'anglais natif et le répétez immédiatement à voix haute — comme une ombre suivant le locuteur avec un décalage de 1 à 2 secondes. Les recherches montrent une amélioration significative de la précision de la prononciation, de l'intonation, du rythme, des liaisons, de la compréhension orale et de la fluidité.

Technique du shadowing : lire le guide complet étape par étape →

Pratique du Shadowing: Multiplying Fractions - The Easy Way! - Apprendre l'anglais à l'oral avec la vidéo

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