Shadowing Practice: Adding Fractions With Unlike Denominators - Learn English Speaking with Video

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.

100

4 plus 2 plus 2 is 8.

101

So 24 plus 45 plus 20 is 89.

102

So our answer for this problem is 89 over 60.

103

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

104

Now let's try another example.

105

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.

107

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

108

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

109

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

110

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

111

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

112

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

113

So therefore, 12 is the least common multiple.

114

Now, 12 divided by 4 is 3.

115

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

116

And 12 divided by 6 is 2.

117

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

118

And 12 divided by 2 is 6.

119

So I'm going to multiply this fraction.

120

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

121

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

122

2 times 6 is 12.

123

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

124

So now we need to add.

125

3 plus 10 is 13.

126

13 plus 6 is 19.

127

So the final answer is 19 over 12.

128

So that is it for this video.

129

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

130

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

131

Thank you.

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Vocabulario y notas de pronunciación para esta lección

Esta lección de conversación de nivel B1 se basa en el vídeo “Adding Fractions With Unlike Denominators”. Las palabras que más se repiten: fraction, plus, multiply, add, common. Este vídeo tiene 131 frases y 1050 palabras para practicar shadowing. La parte hablada dura 10:10. El hablante habla despacio, unas 103 palabras por minuto, así que hay tiempo para imitar cada sonido. El 89 % de las palabras está entre las 3.000 más comunes del inglés, por lo que el vocabulario es fácil de seguir.

Vocabulario clave de este vídeo

Las 13 palabras más avanzadas del vídeo, con su pronunciación y significado:

Palabra	Pronunciación	Significado
fraction sustantivo	/ˈfɹæk.ʃən/	fracción
divide verbo	/dɪˈvaɪd/	desunir, dividir
technique sustantivo	/tɛkˈniːk/	técnica
pause sustantivo	/pɔːz/	pausa
improper adjetivo	/ɪmˈpɹɑ.pɚ/	improprio, impropio
calculator sustantivo	/kæl.kjə.leɪ.tɚ/	calculador, calculadora
multiply verbo	/ˈmʌltɪplaɪ/	multiplicar, amochiguar
denominator sustantivo	/dɪˈnɒmɪneɪtə(ɹ)/	denominador
numerator sustantivo	/ˈnuː.məɹˌeɪ̯.təɹ/	numerador
subtract verbo	/səbˈtɹækt/	restar, sustraer
identify verbo	/aɪˈdɛn.(t)ə.faɪ/	identificar, funar
whenever	/wəˈnɛvɚ/	cuando quiera, cuandoquiera
familiar adjetivo	/fəˈmɪl.jəɹ/	familiar

Phrasal verbs que vas a escuchar

Palabra	Pronunciación	Significado
check out verbo		investigar, chequear
go ahead verbo	/ˌɡoʊ əˈhɛd/	venga, adelante
add up verbo		adicionar
get back to verbo		responder / contestar (en un rato), volver / tornar a contactar
get over verbo		superar, sobreponerse a

Frases que vale la pena repetir

Frases cortas y completas del vídeo que puedes reutilizar en la conversación diaria:

Let's do it the old-fashioned way.
What should you do?
How can we do so?

Gramática en este vídeo

Las estructuras que más usa el hablante, con las palabras exactas del vídeo:

Estructura	En el vídeo
Superlativos the -est / the most … — lo más alto o lo más bajo de un grupo	the least common · the lowest
Posibilidad con “might / may” might/may + verbo — algo posible pero no seguro	might find · might even be
Futuro con “going to” be going to + verbo — un plan o algo que se ve venir	we're going to talk · we're going to add · i'm going to post
Obligación: must / have to / need to decir que algo es necesario	need to add · need to write · need to multiply

Pronunciación a tener en cuenta

El hablante usa 21 contracciones y formas reducidas, como I'm, you're, we're. Dilas en su forma corta, tal como las oyes.

Palabras largas — cuida el acento: calculator /kæl.kjə.leɪ.tɚ/, denominator /dɪˈnɒmɪneɪtə(ɹ)/, numerator /ˈnuː.məɹˌeɪ̯.təɹ/, identify /aɪˈdɛn.(t)ə.faɪ/

Sonidos difíciles para hispanohablantes:

/v/ — no es /b/: los dientes tocan el labio inferior: divide /dɪˈvaɪd/, whenever /wəˈnɛvɚ/

Cómo practicar con este vídeo

Escucha el vídeo entero una vez sin hablar y anota las palabras que no conoces.
Haz shadowing frase por frase a velocidad normal, repitiendo cada una hasta que tu ritmo coincida con el del hablante.
Grábate y compara con el original, prestando atención a palabras como fraction, divide, technique.

¿Qué es la Técnica de Shadowing?

Shadowing es una técnica de aprendizaje de idiomas respaldada por la ciencia, desarrollada originalmente para la formación de intérpretes profesionales y popularizada por el políglota Dr. Alexander Arguelles. El método es simple pero poderoso: escuchas audio en inglés nativo y lo repites en voz alta de inmediato, como una sombra que sigue al hablante con solo 1-2 segundos de retraso. A diferencia de la escucha pasiva o los ejercicios de gramática, el shadowing obliga a tu cerebro y músculos de la boca a procesar y reproducir simultáneamente patrones de habla reales. Las investigaciones muestran que mejora significativamente la precisión de la pronunciación, la entonación, el ritmo, el habla conectada, la comprensión auditiva y la fluidez al hablar, convirtiéndola en una de las metodologías más efectivas para la preparación del IELTS Speaking y la comunicación en inglés en el mundo real.

Técnica de shadowing: lee la guía completa paso a paso →

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