تدريب Shadowing: Adding Fractions With Unlike Denominators - تعلم التحدث بالإنجليزية عبر الفيديو

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.

106

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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المفردات وملاحظات التحدث لهذا الدرس

هذا الدرس في المحادثة بمستوى B1 مبني على الفيديو “Adding Fractions With Unlike Denominators”. أكثر الكلمات تكرارًا في الفيديو: fraction, plus, multiply, add, common. يحتوي هذا الفيديو على 131 جملة و1050 كلمة للتدرب على الترديد. مدة الكلام 10:10. يتكلم المتحدث ببطء، بمعدل 103 كلمة في الدقيقة تقريبًا، فيكون لديك وقت لتقليد كل صوت. 89% من الكلمات ضمن أكثر 3,000 كلمة شيوعًا في الإنجليزية، فالمفردات سهلة المتابعة.

أهم المفردات في هذا الفيديو

أصعب 10 كلمة في الفيديو، مع النطق والمعنى:

الكلمة	النطق	المعنى
fraction اسم	/ˈfɹæk.ʃən/	قِطْعَة
divide فعل	/dɪˈvaɪd/	قَسَّمَ
technique اسم	/tɛkˈniːk/	أُسْلُوب, تِقْنِيَة
pause اسم	/pɔːz/	تَوَقُّف, وَقْف
calculator اسم	/kæl.kjə.leɪ.tɚ/	حَاسِبَة, آلَة حَاسِبَة
multiply فعل	/ˈmʌltɪplaɪ/	ضَرَبَ
denominator اسم	/dɪˈnɒmɪneɪtə(ɹ)/	قَاسِم, مَقَام
numerator اسم	/ˈnuː.məɹˌeɪ̯.təɹ/	بَسْط
whenever	/wəˈnɛvɚ/	مَتَى, مَتَى مَا
familiar صفة	/fəˈmɪl.jəɹ/	مَأْلُوف

جمل تستحق التكرار

جمل قصيرة وكاملة من الفيديو يمكنك استخدامها في الحديث اليومي:

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

القواعد في هذا الفيديو

أكثر التراكيب التي يستخدمها المتحدث، مع العبارات نفسها من الفيديو:

التركيب	في الفيديو
صيغة التفضيل the -est / the most … — الأعلى أو الأدنى في مجموعة	the least common · the lowest
الاحتمال بـ “might / may” might/may + فعل — شيء ممكن لكنه غير مؤكد	might find · might even be
المستقبل بـ “going to” be going to + فعل — خطة أو شيء واضح أنه سيحدث	we're going to talk · we're going to add · i'm going to post
الوجوب: must / have to / need to قول إن أمرًا ما ضروري	need to add · need to write · need to multiply

نطق يحتاج إلى انتباه

يستخدم المتحدث 21 من الصيغ المختصرة، مثل I'm, you're, we're. انطقها بصيغتها القصيرة كما تسمعها.

الكلمات الطويلة — انتبه لموضع النبر: calculator /kæl.kjə.leɪ.tɚ/, denominator /dɪˈnɒmɪneɪtə(ɹ)/, numerator /ˈnuː.məɹˌeɪ̯.təɹ/, identify /aɪˈdɛn.(t)ə.faɪ/

أصوات يجدها متحدثو العربية صعبة:

/p/ — ليس /b/: انطقه مع نفخة هواء: pause /pɔːz/, improper /ɪmˈpɹɑ.pɚ/, multiply /ˈmʌltɪplaɪ/
/v/ — ليس /f/: مع اهتزاز الأوتار الصوتية: divide /dɪˈvaɪd/, whenever /wəˈnɛvɚ/
تتابع الصوامت — لا تضف حركة بينها: fraction /ˈfɹæk.ʃən/, improper /ɪmˈpɹɑ.pɚ/, calculator /kæl.kjə.leɪ.tɚ/, subtract /səbˈtɹækt/

كيف تتدرب بهذا الفيديو

استمع إلى الفيديو كاملًا مرة واحدة دون أن تتكلم، ودوّن الكلمات التي لا تعرفها.
ردّد جملة جملة بالسرعة العادية، وكرّر كل جملة حتى يتطابق إيقاعك مع المتحدث.
سجّل صوتك وقارنه بالأصل، مع الانتباه إلى كلمات مثل fraction, divide, technique.

ما هي تقنية التظليل الصوتي؟

التظليل الصوتي (Shadowing) تقنية تعلم لغة مدعومة علمياً، طُورت أصلاً لتدريب المترجمين الفوريين المحترفين. الطريقة بسيطة لكنها قوية: تستمع لصوت إنجليزي أصلي وتكرره فوراً بصوت عالٍ — كظل يتبع المتحدث بتأخير 1-2 ثانية. تُظهر الأبحاث تحسناً كبيراً في دقة النطق والتنغيم والإيقاع وربط الأصوات والاستماع والطلاقة.

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