쉐도잉 연습: Adding Fractions With Unlike Denominators - 영상으로 영어 말하기 배우기

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.

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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.

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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.

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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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"Now it's your turn." – 시청자에게 연습 기회를 주는 친절한 표현입니다.
"Feel free to pause the video and try those examples." – 시청자가 스스로 실습할 수 있게 권장하는 말입니다.

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이 비디오는 영어 쉐도잉 연습에 최적입니다. 설명자가 천천히 명확하게 말하는 부분을 따라하기 위해 shadowing site를 이용하거나 직접 반복해 보세요. 특히 "cross multiply"나 "improper fraction"과 같은 수학 용어의 발음과, "So let's start with this example."와 같은 연결 구의 리듬을 주의깊게 듣고 따라하세요. 이를 통해 영어 발음의 자연스러움과 말하기의 흐름을 개선할 수 있으며, shadow speech 연습을 통해 기억력과 반응 속도도 향상시킬 수 있습니다. 작은 예제부터 차근차근 따라해 보면, 수학뿐만 아니라 일상적인 설명에서도 자신감 있게 영어를 사용할 수 있을 거예요!

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문형	영상 속 표현
최상급 the -est / the most … — 집단에서 가장 높거나 낮은 것	the least common · the lowest
“might / may” 가능성 might/may + 동사 — 가능하지만 확실하지 않은 일	might find · might even be
“going to” 미래 be going to + 동사 — 계획이나 곧 일어날 것이 분명한 일	we're going to talk · we're going to add · i'm going to post
의무: must / have to / need to 어떤 일이 필요하다고 말할 때	need to add · need to write · need to multiply

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