Combining like terms introduction | Introduction to algebra | Algebra I | Khan Academy

In simple addition we learned to add all the numbers together to get a sum. In algebra, numbers are sometimes attached to variables and we need to make sure that the variables are alike before we add the numbers.

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Algebra I on Khan Academy: Algebra is the language through which we describe patterns. Think of it as a shorthand, of sorts. As opposed to having to do something over and over again, algebra gives you a simple way to express that repetitive process. It's also seen as a "gatekeeper" subject. Once you achieve an understanding of algebra, the higher-level math subjects become accessible to you. Without it, it's impossible to move forward. It's used by people with lots of different jobs, like carpentry, engineering, and fashion design. In these tutorials, we'll cover a lot of ground. Some of the topics include linear equations, linear inequalities, linear functions, systems of equations, factoring expressions, quadratic expressions, exponents, functions, and ratios.

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[ChanceTheCheetah]

This is better explained than any school math lesson I've seen on the topic.

[scrubs]

everyone:

Kahn academy: CHucK NoRRiS

[ashleyhernz]

BRO THIS LEGIT HELPED ME SOO MUCH I DONT UNDERSTAND MY TEACHER BECAUSE ALL HE DOES IS SOLVE THE PROBLEM AND EXCPECTS US TO SEE WHAT HE DID. FIGURE OUT AND IM SLOW SO THIS REALLY HELPED AND I HAVE A TEST TOMORROW IM SO GLAD YOU EXIST

[aaronholmberg]

This is literally the best Khan Academy video of all time. It earned 10 Oscars, 5 Emmys, 4 People's Choice Awards, The Congressional Medal of Honor, the Nobel Peace Prize, and generated over 897.6K Purple Hearts from its viewers. Sal Khan was knighted twice and is now fully immune to all current and future strains of covid.

[MahiraAziz]

nobody:
nobody ever:
not even my teacher:
Sal Khan: Explaining algebra with ChUcK nOrRiSeS is TOTALLY normal

[blackgamer]

Man, he got straight to the point when he started the video.

[Bigglesworthicus]

Chuck Norris is indeed a *very* tangible thing

[dariusukun]

This guy just explained and saved us an entire 4 week session of back and forth. Thank you.

[TooWongCool]

But I think the 5 Norri would get hungry and eat the 9 plums.
I was waiting to hear this.

[ADrunkenMic]

this really helped me alot i was struggling alot and this helped break it down and it did in in a humorous way in my opinion

[fireniro]

omg this made so much more simplier how my teacher explained it. and quite entertaining

[nv]

No one:

Literally no one:


Khan Academy: So lets say that we have 2 chuck norrises or two chuck norri...

[inu]

he's adding more Chuck Everyone The World Is Dommed!!!

[berryblusherr]

Hi Khan. I am preparing for placement exams for college and as a 33 year old woman, I haven't been to school in nearly 14 years.

thank you for all that you do. one day in the near future I will return having mastered all of this material.

xoxo from Chicago

[분꽃나무]

13강 : Algebra 1 - Unit1 - lesson 4 - 1/4
Unit1 Algebra foundation
lesson 4 combining like terms
1/4 Intro to combining like terms

4. this as 디세스 0:22
6. this is just 디시저슷 0:33
6. ~s and this is just 슨 디시저슷 0:33
8. total and 토를른 0:47
14. do that as an 두대래전
18. And if you 애니퓨 1:57
18. think about it 띵커바릿 1:57
24. add another 애러나더 2:40
26. Well, I wouldn't add the 월라우든 내더 2:45
35. add the y 3:30 3:31
29. And would 애누욷 2:55
33. What do I have now? 워루아이 해브 나우 3:20
35. And the I'd 앤데나읻
35. to that I add 투대라이앧 3:32
35, 36. If I have 3:31 3:36
42. what would happen if I were to have 웟욷 해쁘니쁘 아이워르 해애브 3:59
44. This is just 디시즈저슷 4:12 4:13
34. Well, I can't add the 월아이캔 애디 3:22
46. well, I got 웨아갓 4:17
46. Well, that means I 웨댓민자이
47. well, I've got 4:24
47. you'd say 윧쎄이 4:24
47. And then I got another 앤데나 가러나더 4:27

18, 20. multiply 타. …에 (…을) 곱하다((by)).
2 multiplied by 4 : 2 곱하기 4
multiply 5 by 3 : 5에 3을 곱하다
Multiply 2 : 2를 곱하다

1. 0:01
2. 0:07 0:13
3. 0:14 0:15 / 0:17
(Norrises) And this might seem a little bit obvious, / but ~
시즌디스 마잇씸

4. 0:20 as 0:22 two chuck Norrises 0:31
~ as literally a Chuck Norris plus a Chuck Norris.
5. 0:26 0:31
6. 0:31 and 0:33 0:34
(Norrises) You could also do this 2 times Chuck Norris, and this is just another way of representing it.
노리슨 디시저슷 ~ 레프리제닝잇
7. 0:35 0:36

8. 0:45 0:47
And so we would have a grand total-- and this might be very simple for you.
우르해버 그랜 토를른
이렇게 나타내면 총 개수를 쉽게 구할 수 있어요
gránd tótal 총계, 총합계, 총개수
9. 0:49 0:50 노리시스
10. 0:54

11. 1:00 1:02
Now, let's get a little bit more abstract here. ~ is a very tangible thing.
레츠게러 리를빗 업스트랙 히얼. 시즈 어베리 탠저블 띵
이제 사진처럼 구체적인 사물이 아닌 추상적인 값으로 생각해 봅시다.
tangible 유형의, 실체가 있는, 현실의, 실제의, 명백한, 확실한
12. 1:05
So let's go to a little bit more of traditional algebraic notation.
대수학적 표기법으로 나타내 볼게요

13. 1:09 this 1:13 and 1:16 how many 1:21
14. 1:23 1:24 / 1:25 /we 1:27/ but 1:29
Well, once again, 2xs, that's 2 times x.
You could do that as an x plus an x.
We don't know what the value of x is.
But whatever that value is, we can add it to itself
x의 값은 모르지만 값이 얼마이든지 덧셈은 할 수 있어요.
1:32 /let 1:35 / 1:37
And then 3x's (are they're) going to be that value.
Let me do that in that same green color.
3x's are going to be that value plus that value plus whatever that value is.
15. 1:44
16. 1:47
17. 1:50
18. 1:57 all 1:58 is we 2:00 2:02
And if you think about it, all we really did-- and hopefully, you conceptually get it-- is we just added the 2 numbers that were multiplying the x.
올위 리얼리 디든 호쁠리 유 컨셉슈얼리 께릿 이즈위 저슷 애릿 더투 넘벌 잿월 멀티플라잉 더엑스
지금까지 계산한 과정은 x에 곱해진 두 수를 더한 것과 같습니다.

19. 2:04 2:05 2:06
And these numbers, the 2 or the 3, they're called coefficients.
디즈 넘벌저 투 오얼더뜨리 데얼 콜드코어삐션츠
20. 2:07 but it 2:08 this 2:10 that's 2:11
Very fancy word, but it's just this constant number, this regular number that's multiplied by the variable.
베리 뺀시 워얼, 뻐릿쩌슷띠스 칸스턴 넘벌, 디스 레귤러 넘벌 댓츠 멀티플라잇 바이더 베리어블
계수는 변수에 곱해진 상수를 의미합니다.
constant 정수, 항수 <-> variable

21. 2:13
계수 2와 3을 더해서 5x를 구할 수 있었어요.

22. 2:17
23. 2:18 2:19
Let's go back to this original expression, the 2 Chuck Norrises plus 3 Chuck Norrises.
빽투디 써리지널 익스프레션
24. 2:23 2:38
25. 2:42 2:43

😮26. 2:45 2:46
Well, I wouldn't add the 7 to the 2 to the 3 plus 2.
월라우든 내더 쎄븐 트더투 르더뜨리 플러스 투
계수들을 그냥 더하면 안됩니다
27. 2:48
28. 2:49 they're 2:52
You have 2 Chuck Norrises and 3 Chuck Norrises, so they're still going to simplify to 5 Chuck Norrises. 노리시즌
사진 2장과 3장은 합쳐서 사진 5장이라고 할 수 있지만
😮29. 2:55
And (then we) would separately think about the plums.
애누욷 세퍼럿리 띵커바웃더 플러엄
자두는 따로 생각해야 합니다
😨😥30. 2:57 2:58
We have 7 plums, (and) we're adding another 2 plums.
스 뤠딩어나더 투 플러엄스
31. 2:59
32. 3:02 so 3:04

33. 3:07 3:08 instead 3:10 what 3:20
Similarly, over here, if I had, instead of just 2x plus 3x, if I had 7y plus 2x plus 3x plus 2y, what do I now have,
씨머럴리 오버히얼, 이프 아이해애드, 인쎄러브저스 ~ 워루아이해브 나우

34. 3:22 3:24
Well, I can't add the x's and the y's.
월아이캐앤 애디 엑시즌더 와이즈
They could very well represent a different number.
x와 y는 다른 값을 나타내므로 서로 더할 수는 없습니다
very well 확실히, 명백히; 좋아

35. 3:26 / 3:28
So all I can do is really add the x's. And then I get the 5x.
쏘올라이캔두 이즈리얼리 애(드)디 엑시즈.
x의 계수끼리 계산하면 5x가 되고
3:30 / 3:31 3:32 3:33 3:35
And then, I'd separately add the y.
앤데나읻 쎄퍼럴리 앧더 와이
If I have 7y's and to that I add 2y's, I'm going to have 9y's.
(이프아이 햅 : 엄청 빠르고 약하게) 쎄븐와이즈 앤투대라이앧 투와이즈, 암고느해브 나인 와이즈
y의 계수도 더해주면 7y+2y=9y가 됩니다

36. 3:36
37. 3:40
38. 3:43
39. 3:45 /3:50

40. 3:56
So hopefully, that makes a little sense.
쏘 호뿔리댓 메익슬 센스
😢41. 3:57 3:58
Actually I'll throw out one more idea.
액츄얼아을 뜨로아웃 원모얼 아이디어
한 가지 개념을 더 살펴봅시다
ㆍㆍㆍ
throw sth out 1. (별로 깊게 생각하지 않은) ~을 말하다[내뱉다] 2. (제안·아이디어 등을) 물리치다[거부하다/기각하다]

42. 3:59, 4:00 /2x 4:02
So given this, what would happen if I were to have 2x plus 1 plus 7x plus 5?
웟욷 해쁘니쁘 아이워르 해애브
2x+ 1+ 7x +5를 간단히 정리해 봅시다
43. 4:08/ 4:09 4:10 but 4:11
~. you might be tempted to add the 2 plus the 1, but they're adding different things.
유마잇비 템팃드 애더 투 ~, 버떼얼 애링 디뻐런 띠잉즈
2x의 계수 2와 상수 1은 서로 더할 수 없어요
be tempted to do ~하고 싶다, ~하도록 유혹당하다
44. 4:12
~. This is just the number 1. 디시즈저슷 더 넘벌원
2x는 변수항이고 1은 상수항이기 때문이죠.
45. 4:14 4:15
So you really just have to add the x's together.
리얼리저슷 햅투 애드디 엑시즈
그러므로 x의 계수끼리만 계산해줘야 합니다

46. 4:17 4:18 And 4:19 /4:21
So you're going to say, well, I got 2x's. 쏘유고느 쎄이, 웨아갓 ~.
And I'm going to add 7x's to that.
Well, that means I now have 9x's.
웨댓민자이핻 나우해애브
2x와 7x를 더하면 9x가 되고

47. And then 4:23 separately 4:24 I've 4:25 / And then 4:27 / 4:28
And then, separately, you'd say, well, I've got just the abstract number 1. 쎄퍼럴리, 윳쎄이 웨아이브갓 저슷띠 앱스트랙 ~
And then I've got another 5. 앤데나 가러나더 빠이브
1 plus 5 is going to be equal to 6.
상수끼리 더하면 1+5=6이 됩니다
ㆍㆍㆍ
abstract 이론적인; 관념적인, 공론적(空論的)인.
.

[icewave]

This video is so nostalgic to me, it was very helpful when I was learning algebra, and more importantly it was the first time I heard about Chuck Norris

[melodiesformath]

This video was a nice refresher! These fundamental concepts are essential to understanding higher-level math and are what inspired us to create original songs explaining math concepts!

[Kambra]

Lol, I think Sal might have watched Martial Arts movies in the past ;)

[Jillybean]

Leave it up to the amazing and majestic Khan Academy to use Chuck Norris as an example in Mathematics.

[theblacktigress]

You deserve so much, helping people around the world. I would have failed AP Maths.