I've never heard of a "shifting rule." I was taught to do just as you said; isolate X by subtracting from both sides.

This is how I was always taught. Or rather, I remember the teacher putting the minus threes (or plus threes or whatever) on either side of the equals sign, and we were supposed to intuitively understand what was happening without being told. A lot of algebra was like that: first a very brief, often unhelpful explanation, then a lot of problems solved in detail on the blackboard.

This is the right way to teach.

Wow, I didn't know that doing the same operation to both sides was taught like that. I feel like if I was taught that way I might have started to hate math.

This is really my favourite physics channel ! It explains things fundamentally and with pure logic ! Nothing is admitted, everything is about building step by step with pure logic without learning ! It's like the difference between learning how to build an house , or using pure logic and elementary "bricks" to try to build the house from scratch by ourselves !

when I first started inequalities chapter in 11th I had log forgotten about this concept but inequalities taught it again to us

Started teaching my 5yo equations, and started right with subtracting/adding things on both sides, my wife was passing by and said - just tell him about shifting, but I’ve declined it as this is not how the maths works, and 3 days after i see this video

One of my math teachers tought us, to think of it as an "old" balancing scale, which has to be always balanced. Found that analogy quite helpful. Greetings to Herr (Mr.) Benner!

@algirdasltu1389

4 ай бұрын

Mine did a mix of both lol

Ok this was really but really good because I was, say, "ill-conditioned", to shift around as you said. So even though I know and do it "the right way" many times with far more complex equations, I've never noticed how the shifting is really an *unnecessary* oversimplification of the actual correct procedure until you said it! Now this is really important because when I was trying to teach my kid to "shift around", he would often forget to "invert" the sign or the operation, because as you said, that was just an arbitrary rule he had to just memorize, but couldn't. Had I taught him the correct procedure right from the start, he would have not struggled at all!!

Im autistic and I’ve been teached the „shifting” method. I remember how I was struggling with this bc it wasn’t intuitive, I needed to remember that and I was like “but WHY?!”, like I was missing an important piece of information. Now it makes perfect sense! It’s logical. It’s obvious. Years after my teacher firstly introduced equations in math class… I hate “it is what it is, just accept it”, it need to be logical for me.

Actually in my case I invented the "shifting rules" by myself and later in school we were taught that in contrast to that, equational reasoning works like a balance. If you put or remove the same amount of weights to or from both sides then the balance will remain in equilibrium. The general rule is, that if x=y then for any function f, it also holds f(x)=f(y). This is connected to the extensionality of functions. When we are talking about addition, subtraction, multiplication and division then there is not much difference between the shifting rules and the balance metaphor. However, I had serious debates with mathematicians whether squaring or extracting the square root is allowed in equational reasoning. Of course it is. These are just special cases for f. However, people tend to combine application of f with subsequent simplifications that can be wrong. For instance: x²=25. Take square root on both sides yields sqrt(x²) = sqrt(25), and not x=5. It certainly holds sqrt(25) = 5, but sqrt(x²) is not equal to x, but to |x|.

Actually you have to do it as X + 3 = 5 (X + 3) + -3 = 5 + -3 X + (3 + -3) = 2 associative law X + 0 = 2 summation of inverses X = 2 identity law There are no laws for subtraction and division. They are shorthand for addition and multiplication of inverses. So (x - 1) - 2 is not equal to x - (1 - 2) but (x + -1) + -2 = x + (-1 + -2). This is really key to understand what is happening.

In general functions preserve equality if you respect the domain, no manner what system

I was never taught this "shifting rule" in school. This is the first I'm hearing about it. I was tought to always balance the equation. If you do something on one side, do it on both sides. Always. This other method does sound pretty devoid of learning, ironically.

Thank you for teaching the correct rule. The shifting "gimmick" worked on this very simple equation - but this is a physics oriented channel. Physics equations are rarely X+3 = 5 simple. You teach it right the first time and it saves the student frustration later on when the "gimmick" shortcut no longer works.

Such a simple and a great video Thank you

your explanation is exactly how i was taught about it. In general, the equal sign is telling you that whatever is in the right and whatever is in the left are two representations of the same number. So, applying any function to both sides respects equality... in symbols if x=y then f(x) = f(y) for any function... However, here is what blew my mind: how different my life would've been if instead of explaining this to me, they had made me memorize all those other rules? 🤯

Avinash sir was talking about this att stayqrious few months ago... interesting...my dad had told me this stuff when i was learning addition in lower grades luckily

Sir Mahesh I love your lectures, how can I get all of your physics video contents

Sir I also know the definition of flux but what is really field lines? How can Electric field which is just a region be equal to fix per unit area.l have no idea abt all these

A new insight.❤

Hey thanks ! I am a curious physics student in 12th please make video on equation of trajectory of projectile with gravitation variation. g(h) =g(R/R+h) ^2

@toffi2390

Ай бұрын

Did you write it up properly? R/R+h is just 1+h. Did you mean g(R/(R+h)) ?

Please post video on Multiplication logic

Sir can you please make a video on how to read conceptually as everyone can read books but not everyone can understand

finally, a video from you where i have discovered the lesson myself before!

That is so sad that this is skipped. Understanding the logic of methods are fundamental to greater literacy down the line. I may use “shifting” to visualize mental math, but I was still taught the concept.

does that will also hold true if we multiply or divide LHS & RHS by 0 ?

@magma90

3 ай бұрын

If we have an equation such as x+3=5 we can multiply both sides by 0 and arrive at 0*(x+3)=0*5 which then simplifies down to 0=0, this doesn’t help us with solving for x, but it will still keep the equality to be true. If we had 0*x=0*(x+1) we can attempt to divide by 0, however we get 0/0 which is undefined as it leads to x=x+1 which when we subtract x gives 0=1. In general if we have an equation x=y we can take any function f and apply it to both sides of the equation giving f(x)=f(y), this does not imply the opposite however, if we have f(x)=f(y) this doesn’t mean that x=y. however if we had a function g such that g(f(x))=x for any value of x, then we could take f(x)=f(y) and apply g to both sides giving g(f(x))=g(f(y)), then because of how g was defined we get x=y. this only works if f is bijective, meaning there doesn’t exist values x and y such that x≠y but f(x)=f(y). The function x^2 is not bijective because (2)^2=(-2)^2, this means that if x^2=y^2, we do not know if x=y.

If x + 3 = 5, then am I the only one that can see that x = 2 without calculation? Because I already know that 2 + 3 = 5. What else could it be?

OK. Now, tell me: in fractions we denote a half by 1/2. Why should we keep 1 in the numerator when 1 is gone by braking it in two halves? I.e. One became two halves of one and one does not exist anymore.

@carultch

6 ай бұрын

Because 1 is the multiplicative identity, that is included as a placeholder, for whatever else might be divided by 2 in its place. Since "/2" doesn't make sense without something upstairs, we don't write the reciprocal of 2 that way, and instead we include the multiplicative identity as a de-facto numerator, so we can express a complete thought when identifying the number equal to the reciprocal of 2. You could write it as 2^(-1) if you prefer.

@user-ky5dy5hl4d

6 ай бұрын

@@carultch Your point is valid but only in abstract approach of math. But it is different in reality. When you have a stick of whatever the length and you call it one and then break it in half, the one length disappears. You have two lengths of two different sticks; shorter but two not one. So, one is gone and one was replaced by two. The same with multiplying by zero. In reality when you multiply one by zero it is one.

Sir I know the meaning of guass law but not able to solve questions of neet and not able to think differently

Hello sir, I am from Bangladesh.I want to make video like you in Bengali like you.Where can I get tutorial for making such video for windows in sketchbook.. Like Electric motor video on Khan Academy India English.

I remember posting this very question on the Khan Academy - where does minus this + that come from...? Who says so..etc. I worked it out by subtracting marbles from both sides in my mind. It was the same for 0÷1 etc. i.e. there is no = sign for the marbles to hit or 0 jumps all over the place. I tried solving X+3=5 by dividing both sides by 3. I couldn't get further than this: (X/3) + 1 = 1.66667 I sure thats not right.

@ausgoogtube01

6 ай бұрын

No wait! It almost is! Eureka! Subtract 1 from both sides gives: (X/3) = 0.66667 0.66667×3 = X X = 2.00001 Horay! Well...close enough.

@entertainme121

4 ай бұрын

@@ausgoogtube01 lol, thank you. I got stuck too. I would have given up if I didn't see your comment :) I wish I had the eureka moment, though. :(

This is how my 7th grade teacher taught us

Is this not how it's normally taught? I grew up in a fairly poor area in Arizona (which is not known for having the best education system), and this is how we were taught.

This kind of videos are priceless

I started the video and Ik why it isn’t right. I then also pulled it to min 3 or something where he was saying let the kid explore and I watched the full video to learn how to teach authentically

i feel bad that noone recognises him as the one behind khan academy

I've just discovered your channel, and this is the second video I've watched. The first one was "the only video on youtube explaining why light slows down in glass", which I need to think about some more. It's quite surprising to see that one day you make a video explaining a subtle phenomenon in physics and another day you talk about elementary algebra. There are both pros and cons to this diversity as I'm sure you realise! In this video, you assert that many students learn by rote that e.g. addition "becomes" subtraction when you move it to the other side of the equation without ever understanding why. The answer to the "why" being that a = b implies f(a) = f(b), which applied to this example tells us that x + 3 = 5 implies x + 3 - 3 = 5 - 3, from whence we get x = 5 - 3. I disagree with your framing of the situation. According to you, a teacher gives a student incorrect information by teaching them a fictitious "shifting rule". But the "rule" is just a shortcut, and the only thing that's "incorrect" in this situation is the teacher's assumptions about the student's prior knowledge. The hypothetical teacher assumes that the student already knows that the "shifting rule" is just a shortcut, and fails to realise that they might not have internalised the underlying "why".

semantics. it's not wrong at all, it just doesn't explain it in depth is all. the person simply didn't show the full work, but it's still correct.

I didnt get an answer from my teacher

Yeah brother. I learned you must apply the same operation to both sides of the equation.

@Physics_Dude

5 ай бұрын

Every teacher (including myself) knows this. I'm not sure why this video was even made.

our schooling system is broken if someone has to watch a youtube video to learn this!

idk a single person who taught or through shifting rules

If a + b = c, then a = c - b. That is not a myth!! I don't understand the point of this video.

@michele3900

28 күн бұрын

Because it fails with complex equations where the real math happens.

i learned this method first then i learned transposing

This is how it's thought in England

It is a myth. I was even taught this method but on Khan Academy. I learned this intuition from this man.

Clickbait ! This guy will teach you how to breathe.

now my eyes are opened ๏_๏

😂😂 Prove it that it is wrong

The whole video feels like a straw man argument. No one has claimed that positive becomes negative or multiply becomes divide.... Except you. The usual approach to such equations is to write on the side which mathematical operation is applied to both sides of the equation: x + 3 = 5 | -3 x + 3 - 3 = 5 - 3 x = 2 This is how every child learns it at school.

@name-nam

3 ай бұрын

its not a strawman argument. look at the comments, plenty of people agree that this part wasnt taught to them, and they just had to accept the shifting rule

@abhijeetvaidya1638

2 ай бұрын

i think in context of indian education system its valid , i don't know how its has been taught in other countries.

What about inequalities when the sign changes? I was just told thats how it is and to not question it.

Dude stop reinventing the wheel. Get back to your physics. Stop confusing people.

It would probably be better to show that -3 = -3 (don't forget the equal sign) so that they will get used to that now and see that combining linear equations later will not be so confusing.

Don't spread wrong stuff man, i mean i really like your physics video but its so embarrassing to watch this. If you know A=B Do you write it like this everytime A+1-1=B+0 No right because you know adding or subtracting zero means nothing over here. There is nothing wrong about it. Its not rule you could say its art or skill (or observation that this is true)you learn from practicing maths. I will agree that it should not be introduced to young kids, first thing that they learn cause it somewhat limits their creativity. They should figure this out themselves. I did that way and i think it will be much more fun that way.

Still the equations do not show the whole picture. Is it allowed to apply squaring to both sides of an equation? This depends on what you consider "allowed". If x=y, then x²=y². In this sense, squaring is allowed. However, it can turn inqualities into equations, e.g. x² = (-x)² although x=-x does not hold for x other than zero. In German school we are taught equation transformations and are told to specify the set of solution at the end. I do not think this is a good idea, because this way the final set of solutions comes out of thin air and people easily forget to verify their solutions. I propose we work with the set of solutions from the beginning. E.g. {x : sqrt(x) = 30-x} = {x : sqrt(x)+x = 30}, because the transformation is reversible. But {x : sqrt(x)+x = 30} is a subset of {x : (sqrt(x)+x)² = 900}, because the equation transformation is not reversible. Thus we know, that at the end we have to check all elements of the final set, whether they are also contained in the initial set.

I. Am. Mind-blown.

You must prove that x + 0 = x. I am sure that you can’t do it. Let me know so I can show you how its done.

@appl3thegr3at64

5 ай бұрын

x + 0 = x x = x done