the equation in the video title does not match the equation in the video itself. Btw, the equation in the video could arguably be simplified to 1+(y/x).

@silverhammer7779

11 ай бұрын

He says (X + Y)/X is the simplest form, then proceeds to show why it is NOT the simplest form. Using his explanation, the original expression can be simplified to 1 + Y/X.

@user-ky5dy5hl4d

11 ай бұрын

This can be correct. But how would you have 1+(yx) and the you would want to get back to x+y/x? You would have to turn 1 to x/x and multiply 1+(yx). And that is somehow a wierd transformation.

@silverhammer7779

11 ай бұрын

@@user-ky5dy5hl4dThe question was, what is the simplest form of the equation as originally presented? How you would transform 1 + Y/X back into the original equation does not matter.

@user-ky5dy5hl4d

11 ай бұрын

@@silverhammer7779 Thanks for the opinion.

@warblerab2955

11 ай бұрын

@@user-ky5dy5hl4d 1. it would not be 1+yx, it would be 1+(y/x). 2. it would not be a weird transformation at all. You would would just have to multiple 1+(y/x) by x/x. (x/x=1). You would end up with (x(1+y/x))/x, which = (x+y)/x.

My answer was 1 + X/Y. I suppose it depends on what you think is the simplest form.

@JohnnyHughes1

7 ай бұрын

Agreed .. I think your answer is correct.

@RodCalidge

6 ай бұрын

Your answer should have been 1+y/x

@marknewkirk4322

6 ай бұрын

@@JohnnyHughes1 "almost correct" - see below.

Great channel! I'm an artist and close to retirement. But I used to enjoy math (many) years ago and your videos are getting me back into it. It's especially nice to realize that I remember more math than I thought I would!

Got it! Thank you for your videos. I try to do at least one problem per day. I am learning and also being refreshed at the same time. I appreciate your show.

I can only see 1+y/x as a simpler form. Don't see any other options.

@danieldennis9831

11 ай бұрын

I see this is a trick question. I've written a few of these. My father wrote a few of these for quizzes. But I wonder why 1+y/x isn't acceptable as a simpler form. If there was a variable on the other side, e.g. z, I can see the original being the simplest because x+y=xz

@iowapanner2223

4 ай бұрын

I also like 1+ y/x as a simpler and less 'busy' form.

Where were you when I did maths in the seventies during my school years? I only "discovered" maths when I did Stats in College. Great explanation. My motto is "to understand is to know". Many thanks.

@1128lrc

11 ай бұрын

I agree big time. I bombed in Algebra in Hi school. When I finally got the courage to even think about it. But I just didn't get it. I actually started to understand some here. Would have to watch it a couple of more times. lol.

1+y/x seems to work as well. I don't know if it is simpler though.

@mikefeher6778

11 ай бұрын

This would have been my answer.

@juliecranford534

11 ай бұрын

That’s what I did as well. But I thought the same thing and am not sure if it’s any simpler than the original.

@Remember_when

11 ай бұрын

That's what I got.

@geraldaird1548

11 ай бұрын

This was my answer, but does it simplify?

@jazzdirt

11 ай бұрын

Yes same x/x + y/x

What an excellent teacher.

I'm DEFINITELY learning 😊. My initial thought was that the answer was Y, but then i plugged numbers into the variables and figured it out BEFORE I even hit play. Thanks!!

If I gave you the expression y/x + 1 and asked you to simplify, I doubt you’d transform it into (x+y)/x. Maybe I’m wrong, but if not, it seems like you’re using a curiously asymmetric definition of “simplify.”

@juliecranford534

11 ай бұрын

Good point. I hadn’t thought of it like that! (That’s what I did to “simplify.”)

Just subscribed. I am 66 years young-ish and my math skills are very rusty. Came across your channel this week and finding it very helpful, thanks😀

1+Y/X

@steveo1552

10 ай бұрын

That's what I came up with :)

@Remilation

10 ай бұрын

@@steveo1552 same cause i went x/x + y/x and x/x should always be 1 but adv algebra get into logs and i suck at those so i wasn't sure if you can go 1+ y/x

@darin7220

10 ай бұрын

Yup. That's what I got 2 different ways. First using @remilation's approach below but also works to factor out the X from the X+Y for X(1+Y/X)/X then cross canceling the X for 1+Y/X. This seems to be a silly way of doing things but I have run into the need to do it in the real world.

It can be simplified further. x/x + y/x=1+y/x.

@johnnygeneric161

9 ай бұрын

Yeah, I saw that, too.

Thank you so much for the material.

x/x + y/x = 1 + y/x... working very well for me ! Is it the simplest terms, I don't know but I had to do something for showing off...

@jiameru

5 ай бұрын

I agree with you since x divides x as well as y therefore x/x = 1 and y/x = itself

I think you confused some people with this 🙂 A lot of people are probably scratching their heads, saying that it's already in its simplest terms. Yes, you could say as some have commented, 1 + y/x, that is correct, but not simpler and no reason to do that, unless this was a different problem and you needed to break up the fractions as a step in the solution.

Thank you for all you do. Is it possible to get to the answer of each problem first and then explain!

I enjoyed learning algebra many years ago in high school. These ones you post are challenging, but I find myself trying to solve each one I see.. Thanks for the fun lessons.

I see y/x + 1 as a possible simplification! Even the case x=0 is handled that way! Ex.: x=2, y=4 -> 4/2 + 1 = 2 + 1 = 3. Same as (2 + 4) / 2 = 6/2 = 3.

Is 1+y/x a valid answer?

@leftovertech

10 ай бұрын

Fundamentally, yes. It is a different form and some consider it simpler.

Thank you for a bit of a jog there is a redundancy in the problem its x / x and blended so if you separate the problem you have x/x + y/x is that an approach anyone can chime in

@iowapanner2223

4 ай бұрын

That's what I did, and to me 1+ y/x looks less busy.

I believe the x+y/x could be simplified to x/x+y/x = 1+y/x which is the same answer as your numbered example.

@thehoneybadger8089

11 ай бұрын

z

@alanmadeira-metz3531

10 ай бұрын

Why is that simpler? You had 1 fraction, now you have 2. 🙂

@ianirvine414

10 ай бұрын

You put in the number 1 which came from nowhere.

@pmw3839

8 ай бұрын

@@ianirvine414. The number 1 came from x/x. (x + y) / x = x/x + y/x = 1 + y/x

Lets write the question like this: (x+y)/x. Would this expression mean the same thing: x/x+y/x? An example with the values x=2, y=4: (2+4)/2 = 6/2 = 3 and 2/2 + 4/2 = 1+2 = 3. I was thinking that the x/x part would solve something, but it seems not to be the case.

You actually never answered the fundamental question about the equation itself. You need to explain that the denomination “X” can be extracted for each Numerator so that X+Y divided by X is equal to “X/X” + “Y/X”. Using examples is good, but you need to explain the structure of the equation itself.

Y/X is my answer. You can split (X+Y)/X into X/X +Y/X, then the X/X cancel each other out and you are left with Y/X, which I would argue is the simplified version of (X+Y)/X. Edit: Nevermind, it would be 1+(Y/X), which is arguably not a simpler version. Its been a while since I've had to do these and am strangely enjoying attempting them.

Without watching the video or reading other comments: (x + y) / (x) = (x/x) + (y/x) = (y/x) + (x/x) = (y/x) + 1 = Best regards Marcus 😎

I don't see how anyone could get "y." The only answer is obviously 1 + y/x. That is, (x + y)/ x = x/x + y/x. By the way, the title beneath the video shows "(x + y)/y = ?" The answer to that is 1 + x/y.

OK .. I'll do it and then look at your solution (X + Y)/X = X/X + Y/X = 1 + Y/X I think the 'mistake' you are refering to is that people will forget that X/X = 1 and will say that X/X + Y/X = Y.

The equation in the video title does indeed match, it’s been solved already, but is giving another example of possibly a different form of the same equation, or showing a variation of the answer for a similar equation.

1+ y/x

I thought the answer was y/x + 1. If you plug in x=2 and y=4 you do get 3.

I got the correct answer inputting your numbers but used a different methodology. Because division supercedes addition I changed the equation to x/x + y/x or 1 + y/x. Is this a correct analogy?

@alanmadeira-metz3531

10 ай бұрын

It's correct, but not simpler than the original. Don't need to do anything to the original.

@iowapanner2223

4 ай бұрын

@@alanmadeira-metz3531 I really think 1+ y/x is less 'busy'.

(x + y)/x = a x + y = ax y = (ax) - x y = (a - x)(x - x) y = 0 x + 0 = ax x = ax a = 1 (x + 0)/x = 1 ✓

Where can I find a glossary of math terms?

This could be simplified to (1 + y/x), right?

He actually did not show how he arrived at (X+Y)/X )= (X + Y)/X . Ex. Since x and y have a common denominator which X, it could be written --> x/x + y/x --> 1 + y/x. Since 1 is x/x, then x/x + y/x can be written as ( x + y)/x. Since they didn't say what it is equal to, then that is the answer. But If make it equal to 0, then we have 1+ y/x =0 --> y/x = -1 --> y =-1x and x= y/-1. If we make it equal to 1, then we have 1+ y/x = 1 --> y/x = +1 -1) --> Y/x =-0. And so on. But it were X + (y/X) = ? then it would a whole different scenario. We would have (x^2 + y)/x.

I thought when there was addition or subtraction in the numerator, you could basically divide each term by the denominator. I mean, doesn't (x + y) / x basically mean x is the LCD, meaning it's = (x/x) + (y/x)? This would = 1 + (y/x), right? Not sure if that's really "simpler" or not, but would it be valid?

Couldn't you treat the division of x as a multiply by 1/x the quantity of x+y as with distributive property. This would give you x/x + y/x. This would result in 1+y/x with x can't being equal to 0

How is x + y / x simpler than 1 + y/x?

I personally find it more interesting WHY someone could do it wrong over knowing how it can be done correctly. Understanding why people make mistakes like that and what's their thinking process is can be very important!

@barrydouglas6276

10 ай бұрын

Put shortly most people like affirmation that their views are correct. When some loud strangers tell you just how correct you are it's mostly impolite people like me who think and sometimes say "Who the f*** are you to ascribe your views to mine? I think the why is well understood - being unpopular and correct is way less desirable to many than being popular and incorrect.

@SpamSucker

8 ай бұрын

Too many people just guess and move on, without taking the time to e.g. plug in some example numbers to test, or to remind themselves of PEMDAS rules etc. Not enough teachers discourage the guessing approach (too negative, I suppose… instead we coddle them with “good thinking, but…” nonsense.) If you have to guess, it’s an admission that you don’t know how to do it.

I actually subscribed because its interesting now for some reason.

My career I used a ton of math. Trig was the one I used the most. Finding the sides of a RT or the angle of a RT in order to right programs for CNC machines. This is eye opening and something that I enjoy very much!!

@adam_of_all_trades_no_mast8388

10 ай бұрын

I use to work at a vocational high school where we trained precision machining and I recall doing a class with them and telling them .0001 of an inch is also a fraction and they didn’t believe me. I showed them and light bulbs went off! 😆

(X+Y)/X=? = (X/X)+(Y/X) = 1+(Y/X) ##### (X+Y)/X=1+(Y/X) Multiply both sides by X ##### X+Y=X+Y So far so good. Subtract X+Y from both sides of the equation leaving 0=0 Just a thought.

This could have been a 2 minute video.

(x + y) / x = 1 + y/x

= x/x + y/x = 1 + y/x y/x = -1 y = -x

@elenarozkin4645

11 ай бұрын

1+y/x≠0 --> y/x≠-1 --> y≠-x No equation was given.

@AtomicExtremophile

11 ай бұрын

You're answer is incorrect. We aren't given an equation, we are given an expression...

(x+y)/x = x/x + y/x = 1+ y/x.

I'm sorry, but I don't get it. I just watched multiple videos of you teaching me to use PEMDAS. So WHY are we doing addition first?

I once got a 100, and my mommy was so proud she put my speeding ticket on the refrigerator.

Made a simple problem difficult!

x+y/x can also be written as x/x+y/1 (x/x=, 1+y/1=y which leads to y. In any case, the solution is Y.

@BrettWMcCoy

7 ай бұрын

Incorrect. It becomes x/x + y/x, which reduces to 1 + y/x

@nenadmitic5124

7 ай бұрын

You don have 2X, so listen. X+Y/X=x/x+y/1, you wrote x/x+y/x witch is x+y/2x. Go to school again. @@BrettWMcCoy

@BrettWMcCoy

7 ай бұрын

@nenadmitic5124 Sorry you're way off there. Watch the video.

I like propagating the divisor. Thus, (2 + 4)/2 is equal to 2/2 + 4/2 = 3

7:10 What about 6 and 1? aren't those factors of 6?

so what was the answer?

I hope you don't take this the wrong way but I believe you did an excellent job of showing how not to do the problem but not an excellent job in showing how to correctly do the problem. The only logical answer I could come up with is: (x/y) + (y/y ) which = (x/y) +1. If your intent was just to give a clue then you succeeded but if your intent was to show how to get the answer, then I'm not so sure you did.

@alanmadeira-metz3531

10 ай бұрын

It's x/x + y/x. There is no y in the denominator. The original fraction is already in its simplest form.

@oldnewtimer4662

10 ай бұрын

Just substitute simple numbers & you'll see how wrong you are. Try using x=12 y=4 @@alanmadeira-metz3531

(x+y)/x = x/x + y/x = 1 + y/x

Ok, so you can only cross cancel with multiplication?

WOW - I GUESS YOUR INITIAL DISPLAY OF THE QUESTION APPEARED AS AN EQUATION. WE SUGGEST THE QUESTIONS MUST BE CLEARLY DISPLAYED TO AVOID ANY MISUNDERSTANDING. THANK YOU.

@davidbeckenbaugh9598

11 ай бұрын

Why are you yelling?

@F.S.L.C.

11 ай бұрын

@@davidbeckenbaugh9598 WE DO NOT REPLY NON MEMBER - YOU ARE NOT INVITED HERE - BYE

@davidbeckenbaugh9598

11 ай бұрын

@@F.S.L.C. You do not seem to be facilitator on this site. So, I ask again, why are you yelling at me?

(x^2 + x*y) / x is NOT equal to x + y (x^2 + x*y) / x is equal to x + y ONLY WHEN x = 0 is exempted.

Multiple by 1/x reciprocal x/1: x(x+y):xtimes x, +xy?...

y=-x ........ y0, x0 .

3 +3 divided by 3 but you cant do anything unless you give values to X or Y if X or Y are Zero then the anwer is pretty simple 0 + 0 divided by 0 = 0 Zero

it sems to me simplifying just means dividing out the "x" so the answer is just y.

OK, why you didn't say 1 + (y/x) is the answer I don't know. But it is another way. Original problem could be written as (x/x) + (y/x) which then of course means 1 + (y/x).

👏👏👏👏👏

I would have made it 1+y/x.

Your heading to this video was (x + y)/y = ? You address with tacit brackets (x+y)/x = ?. Notice an inconsistency in the denominator? I'll assume denominator x. There are too many degrees of freedom to establish a single solution. I do find it simpler to think of the equation as x + y = ?x. This is particularly useful if x = 0.then y = 0 and ? can roam freely. The divide by zero is intriguing to some but the result of confronting infinity is avoided by multiplying by x on both sides - I suggest this is a simplification. The zero can also be achieved by x = -y and but now ? has to be 0 If ? = 0 then x and y are free to assume any values as long as they are polar opposites.Again I think this is clearer from x + y = ?x. than the initial (x + y)/x = ? as put on the board.

@kmcdaniel

10 ай бұрын

Huh?

Y= -X ?

You have nothing to do with this equation If xy/x, you can cancel x, but it's x+y/x

@leftovertech

10 ай бұрын

I started to set this equal to zero and solve for the two possibilities. Before I even got started, I realized that the thumbnail did not represent an equation at all.

Let's say x = 123 and y = 369. You're saying that doing (123 + 369) / 123 = 492 / 123 = 4 is simpler than doing 1 + 369/123 = 1 + 3 = 4. The first way I needed pencil and paper or a calculator, the second I did in my head, so which really is simpler?

Unless you put values to X and Y it is simply a trick question with no real answer. The maths excursion may help people understand the process but the quiz is unsolvable.

(X+Y)/X can be simplified to 1+Y/X.

I feel terrible because when I started I used 8 as x and 9 as y then added 8+9 for 17 then divided by 8 and got 2.125 for the answer rather than 3. So, where did I go wrong? The I added 5 + 7 then divided by 5 to get 2.4 then felt worse.

@lamper2

11 ай бұрын

3 isn't ALWAYS going to be the answer. only for the numbers he used as an example. I think you did both correctly for the numbers YOU used.

You sort of gloss over it, at the least it's not well emphasized, but you seem to be saying that the expression is already in its simplest form. I don't know how "Simplest form" is defined, so I have to take your word for it. Explicitly, I see: (1 + y/x)) as equally simple.

what about simplifying to 1 + y/x? Because (X+Y)/X = X/X + Y/X

I get y/x.

Using mental math, is it 1 + y/x?

I multiplied each side by X, replaced the ? with Z, then subtracted X from each side. Y = XZ - X or Y=X(Z-1) or Y/X + 1 = ?. Heh, don’t think I really simplified it that much

@MartinHermans-dw3is

7 ай бұрын

i got that too, but i broke the term in x/x + y/x = 1 + y/x. not really simpler tho.

Could ypu not simplify it by saying 1+y/x?

When you said it couldn't be solved further, you shoukd have ended it there. But you went on to show why, by plugging in numbers and confused most people. They seem to think you are saying the answer 6 at tiems or 3 at tiimes.

Equation on blackboard is different than the one in the title. On board equation can’t be simplified

x+y/x = x/x + y/x = 1+ +y/x

Some of you are assuming that since x/x = 1, x must = 1. Not a good assumption. 63/63 also = 1. In that case, 1 + y/63 = ?

@kmcdaniel

10 ай бұрын

x/x is defined as 1 for all non zero values.

What about 1 + (y/x)?

Here is my solution before watching the video: (x+y)/x = x/x + y/x = 1 + y/x

can't be simplified any further. (x+y)/x can't be simplified any further. It would be a different story if this was multiplication: (xy)/x. In this example, (xy)/x = y. You can cross cancel the x. In the prior example, since it is addition, you cannot cross cancel the x.

@visnjalivancic3953

9 ай бұрын

ofcorse you can cancel x , the correct answer is -y

The title does not match the image. Anyway, (x+y)/x is the same as x/x + y/x or 1+y/x.

This!! This is why it makes no sense!!! There is no reason for a problem like this!! I am in my 70s. It doesn’t make any more sense now than it did 50 years ago!!

Why the complicated explanation? It's just distributive multiplication: (1/x) (x + y) = x/x + y/x = 1+ y/x

Go back to school. Multiplication and division take precedence. You cannot add 2+4 2+4/2=3 is not the correct answer, you must first shorten the fraction 2+4/2=4

How about 1 + Y/X as an answer?

I think you may have made a error in the title. Doesn't actually change anything, but the Thumbnail and explanation are about (x+y)/x=? and the title says (x+y)/y=?

I got 1 + y/x = ? and realized it wouldn't go any further. If it were (x + y)/x = 0, you could simplify more and get x = -y. But since it is (x + y)/x = ? we can't do normal formula manipulation on the right side of the =.

@BrettWMcCoy

7 ай бұрын

Yep, that's what I got when I made it a linear equation, I ended up with y = -x

Take for example let x=0 and y=2 ans = 0

I think your use of '?" in an algebraic equation could be very confusing. '?' is NOT an algebraic variable. What you mean, I'm guessing, is what is the best simplification. Which seems to be 1+y/x.

Anyone? Why is this wrong? In order to remove the denominator I multiplied both sides by ‘X’ so X + Y= X, so X + ?= X, therefore Y = 0.

My answer is 1 + y/x. So if x is 2. and y is 6 it gives me 4 let's try yours (x+y)/x giving you (2+6)/2 which is 4 but you are saying it is 6

I'm confused...I thought it would simplify to x/x + y/x and then to 1 + y/x.

I AM 77 years old and want to repeat the comment “Where were you when I was in school.” It took years to fine PEMDAS. Without this tool algebra and beyond was a crap shoot. Sometimes I would get a correct answer and then the next time I wouldn’t. Math was so frustrating.

@mastertechnician3372

11 ай бұрын

Judy, how many times in 77 years you needed to use this in your day to day life? Useless garbage. That basic 100 pennies make a dollar you use every day. You spend half of $100 you had you still have $50 is the way of life. This x, y Square root and 3 power stuff is useless.

I respectfully disagree. I think it Can be simplified. It can be simplified to 1 + y/x. If you rewrite the original equation to ×/× + y/x.