(x + y)/y = ? Many Will Get WRONG! Avoid this common Math Mistake!
HTML-код
- Опубликовано: 10 сен 2024
- How to simplify a fraction or rational expression by cross canceling like factors.
TabletClass Math Academy
Help with Middle and High School Math
Test Prep for High School Math, College Math, Teacher Certification Math and More!
All Courses - TCMathAcademy....
✓Help with Middle and High School Math (Public/Private Schools)
✓High School & College Math Test Prep
✓Teacher Certification Math Test Prep
✓Homeschool Math Program and Courses for Pre-Algebra, Algebra 1, Geometry, Algebra 2 and Pre-Calculus.
Popular Math Courses:
Math Foundations
tabletclass-ac...
Pre-Algebra
tabletclass-ac...
Algebra
tabletclass-ac...
Geometry
tabletclass-ac...
Algebra 2
tabletclass-ac...
Pre-Calculus
tabletclass-ac...
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).
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.
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.
@@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.
@@silverhammer7779 Thanks for the opinion.
@@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.
I can only see 1+y/x as a simpler form. Don't see any other options.
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
I also like 1+ y/x as a simpler and less 'busy' form.
My answer was 1 + X/Y. I suppose it depends on what you think is the simplest form.
Agreed .. I think your answer is correct.
Your answer should have been 1+y/x
@@JohnnyHughes1 "almost correct" - see below.
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.
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.
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.”
Good point. I hadn’t thought of it like that! (That’s what I did to “simplify.”)
1+y/x seems to work as well. I don't know if it is simpler though.
This would have been my answer.
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.
That's what I got.
This was my answer, but does it simplify?
Yes same x/x + y/x
It can be simplified further. x/x + y/x=1+y/x.
Yeah, I saw that, too.
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😀
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!!
What an excellent teacher.
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.
1+Y/X
That's what I came up with :)
@@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
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.
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...
I agree with you since x divides x as well as y therefore x/x = 1 and y/x = itself
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.
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.
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.
z
Why is that simpler? You had 1 fraction, now you have 2. 🙂
You put in the number 1 which came from nowhere.
@@ianirvine414. The number 1 came from x/x.
(x + y) / x = x/x + y/x = 1 + y/x
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
That's what I did, and to me 1+ y/x looks less busy.
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.
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!
Is 1+y/x a valid answer?
Fundamentally, yes. It is a different form and some consider it simpler.
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 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.
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.
I thought the answer was y/x + 1. If you plug in x=2 and y=4 you do get 3.
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
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.
This could be simplified to (1 + y/x), right?
How is x + y / x simpler than 1 + y/x?
Thank you so much for the material.
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.
This could have been a 2 minute video.
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?
(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 ✓
= x/x + y/x
= 1 + y/x
y/x = -1
y = -x
1+y/x≠0 --> y/x≠-1 --> y≠-x No equation was given.
You're answer is incorrect. We aren't given an equation, we are given an expression...
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?
It's correct, but not simpler than the original. Don't need to do anything to the original.
@@alanmadeira-metz3531 I really think 1+ y/x is less 'busy'.
Multiple by 1/x reciprocal x/1: x(x+y):xtimes x, +xy?...
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.
Incorrect. It becomes x/x + y/x, which reduces to 1 + y/x
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
@nenadmitic5124 Sorry you're way off there. Watch the video.
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 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.
It's x/x + y/x. There is no y in the denominator. The original fraction is already in its simplest form.
Just substitute simple numbers & you'll see how wrong you are. Try using x=12 y=4 @@alanmadeira-metz3531
(x + y) / x = 1 + y/x
(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.
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.
(x+y)/x = x/x + y/x = 1+ y/x.
Thank you for all you do. Is it possible to get to the answer of each problem first and then explain!
y=-x ........ y0, x0 .
You have nothing to do with this equation
If xy/x, you can cancel x, but it's x+y/x
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.
Made a simple problem difficult!
I like propagating the divisor. Thus, (2 + 4)/2 is equal to 2/2 + 4/2 = 3
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.
ofcorse you can cancel x , the correct answer is -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.
it sems to me simplifying just means dividing out the "x" so the answer is just y.
I would have made it 1+y/x.
(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.
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
Equation on blackboard is different than the one in the title.
On board equation can’t be simplified
what about simplifying to 1 + y/x? Because (X+Y)/X = X/X + Y/X
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'm confused...I thought it would simplify to x/x + y/x and then to 1 + y/x.
Take for example let x=0 and y=2 ans = 0
Where can I find a glossary of math terms?
(X+Y)/X can be simplified to 1+Y/X.
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?
Common mistake; who by? 4 year olds?
(x+y)/x = x/x + y/x = 1 + y/x
Y= -X ?
The title does not match the image. Anyway, (x+y)/x is the same as x/x + y/x or 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.
Huh?
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.
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.
Why the complicated explanation? It's just distributive multiplication: (1/x) (x + y) = x/x + y/x = 1+ y/x
Why would they try to cross cancel. When anything divided by itself is 1. They just try to confuse people but they confusing themselves
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.
Why are you yelling?
@@davidbeckenbaugh9598 WE DO NOT REPLY NON MEMBER - YOU ARE NOT INVITED HERE - BYE
@@F.S.L.C. You do not seem to be facilitator on this site. So, I ask again, why are you yelling at me?
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
Your videos are unhelpful and confusing. You say here that the expression cannot be simplified. Try telling that to any physicist who is trying to integrate or differentiate an expression of that type. He will always simplify it to 1 + (y/x). How long did you say that you had been confusing children with your misplaced pedantry?
Using mental math, is it 1 + y/x?
The title is (x+y)/y = ....but.....the picture shows divided by 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?
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.
so what was the answer?
x+y/x = x/x + y/x = 1+ +y/x
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.
Could ypu not simplify it by saying 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!!
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!
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.
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.
What about 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 = ?
x/x is defined as 1 for all non zero values.
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.
I think we have a Fake News problem here. It is not even faintly credible that 99% of any audience get this wrong.
It's nice that you're out there trying to teach arithmetic, John. It is *not* nice that you are telling stupid lies to do it.
Ok, so you can only cross cancel with multiplication?
I simplified it to 1 plus y/x.
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.
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 =.
Yep, that's what I got when I made it a linear equation, I ended up with y = -x
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 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.
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.
I wonder that this is a problem. It can't get much simpler than this.
7:10 What about 6 and 1? aren't those factors of 6?
I get y/x.