Fractional part of x

[@m.h.6470]

Solution: x + 3{x} = 11 let x = k + {x}, where k is an integer, so we have k + {x} + 3{x} = 11 k + 4{x} = 11 since both k and 11 are integers, 4{x} also has to be an integer. also, the boundaries of {x} are 0 ≤ {x} < 1. therefore {x} can only be 0, 1/4, 2/4 or 3/4, as no other fraction in that range, multiplied by 4, results in an integer. {x} = 0 → x + 3 * 0 = 11 → x = 11 {x} = 1/4 → x + 3/4 = 11 → x = 41/4 {x} = 2/4 → x + 6/4 = 11 → x = 28/2 → x = 19/2 {x} = 3/4 → x + 9/4 = 11 → x = 35/4 therefore x ∈ {35/4, 19/2, 41/4, 11}

[@m.h.6470]

After watching the video: Stunned, how complicated you can make a very simple task!

[@PrimeNewtons]

Would you like to recommend your own videos. Email me some links. I'm sure I can learn one or two things from your style. Never Stop Learning!

[@m.h.6470]

@@PrimeNewtons Sorry, I don't make videos. I don't have time for it. I am a software developer with focus on writing and optimizing algorithms to analyze data (mostly statistical, but often also logical). So this kind of math is literally my bread and butter...

[@PrimeNewtons]

From experience, if other viewers find your solution easier to understand, they would give it a thumbs up. Use that as a yardstick. I'd pin your comment.

[@PrimeNewtons]

@m.h.6470 I actually see your point. When, it's obvious, your way is the way.

[@muhammedrayan4048]

guys like the video cause this guy deserves the world

[@butch2kow549]

Notice that the coefficient of k divided by the denominator of x is the difference between two consecutive solutions of an equation of this type(whatever you want to call or name this equation). Furthermore, the number of solutions is the sum of the coefficients of x and {x} in the original equation. I always enjoy your videos.

[@savaesmek]

i thought about writing x as [x] + {x} so the equation becomes [x] + 4{x} =11 which means 4{x} is an integer but {x} is also lower than 1 this can happen only if {x} ={0/4,1/4,2/4,3/4} and then you just solve for each case

[@boguslawszostak1784]

[x] + 4{x} =11 is positive integer, so 4{x} =11 - [x] is integer. {x} is nonnegative so 4{x} in Natural number less then 4 4{x}

[@markusmcgee]

Software developer here. I love the videos. I also studied mathematics. Watching your videos get are pleasant mental gymnastics for me!!!

[@punditgi]

Prime Newtons raises the floor of math knowledge! 🎉😊

[@jennymarx9228]

I really appreciate your efforts in making us clear in mathematics... because of you I developed interest in mathematics sir 😊😅

[@77Chester77]

Please keep the high quality of your videos (i.e. interesting math problems presented in your great unique way)! Even if it means to lower the quantity ;-)

[@PrimeNewtons]

Thank you!

[@mtk2iscool247]

Great video!

[@nothingbutmathproofs7150]

Nice job! I have never learned anywhere (other than here!!) that {x} = the fractional part of x. Thanks. Here's a topic for a new video. Show how you can use the the floor of x to round off numbers to any decimal place of your choice.

[@PrimeNewtons]

Are you assuming I already know how to do that 😏. Haha, that's great faith you have in me.

[@nothingbutmathproofs7150]

You're the best. I thought that knew everything. Say you have 7.8. Add .5, then just take the integer part and you'll round off 7.8 to 8. If you have 7.3, add .5, get 7.8, take integer part and get 7. If you want to round off 7.3892 to two decimals, then multiply 100, do the trick like above and then divide by 100.It's very cool. I bet that you knew this(??). let me know.

[@thorhilda]

I found it more intuitive to start with 0

[@dirklutz2818]

Fantastic!

[@ReyazulislamReayal]

amazing class sir❤

[@jamesharmon4994]

I followed you every step of the way, understanding it, but I doubt I could do it myself yet.

[@adw1z]

The shortcut for this problem is to notice that 4{x} must be an integer, which means {x} can only take some modulo multiple of 1/4 - however, your video is better IMO, as it allows u to solve any general problem of this kind e.g. if we had a mix of fractional and negative terms, or even if we had a simultaneous system of such equations, your approach is fool-proof

[@kragiharp]

With your videos I never stop learning. Thank you for living. ❤️🙏

[@shahmatsimplex4144]

I have taken many advanced math classes back in the early 80s and can't remember LambertW, or equations with floors or fractional parts. Did I sleep through those classes or am I suffering from senility?Your videos are awesome, great handwriting, and teaching style.

[@VimrrezvBvqeri]

🤩🤩

[@ひろ-j9s]

That would be great.❗️ Polite and easy to understand . 🇯🇵

[@vitotozzi1972]

What a beautiful equation!!! Thanks friend!

[@brenobelloc8617]

Cleaning the floor funcion with my brain. Thank you so much sir.❤

[@treybell40501]

.75 difference was beautiful. I wonder if there’s like a pattern like that or similar for all sets

[@falbert86]

so fun to start the day with one of your videos!

[@randomchshorts]

I love your videos

[@JourneyThroughMath]

My biggest hang up was not knowing the definition of {x}. I spent a little too much time trying to think what times of rational numbers added to 3 times the fractional part gives us an integer. So I knew that the answer would be in fourths. After that, I got stuck. Great video though

[@CashueTM]

Does this (fractional part of x) only work for rational numbers?

[@PrimeNewtons]

Irrational numbers have no finite fractional parts. So, yes, it only works for rational numbers AFAIK

[@jovemmeninoel526]

hello form brazil! its 5:12 here

[@enderguz3213]

I solved it by spliting x into floor(x) and fractional(x) giving floor(x)+4*fractional(x)=11 and since floor(x) is an integer it must then imply that 4*fractional(x) is also an integer and since the fractional part of a number is allways less than 1 and greater than or equal to 0 fractional(x) must be 0/4 or 1/4 or 2/4 or 3/4 plug those into fractional(x) for the original equation and solve for each x giving x = 11 or 10,25 or 9,5 or 8,75

[@WhiteGandalfs]

Using simple symbols the whole thing even becomes trivial to formally write and solve: x + p + 3p = 11 4p = 11 - x p = (11 - x) / 4 = any_int / 4 yields directly 0, 0.25, 0.5, 0.75 (0

[@enderguz3213]

@@WhiteGandalfs ik it is just alot of effort to write formally in a youtube comment 😂

[@lowkeyaspirant89]

Can't we just put the value of x = 11 as in fractional part function when we will put {11}= it will give answer as 0 , so the equation will directly be x=11 and value of x =11 Edit: i am commenting on this by seeing the thumbnail 👍

[@justyourfriendlyneighborho2061]

That is indeed one of the solutions, like Prime Newton said at the start of the video, but there are more solutions

[@lowkeyaspirant89]

@@justyourfriendlyneighborho2061 yes, after commenting, I saw the full video

[@f5673-t1h]

11 - 3n/4 for n in {0,1,2,3}

[@PrimeNewtons]

Interesting. Please share how your solution is so clean

[@Onlyforfun1992tube]

Just like sir Isaac Newton 😊

[@POLMAZURKA]

floor??

[@PabloLlaria]

If a solution is 8.75, how can it be 8 + 3x.75 equal to 11?

[@PabloLlaria]

Sorry, Washington my fault. Its correct

[@Rohan___38]

Sir the thumbnail is having - sign

[@mahoremujini]

Let x= n+d; n+4d=11 Then 4d is an integer ; d= .25 or .5 or .75 or 0 Thus x= 10.25 or 9.5 or 8.75 or 11

[@ILove_ALL]

Here is another way : x + 3.{x} = 11 (k = floor(x)) so that means k + 4.{x} = 11 so we know that {x} is between 0 and 1 so 4.{x} must be between 0 and 4 That means k must be between 7 and 11 but we know that 4.{x} can not be 4 so we got options that k = 8,9,10,11 and when you get these you can find {x} and mix them and get the andwer SOLUTION 2 : ------------------ x + 3{x} = 11 floor(x) + 4.{x} = 11 so 4.{x} € Z {x} € Z/4 0 ≤ {x} < 1 so 4 values : 0/4 1/4 2/4 3/4 If you got 0/4 it means x = 11 If you got 1/4 it means x = 10.25 If you got 2/4 it means x = 9.5 If you got 3/4 it means x = 8.75 Thanks!

[@wes9627]

The fractional part of x must be less than 1 and the integer part of x must be 10. 1/4 +3(1/4)=1, so x=10.25.

[@grosman4934]

8:52 You're just a train

[@jamal369]

Hello again

[@BelBravo]

9.5 is my guess. Cuz .5 times 3 is 1.5 and 9.5 plus 1.5 is 11. But this isn’t systematic. I just know .5 times 3 is 1.5, and 1.5 plus .5 is 2, and 11 minus 2 is 9, so 9.5 is good

[@AmitDash]

My first guess is 10.25

[@JSSTyger]

8.75

[@mystery8420]

There's actually another one, 7.999999999... as 9 repeating can be considered a fractional part

[@1729Calculus]

Please add turkish subtitles

[@축복이-x6u]

asnwer=1 is it

[@Ahmed-kg2gf]

x=E(x)+{x} 4{x}=11-E(x) {x}=(11-E(x))/4 0≤11-E(x)

[@quigonkenny]

Judging from the results, it looks like any equation of the form x + k{x} = n (assuming k, n ∈ ℤ) is going to have k+1 solutions, with one of them being n and the other k solutions each descending in value from n by k/(k+1). So the solutions will all be of the value n - mk/(k+1), where m are the integers from 0 to k.