6÷2(1+2)=???

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  • Опубликовано: 27 мар 2023
  • This problem goes viral on the internet every now and then, so I was very glad to have an opportunity to explain it on the air. I didn't have very long to talk so that's why I gloss over a few details, but the overall point is still true: the (intentional) ambiguity of the mathematical statement is the real issue here. This is not really about order of operations; it's about the importance of clear communication, which is true of mathematics as much as in any other discipline.
    For those who want more detail, Hannah Fry did a great explainer in this article that addresses this same question (though the numbers are different): www.dailymail.co.uk/femail/ar...
    And here is my favourite video, by ‪@MinutePhysics‬, about the order of operations and the deeper issues that it raises about following rules and conventions without understanding: • The Order of Operation...
    More resources available at www.misterwootube.com

Комментарии • 9 тыс.

  • @cheeseaddict
    @cheeseaddict Год назад +5272

    The obvious answer is "5 ± 4"

    • @wetraccoonbetterthantrump
      @wetraccoonbetterthantrump 8 месяцев назад +286

      No, the equation does not have two solutions SIMULTANEOUSLY. Rather it has one solution but we cannot decide which one it is. It may seem like it's the same thing but it's not...
      Edit: stop spamming "it's a joke", I didn't get it initially, it wasnt obvious to me. Regardless I shared useful information atleast to someone. About the argument "9 is the obvious answer", consider solving in using bodmas and pemdas.

    • @jacoposparta9501
      @jacoposparta9501 8 месяцев назад +160

      ​@@wetraccoonbetterthantrumpactually it's very simple, you just have to solve it in order and you get 9, it's not ambiguous and the guy above was just joking

    • @stonecrane167
      @stonecrane167 8 месяцев назад +65

      ​@@wetraccoonbetterthantrumpit's a joke

    • @Alexander-os1ss
      @Alexander-os1ss 8 месяцев назад +41

      @@wetraccoonbetterthantrumpIt’s called a joke, ever heard of one?

    • @AccurateEnd143
      @AccurateEnd143 8 месяцев назад +14

      ​@@wetraccoonbetterthantrumpwell obviously the dude was joking

  • @phosphylliteV
    @phosphylliteV Год назад +19817

    Thank you Eddie, now whenever I see a math problem I can't solve I'll just write "Yes". Harvard, here I come!

    • @RahulGupta-wn8xh
      @RahulGupta-wn8xh Год назад

      This will help you in your confusion
      ruclips.net/video/_HtJTPelgDo/видео.html

    • @dhannywijaya97
      @dhannywijaya97 Год назад +393

      wait for me brooo, I'm coming too!

    • @amanpuri7079
      @amanpuri7079 Год назад +392

      "how to make isaac newton live again?"
      "Yes"
      Marvelous,very inspiring 100/100

    • @attaullahkhan4742
      @attaullahkhan4742 Год назад +149

      I used BODMAS so I got 9. Anyone else ...

    • @amanpuri7079
      @amanpuri7079 Год назад +14

      @@attaullahkhan4742 me too

  • @Xgil2Play
    @Xgil2Play 6 месяцев назад +2530

    "I saw a man with a telescope" is the greatest example he could give

    • @minorknight4491
      @minorknight4491 6 месяцев назад +16

      it should be 'I saw a man through a telescope'

    • @Xgil2Play
      @Xgil2Play 6 месяцев назад +123

      @@minorknight4491 No, Eddie is trying to explain to you the ambiguity of the statement. 6÷2(1+2) is a mathematical ambiguous expression and his example perfectly encapsulates that.

    • @internetextraordinaire1472
      @internetextraordinaire1472 6 месяцев назад

      @@minorknight4491you are too dumb to understand it first try

    • @GanonTEK
      @GanonTEK 6 месяцев назад +46

      ​@@minorknight4491Yes, correct use of language (in this case Mathematical notation) removes ambiguity and clarifies the intended meaning.
      (6/2)(1+2)=
      I think everyone would agree on 9
      6/(2(1+2))=
      I think everyone would agree on 1
      Good notation writing is important. That's why most use two line fractions, they remove ambiguity also and reduce the number of required brackets. They are best practice.

    • @Boomer1665
      @Boomer1665 6 месяцев назад

      @@minorknight4491you are an actual brick, crazy how ur still alive

  • @starbald3895
    @starbald3895 6 месяцев назад +883

    1. Brackets
    2. Exponents
    3. Multiplication and divisions (left to right)
    4. Additions and substractions (left to right)

    • @fahrenheit2101
      @fahrenheit2101 6 месяцев назад +41

      Yes but those don't really make it clear how to interpret 6 ÷ 2(3)
      What does "brackets" mean? It's up to interpretation. In reality nobody writes this ambiguously so you don't even need to care

    • @sergiobricenos
      @sergiobricenos 6 месяцев назад +174

      @@fahrenheit2101 it means multiplication. It has always meant multiplication.

    • @leohenderson2390
      @leohenderson2390 6 месяцев назад +24

      ​@@sergiobricenosIt can be juxtaposition, or implicit multiplication which is the same in algebra, in which 6÷2(1+2) where x= 1+2 would give 1

    • @GrenaedBoi
      @GrenaedBoi 6 месяцев назад +53

      @@leohenderson2390 no 6÷2x, where x = (1+2) would still be 9. Maybe go to school

    • @jiminverness
      @jiminverness 6 месяцев назад +13

      @@sergiobricenos No, it means priority multiplication - implicity multiplication by juxtaposition. In other words, distribute the factor through the parentheses. a(b+c) = ab+ac. Distributive Law.

  • @ryanstudham640
    @ryanstudham640 Год назад +6204

    I strive to have this level of eloquence and patience.

    • @safenomore709
      @safenomore709 Год назад +82

      The answer is 1

    • @varshinilolla3090
      @varshinilolla3090 Год назад +25

      Super agree! You don't often see mathematicians or atleast a normal math teacher adressing the problems faced by normal peopleor students , due to an un-elaborated explanation, while dealing with problems they widely face across not just in their books, but also on daily basis.
      Nevertheless the answer is 9,
      under the rules of a sequential method called BODMAS or even often referred to as PEDMAS. Either ways it means:
      1.Bracket open or Parenthesis
      2.M multiplication
      3.A addition
      4.S subtraction
      I am a great admirer of eddie woo, especially from the calculus, permutations and combinations courses that I went through. It made me obssessed with a subject which I had hated in my earlydays! His reasoning behind math topics isn't often seen around, which makes it more accessible to the general public who has merely taken up with the fundamentals.
      Thanks for the videos, Eddie!

    • @gushers500
      @gushers500 Год назад

      @@safenomore709Exactly! People don’t remember PEMDAS

    • @tedkirik9449
      @tedkirik9449 Год назад +15

      Answer is one

    • @RahulGupta-wn8xh
      @RahulGupta-wn8xh Год назад

      This will help you in your confusion
      ruclips.net/video/_HtJTPelgDo/видео.html

  • @sweepingtime
    @sweepingtime Год назад +4243

    This question might be ambiguous but it teaches us a very important lesson: order of operations is NOT ambiguous and the vast majority of applied math problems don't face this issue, yet in our haste to write equations we may end up confusing ourselves by writing them in an ambiguous way, and that's when mistakes happen.

    • @RazorM97
      @RazorM97 Год назад +47

      Agreed. This is how computers do it too. When in doubt plug it in a calculator

    • @JonGretarB
      @JonGretarB Год назад +107

      @@RazorM97 The problem with that is that calculators solve this in 2 different ways. Because this problem is a problem of a shorthand, linear, method of representing an equation and calculators sold inside us and outside will solve it in 2 different ways. It’s all got to do with if multiplication by juxtaposition has higher precidence.

    • @RazorM97
      @RazorM97 Год назад +25

      @@JonGretarB i can't argue with that, you are correct, from what i've seen in most standard programming languages, the order will still give 9,
      but it's hard to even deny that these can't be arbitrary rules

    • @JonGretarB
      @JonGretarB Год назад +31

      @@RazorM97 I don’t know of any programming language where you can even write the formula with juxtaposition(implied multiplication). You always need to add the star sign in between, removing the ambiguity, and thus the answer would always be 9.
      But programming languages CAN differ in other things. Like what the modulo operator does like I learned the hard way.

    • @pawelzawadzki7307
      @pawelzawadzki7307 Год назад +8

      @@JonGretarB Also in some countries ÷ sign has different meanings. That's why formulas should be written using ISO format and problem is gone ;)

  • @MrStalyn
    @MrStalyn 6 месяцев назад +512

    I'm not a mathematician but an engineer.
    The division sign (÷) is ambiguous because it's interpreted differently depending on the region, and is in fact completely replaced by fractions as you advance in math. I can't recall coming across a math problem made ambiguous by ÷, so yeah this example is meant to be ambiguous. Scientific calculators use ÷ but brackets can / should be used to avoid ambiguity.

    • @neroch331
      @neroch331 6 месяцев назад +6

      what's the difference?

    • @iceyspicey4802
      @iceyspicey4802 6 месяцев назад +3

      🤓

    • @GearlessJoe0
      @GearlessJoe0 6 месяцев назад

      @@iceyspicey4802hey genuine advice… get off the internet 😊

    • @3000-DEN
      @3000-DEN 6 месяцев назад +65

      ​@@iceyspicey4802"wow tgis person is so much smarter than me, i should use this emoji to make them feel bad"
      You:

    • @iceyspicey4802
      @iceyspicey4802 6 месяцев назад +3

      @@3000-DEN Aw but it made you feel bad despite literally nobody talking to you 😂

  • @poisenbery
    @poisenbery 6 месяцев назад +89

    This is why mathematicians don't ever use the divide by symbol.
    We put terms in parenthesis and use a / for division.
    If your math is ambiguous, then it is not notated properly.

    • @GanonTEK
      @GanonTEK 6 месяцев назад +1

      100%

    • @clouq6570
      @clouq6570 2 месяца назад

      genius

    • @pulsar2049
      @pulsar2049 Месяц назад

      It really doesn’t matter, order of operations forces you to go from left to right.

    • @Feynman_Fries
      @Feynman_Fries 26 дней назад

      Exactly what I teach my students. Do away with the × and ÷

    • @AM-qi4ro
      @AM-qi4ro 14 дней назад

      Right on. All this nonsense about "ambiguity. There are well defined rules.

  • @subhapackian3349
    @subhapackian3349 Год назад +3630

    Anchor: 6÷2(1+2) = ????
    Eddie Woo: It's similar to a sentence like 'I saw a man with a telescope'
    Audience: We came for 1 answer and now we have two questions....🤯
    Lol

    • @zmoostofa
      @zmoostofa Год назад +35

      With a telescope, I saw a man

    • @Some1NamedPlays
      @Some1NamedPlays Год назад +42

      @@zmoostofa Why would you saw that man??? AND WITH A TELESCOPE?????

    • @billy.7113
      @billy.7113 Год назад +38

      He answered the question like a politician.

    • @techwithtee8721
      @techwithtee8721 Год назад +2

      We have two equations 😂😂

    • @FanishKumarGupta
      @FanishKumarGupta Год назад

      ​​@@Some1NamedPlays so again a question man is on moon or earth. 😂

  • @j2zel
    @j2zel Год назад +1568

    If you set up the equation with a fraction bar instead of a division symbol, it gets rid of the ambiguity. That's why we don't use division symbols in calculations. It's always a fraction bar.

    • @GanonTEK
      @GanonTEK Год назад +31

      100%

    • @derblaue
      @derblaue Год назад +36

      That's not the whole problem. It's generally ambiguous if non commutative operators are used with juxtaposition. Both is solved by using fractions but you could also always explicitly write out multiplication when used with a non commutative operator.

    • @GanonTEK
      @GanonTEK Год назад +5

      @@derblaue 100%

    • @doughendrie5468
      @doughendrie5468 10 месяцев назад +14

      Why not prove the answer by using the golden rule of algebra.
      6/2(1+2)=1 remove the explicit division be multiplying both sides by 2(1+2)
      6=1*2(1+2) simplify
      6=1*6 proven

    • @affif330
      @affif330 9 месяцев назад +29

      well the answer is actually 9 cus explicit division has priority over implicit multiplication

  • @borderedmike7394
    @borderedmike7394 4 месяца назад +10

    so in an equation we start with brackets so 1 + 2 = 3. Then if we come across a division step or a multiplication step then we must work left to right, like when we read because we don't read right to left. So 6/2 = 3 and then we multiply that by 3 and we get 9.

    • @MrSJPowell
      @MrSJPowell 7 дней назад +1

      That is a way to do it. Just like saying "I saw a man with a telescope" can be interpreted as "I saw a man by using a telescope". It's poorly written, and math nerds will just avoid using the ÷.

  • @nicolasrouze
    @nicolasrouze 6 месяцев назад +163

    Loves that he has clear and élégant way of explaining things. Great teacher.

    • @user-zn1sc4bd4n
      @user-zn1sc4bd4n 6 месяцев назад

      country name

    • @wowzersfyi
      @wowzersfyi 4 месяца назад

      @@user-zn1sc4bd4n Probably Britain, England. Their accent atleast is

    • @vvsdarcy
      @vvsdarcy 4 месяца назад

      @@wowzersfyi its australia

    • @obbyistguywhodoessomeguides
      @obbyistguywhodoessomeguides 3 месяца назад

      @@user-zn1sc4bd4nyou mean what country he’s from?

    • @user-zn1sc4bd4n
      @user-zn1sc4bd4n 3 месяца назад

      @@obbyistguywhodoessomeguides yes you are right

  • @Mngalahad
    @Mngalahad Год назад +2482

    news: so is it 1 or 9?
    eddie: math is a social construct; it can be anything we want.

    • @katheryne-bois
      @katheryne-bois Год назад +74

      Not anything! What he meant is that the 2 only POSSIBLE answers, 1 and 9 are both true because the way it was formulated can be interpreted in both way! Yes 6 divided by 2 is a division, but if the division symbol was the fraction symbol, we would all have understood that the division works as a single number rather than a division in itself to solve, and as now that Fraction Symbol is not there, even with PEDMAS, both answers are both true because the division symbol is not defined to us to have us know if it’s a fraction or not!

    • @LeoStaley
      @LeoStaley Год назад +97

      No, it *isn't* ambiguous. Solve it another way.
      6 ÷ 2(x+1) = 1
      6 ÷ 2(x+1) = 9
      which one of those results in x being 3?
      A term attached to a parenthesis without an operator between them is *part of the parenthesis term*. Any such term must be distributed to the contents of the parenthesis before any other steps in the order of operation can be performed.
      Think of it as if it were a number attached to a variable. 6÷2x=n. If n is 1, then the value of x, the parenthesis phrase, must total to 3. If n is 9, then the value of x, the parenthesis, must equal 2/3.

    • @walidyasin2039
      @walidyasin2039 Год назад +106

      No it's stupid to say either one. The convention is from left to right and precedence of operations with parathesis taking higher precedence so the answer is 9

    • @Mngalahad
      @Mngalahad Год назад +13

      @@walidyasin2039 but like in real life you wouldnt have this confusion. technically reading from left to right doesnt really matter. even if you wanted to solve it, it'd be in like an excel sheet where the confusion wouldnt happen.

    • @trstampf7854
      @trstampf7854 Год назад +10

      ​@@katheryne-bois A fraction bar acts as a grouping symbol. The only way to get a second answer to this problem would be to write it as a rational expression. But that changes the meaning of the expression, and therefore is a different problem resulting in a different answer.

  • @raicyceprine8953
    @raicyceprine8953 Год назад +2314

    That correlation to sentence "I see a man with a telescope" is such a good comparison.
    It makes you view mathematics as a language just like any other language out there: english, chinese, french, computer language, and math language

    • @Hungry_for_LIKES
      @Hungry_for_LIKES Год назад +6

      So true

    • @Bungee75
      @Bungee75 Год назад +10

      Well that's why some languages use comma. And then it's exact.

    • @Bungee75
      @Bungee75 Год назад +14

      @Ashirwad Paswan well in my language it's simple. If you wanted to say that man has a telescope than you say: I see a man, with a telescope. If you omit the comma then you're looking at him with telescope.
      But in maths X(Y) is shorthand for X * (Y)

    • @manankjoshi981
      @manankjoshi981 Год назад

      but language might be tricky, i dont understand how there is no logical correct answer of this?

    • @raicyceprine8953
      @raicyceprine8953 Год назад +5

      @@manankjoshi981 it definitely depends on context. We could solve it using PEMDAS if it's deep & theoretical math.
      Solving it left to right is possible if we are computing in terms of accounting, economics, or finance.
      Both are right answers. Just depends on where the equation is being used

  • @HorizonInternational3000
    @HorizonInternational3000 4 дня назад +2

    Steps to solve:1. Solve the expression inside the parentheses:
    6÷2(1+2)=6÷2(3)
    2. Simplify the division:
    6÷2(3)=3(3)
    3. Multiply the remaining numbers:
    3(3)=9
    Answer:
    9

  • @Two_PlayZ
    @Two_PlayZ Месяц назад +44

    6÷2(1+2)
    Solve brackets
    6÷2(3)
    6÷2×3
    Do division and multiplication from left to right
    3×3
    9

    • @GanonTEK
      @GanonTEK Месяц назад +4

      It depends on which interpretation of multiplication by juxtaposition you follow. That's why it's ambiguous.

    • @bdat6321
      @bdat6321 5 дней назад +4

      what are they teaching ppl these days 😂

    • @Patrick_Raelow
      @Patrick_Raelow 4 дня назад +1

      ​@@bdat6321??

    • @torchvibemedia
      @torchvibemedia 4 дня назад

      How about?
      6÷2(1+3)
      =6/2(3)
      =2/2 or 3/3
      =1

    • @Boy10Dio
      @Boy10Dio 4 дня назад +1

      didn't solve the brackets fully

  • @WritingGeekNL
    @WritingGeekNL Год назад +928

    This is simply why most mathematicians use fractions...

    • @victorcapetillo2070
      @victorcapetillo2070 Год назад +14

      😂.. Might be. I told my wife I just manipulate or set up equations in an order that is faster and more efficient for humans to solve or where I would be more familiar making it easier to solve.

    • @RahulGupta-wn8xh
      @RahulGupta-wn8xh Год назад

      This will help you in your confusion
      ruclips.net/video/_HtJTPelgDo/видео.html

    • @dooflegoof
      @dooflegoof Год назад +18

      fractions wouldn't help because it can be either 6/2(1+2) or 6/2 × (1+2)

    • @NirousPlayers
      @NirousPlayers Год назад +174

      ​@@dooflegoof of course would help
      it's either
      Nominator: 6
      Denominator: 2(1+2)
      6
      -----------
      2(1+2)
      Or
      Nominator: 6
      Denominator: 2
      Then multiply by (1+2)
      6 × (1+2)
      --
      2
      There is no ambiguity

    • @dooflegoof
      @dooflegoof Год назад +42

      @@NirousPlayers ohhhh, right, I didn't picture that in my head when I wrote the comment
      thanks for correcting my mistake

  • @unstabledefusion
    @unstabledefusion Год назад +2124

    If you type 6/2(1+2) into WolframAlpha, it interprets it as (6/2)(1+2) and spits out 9, which makes sense. If the answer is supposed to be 1, it would be written as 6/(2(1+2)).
    EDIT: To clarify my point, I'm thinking like a calculator. For example, if you type 6/2*3 into a calculator, it will say 9 and not 1 because there are no parentheses around the 2 and 3. It's the same as (6/2)*3.
    Both yield the same answer. Even if you're not thinking like a calculator, you just use PEMDAS and therefore go left to right with the division and multiplication. First calculate 6/2, then multiply that result by 3 and you get 9.
    Just type these things into a calculator to see for yourselves. It's really not ambiguous.

    • @thegamingsuneo430
      @thegamingsuneo430 Год назад +107

      From the BODMAS(BRACKETS OF DIVISION MULTIPLICATION ADDITION AND SUBTRACTION) rule you must do the Division first then multiplication then addition and then subtraction so I guess the answer here must be 9

    • @dapplederpgaming8432
      @dapplederpgaming8432 Год назад +189

      @@thegamingsuneo430the answer is 9 based on BEDMAS (brackets exponent division multiplication addition substraction), but it seems like you’re somewhat confused. BODMAS with your explanation doesn’t make sense, what does brackets of division mean? You also seem to think that you should operate in the strict order of division THEN multiplication THEN addition THEN subtraction, but that’s not the case. Division and multiplication have equal priority, same with addition and subtraction. What separates them in terms of order is which one comes first (left to right)

    • @grumpyolddude439
      @grumpyolddude439 Год назад +127

      @@thegamingsuneo430 Neither division nor multiplication holds priority over the other. Once the expreession has been reduced to ONLY multiplication and division, and maybe addition and subtraction...you go left to right and resolve division or multiplication AS ENCOUNTERED. Then if addition or subtraction remains; you repeat. Left to right, and perform in the order encountered.

    • @tajforney2533
      @tajforney2533 Год назад +65

      The entire reason for the confusion is the ÷ symbol. Higher level math doesn't even use it as it creates confusion, so they only use fractions as you can get answers with no confusion. The ÷ sign is for teaching division more than anything, as it looks more like the other math symbols like +, -, and x, making it easier to understand to a child.

    • @dkintheuk
      @dkintheuk Год назад +17

      Surely you mean brackets first...? The very first letter of BODMAS or BIDMAS or BEDMAS is for brackets... You do them first.

  • @anushv2857
    @anushv2857 6 месяцев назад +3

    Can't find a better explanation than this, mark my words

  • @Imegal
    @Imegal 6 месяцев назад +50

    IMO, if a parentesis is right next to a number, it means that number and the parenthesis are together being multiplied. If there is a multiplication symbol between the parenthesis and the number, it would be completely separate.
    For example, I would interpret 6/2(1+2) as 6/((2(1+2)) and 6/2 * (1+2) as (6/2) * (1+2)

    • @triharders2456
      @triharders2456 6 дней назад

      Yep and I guess we can keep doing that

    • @lembarkii8669
      @lembarkii8669 2 дня назад

      well your opinion is wrong lol

    • @BigNasouyi
      @BigNasouyi 2 дня назад

      ​@@lembarkii8669Exactly, the brackets are first and foremost, but we calculate merely what's inside, then once we've done that we look at +-÷x, since that it's ÷ and x priority simply goes left to right, therefore 6÷2x3 is 3x3 which equals 9, that simple

    • @triharders2456
      @triharders2456 День назад

      @@BigNasouyi so the guy in the vid is wrong?

  • @yesno6360
    @yesno6360 Год назад +1498

    For those of you wondering how we get 1, it's due to something called "multiplication by juxtaposition", which means that we assume 2 or more terms put together indicates that we need to multiply them together first before we process other operations.
    To give an example, if we say 6 ÷ 2x, we assume that u multiply 2 and x first, before dividing 6 with it. In other words, you're NOT suppose to have 6 ÷ 2, then × x.
    This is the case with the question presented, where we assume (1+2) is the x, which means we need to multiple 2 with (1+2) first before we take 6 and divide by it. The only reason it's in a parentheses is because, you can't put 2 and 1+2 together directly without it looking like 21+2 instead of 2×(1+2).
    Hope this clears things out, where I'm from, we never really learned pemdas or bodmas...

    • @SL_Beast
      @SL_Beast Год назад +6

      But then again there are are numerous questions like the math question presented in the video and no one would know what method to apply right?

    • @yesno6360
      @yesno6360 Год назад +81

      @@SL_Beast well, the thing is, my peers also never learned bosmas or pemdas, so it never occurred to us to separate parentheses and use multiply.
      If I see 2(1+2), I've never separated it as 2 × (1+2), the first time I've seen this is exactly when this question first appeared. So for me, it has always been just 1 method.
      Same goes for my peers, I've never seen them separate the terms like that. But funny enough, we were never taught the phrase "multiplication by juxtaposition" either, took me a long time to even realise it's a thing. For us, the idea of multiplication by juxtaposition is more like a subconscious decision, or an unspoken rule.

    • @SL_Beast
      @SL_Beast Год назад +12

      @@yesno6360 That's 😎. For us I remember really well that in like 7th grade they added a whole unit dedicated to teach us BODMAS. And the thing is they didn't even teach us PEMDAS it was just BODMAS. And for the longest time I thought BODMAS was an Universal absolute math term and that there wasn't any other math terms besides it that is on the same topic/use as BODMAS. They really should teach these things in school to us.

    • @GanonTEK
      @GanonTEK Год назад +27

      @@SL_Beast The order of operations as it's taught, like BODMAS, is generally fine as it's handy to have a consistent way to simplify expressions that also reduces errors.
      (Give M and D equal priority and go L to R for equal priority, for example).
      It's great for people with a range of maths abilities.
      When you get older and more confident with it, you often stop using the literal BODMAS as there might be easier or alternative ways to simplify.
      For example,
      4 + 3²×10/2 - 4
      You can go in order:
      O: 4 + 9×10/2 - 4
      M: 4 + 90/2 - 4
      D: 4 + 45 - 4
      A: 49 - 4
      S: 45
      You can alternatively also do:
      S: 0 + 3²×10/2
      D: 3²×5
      O: 9×5
      M: 45
      It's perfectly valid for that expression to do that and it's almost BODMAS backwards and it ended up being a step shorter.
      It's all about understanding grouping and the different strengths of the grouping of different symbols.
      Minutephysics did a great short video called "the order of operations is wrong" which talks a little about that.
      Worth a watch.

    • @SL_Beast
      @SL_Beast Год назад +2

      @@GanonTEK thanks! I'll look into this more this looks interesting. :)

  • @johnwalker1058
    @johnwalker1058 Год назад +415

    I feel like the purpose of problems like these is to demonstrate to students why conventions exist, whether they be expressional conventions like in mathematics, or grammatical conventions in written composition. Having a set of rules for how to express something helps to do away with potential ambiguities like this and reduce the chances for miscommunication or misinterpretation.

    • @darkfieldcarnivore3928
      @darkfieldcarnivore3928 Год назад +9

      Yes, words have an agreed meaning for a reason. Even acronyms! Without that established agreement, a conversation can not be constructive.

    • @GooogleGoglee
      @GooogleGoglee Год назад

      Correct

    • @johnl6176
      @johnl6176 Год назад +8

      It also should be an exercise in rejecting improper or imprecise problems. As Eddie Woo pointed out, the problem is ambiguous, it can therefore be rejected as such. Any mathematician would reject this.

    • @darkfieldcarnivore3928
      @darkfieldcarnivore3928 Год назад +1

      @John L I disagree. The agreed language of mathematics that allows for the same result every time dictates this problem be solved in a particular order. Ambiguity only comes when the language is not fully understood.

    • @johnl6176
      @johnl6176 Год назад +1

      @@darkfieldcarnivore3928 So you understand what factorisation is?

  • @Zenix.
    @Zenix. 6 месяцев назад +43

    We change 6÷2(1+2) to 6/2(1+2) so now you just do the equation in the brackets and then it changes to 6/2 x 3 which is 9. For it to be 1, we need to change the equation to 6/(2(1+2)). When the bottom (i forgot what it's called in math terms) is calculated, it'll be 6/6 which is 1.

    • @darss10
      @darss10 6 месяцев назад +1

      Denominator :))

    • @allenchang6185
      @allenchang6185 6 месяцев назад

      How about 6/2(3)?

    • @ewapiksrandeb3966
      @ewapiksrandeb3966 6 месяцев назад +1

      Nope.6/2(1+2) is equal to 3*3 which is 9
      Now why is like this.
      (1+2) is counted first
      Then you need to divide 6 by 2
      And lastly multiply quotient with result of sum 2 numbers which was placed inside of the bracket.

    • @jiminverness
      @jiminverness 6 месяцев назад

      @Zenix. Wrong way round. 6/2(1+2) = 6 over 2(1+2) = 6/2(3) = 6/6 = 1.
      For it to be 9 we need to change the _expression_ to (6/2)(1+2).

    • @KeyUploads
      @KeyUploads 6 месяцев назад

      Facts

  • @ugochukwuudeh6625
    @ugochukwuudeh6625 3 месяца назад +3

    1 and 9 exist in a super position and cannot be determined until the equation is measured

  • @katerinapierce6643
    @katerinapierce6643 Год назад +942

    I'm kinda confused. Equation inside the brackets go first. 1+2 = 3. You have left 6:2x3. : and x are both equally in the order, but : stands before x, so : goes first. 6:2 = 3. You have left 3 x 3 which is 9. If the answer was 1 then it would be written like 6:(2(1+2)). At least this is what I learned at school. Order: Brackets, divide/multiply, plus/minus.

    • @GanonTEK
      @GanonTEK Год назад +203

      Academically, multiplication by juxtaposition implies grouping so writing
      6÷2(1+2) explicitly before you simplify at all is
      6÷(2×(1+2)) which gives 1.
      More literally/programming-wise, multiplication by juxtaposition implies only multiplication so writing it explicitly gives
      6÷2×(1+2) which gives 9.
      Both are widely used so both are valid.
      That's why it's ambiguous.

    • @Counter1V1
      @Counter1V1 7 месяцев назад +6

      Yes thats what i thought

    • @Vipergang1
      @Vipergang1 7 месяцев назад +1

      2

    • @mvpatel6417
      @mvpatel6417 7 месяцев назад +8

      Yeah the OG BODMAS rule (idk about O but i know the meaning) Brackets open->Division->Multiplication->addition->Subtraction (priority order)

    • @Black_______
      @Black_______ 7 месяцев назад +45

      6÷2(1+2). First bracket
      =6÷2×3. Then division
      =3×3. Then multiplication
      =9

  • @denniskoppo4259
    @denniskoppo4259 Год назад +891

    I'm a substitute teacher and problems like this are frequently given on tests to evaluate understanding of the "order of operations". One of the weird things is that some calculators come up with different answers to those problems than others.

    • @GanonTEK
      @GanonTEK Год назад +204

      Questions like this should never be given because it's terrible notation.
      Academically, multiplication by juxtaposition implies grouping so
      6/2(1+2) means 6/(2×(1+2)) = 1
      Programming-wise/more literally, multiplication by juxtaposition implies only multiplication so
      6/2(1+2) means 6/2×(1+2) or
      (6/2)×(1+2) = 9
      Both widely used, hence ambiguous notation.
      Wolfram Alpha's Solidus article mentions the a/bc ambiguity and modern international standards like ISO-80000-1 mention about division on one line with multiplication or division directly after and that brackets are required to remove ambiguity.
      Even over in America where the programming interpretation is more popular, the American Mathematical Society stated it was ambiguous notation too.
      Multiple professors and mathematicians have said so also like:
      Prof. Steven Strogatz, Dr. Trevor Bazett, Dr. Jared Antrobus, Prof. Keith Devlin, Prof. Anita O'Mellan (an award winning mathematics professor no less), Prof. Jordan Ellenberg, David Darling, Matt Parker, David Linkletter, Eddie Woo here etc.
      Even scientific calculators don't agree on one interpretation or the other.
      Calculator manufacturers like CASIO have said they took expertise from the educational community in choosing how to implement multiplication by juxtaposition and mostly use the academic interpretation (1). Just like Sharp does. TI who said implicit multiplication (1) has higher priority to allow users to enter expressions in the same manner as they would be written (TI knowledge base 11773) so also used the academic interpretation (1). TI later changed to the programming interpretation (9) but when I asked them were unable to find the reason why.
      A recent example from another commenter:
      Intermediate Algebra, 4th edition (Roland Larson and Robert Hostetler) c. 2005 that while giving the order of operations, includes a sidebar study tip saying the order of operations applies when multiplication is indicated by × or • When the multiplication is implied by parenthesis it has a higher priority than the Left-to-Right rule. It then gives the example
      8 ÷ 4(2) = 8 ÷ 8 = 1
      but 8 ÷ 4 • 2 = 2 • 2 = 4
      The lesson here is use proper notation
      (6/2)(1+2) for 9
      6/(2(1+2)) for 1
      Those would be valid problems to test students.
      Better yet, two line fractions remove ambiguity and reduce the number of required brackets. They are best practice.

    • @Ninja0Pain
      @Ninja0Pain Год назад +53

      @@GanonTEK This is why I think fractions are way more useful than using ÷. ÷ is a great way to introduce the concept of division, but fractions are much more intentional.

    • @GanonTEK
      @GanonTEK Год назад +22

      @@Ninja0Pain Very true. Fractions on two lines are best practice.
      They remove ambiguity and reduce required brackets.

    • @Paul-fu2xv
      @Paul-fu2xv Год назад +2

      It depends on the syntax of the the calculator

    • @shivskiv7653
      @shivskiv7653 Год назад

      These problems are dumb as hell, it doesn't test anything

  • @Ryvaken
    @Ryvaken 7 месяцев назад +17

    It's refreshing to see a mathematician own up and admit that no, we don't write perfect things that can never be misinterpreted. My favorite is "negative seven squared" because my students get tripped by that or something like that multiple times every semester.

    • @GanonTEK
      @GanonTEK 7 месяцев назад

      100%

    • @Poshgoatgaming123
      @Poshgoatgaming123 7 месяцев назад +1

      mhm yep

    • @djkhemix
      @djkhemix 4 месяца назад +1

      Isn't that just 49? -7 x -7 is 49, no? Why is there an issue? Thanks!

    • @baldability
      @baldability 4 месяца назад +3

      @@djkhemixit could be interpreted as (-7)^2 or -(7)^2, resulting in either 49 or -49

    • @djkhemix
      @djkhemix 4 месяца назад +1

      ​@@baldabilityoh. Thank you

  • @Flyboy207
    @Flyboy207 5 месяцев назад +3

    I would say that with order of operations being left to right (or so I was told) it’s 9. However if you put the 6 under the rest of the equation, all ambiguity goes away, and it’s 1. Then again, I barely passed Algebra 2.

  • @Dalinar_Kholin
    @Dalinar_Kholin 8 месяцев назад +1784

    As someone who knows 6th grade math, I see this as an absolute win.
    Edit 1: Damn ya'll need to stop arguing down there. It ain't that deep XD
    Edit 2: Ya'll I told you to stop and you just heated it up like an oven

    • @beasthuntermohit567
      @beasthuntermohit567 7 месяцев назад +54

      well as a programmer, I see this as an absolute loss

    • @Dalinar_Kholin
      @Dalinar_Kholin 7 месяцев назад +7

      @@beasthuntermohit567 I feel for you

    • @beasthuntermohit567
      @beasthuntermohit567 7 месяцев назад +16

      @KazamaKazuyoshi458 They aren't. 1 and 9 are both correct answers depend on how you write it or what is the context.

    • @OREO_____
      @OREO_____ 7 месяцев назад +8

      @@beasthuntermohit567 it dosent make sense to get 1 like we have always been taught to do these kind of questions by pemdas or Bodmas

    • @beasthuntermohit567
      @beasthuntermohit567 7 месяцев назад +24

      @@OREO_____ It makes. Look it as a fraction. 6/2(2+1)
      =6/2*3
      =6/6
      =1

  • @tambuwalmathsclass
    @tambuwalmathsclass Год назад +231

    I tried so hard to convince my heart to accept 1 as the answer but all efforts seem abortive.
    I'll go with 9

    • @JitenderKumar-kn7bj
      @JitenderKumar-kn7bj Год назад +54

      1 is the answer

    • @usmanbelloahmad6461
      @usmanbelloahmad6461 Год назад +10

      I have seen this in a comment section maybe it will add some light ( 6÷2(2+1) we can assume 2+1 to be x then we have 6÷2x by simplifying the fraction we have 3÷x recall x=2+1=3 we have 3÷3=1)

    • @bimbapanthi9547
      @bimbapanthi9547 Год назад +14

      Depends if you follow the universally accepted rule of BODMAS or some random American rule. If you follow BODMAS it is 1.

    • @user-fp8vl3mb2i
      @user-fp8vl3mb2i Год назад +43

      ​@@usmanbelloahmad6461no you are wrong it is 9 at least according to math we know of 6/2(2+1) is not 6/(2(2+1))

    • @spiderjerusalem4009
      @spiderjerusalem4009 Год назад +9

      the fact that many people still debate over this is so ludicrous, instead of just accepting that the division notation is the heart of the whole matter, get over it, be thankful that fractional is more common instead, and search out for questions that aren't trivial (i.e. number theory, combinatorics/permutation/star&bars, trig, calc, ineq, ode/pde, group theory, abstract alg, etc, as long as it isn't at the level of this overrepeated problem)

  • @JorJorIvanovitch
    @JorJorIvanovitch 7 месяцев назад +9

    In symbolic logic, as in mathematics, the coefficients of parentheses are addressed before other operators in the "left to right" reading of PEMDAS. Just like exponents on parentheses come after the contents inside the parentheses are calculated, so coefficients come after the exponents. Maybe this is because you can use a logarithmic manipulation to make the exponent into a coefficient? I have never had any math teacher from elementary through university who would say that answer is 9. Sure they would use a fraction or brackets more effectively to make it more obvious, but they would still address the coefficient of '2' operating on the parenthesis prior to the division operator following the 6.

    • @Anonymous-8080
      @Anonymous-8080 8 дней назад

      There's PEMDAS and then there's BODMAS. I mean to say Multiplication and Division has the same priority that's why the problem arises.

    • @JorJorIvanovitch
      @JorJorIvanovitch 8 дней назад

      @@Anonymous-8080 still doesn't address the coefficient of the parenthesis.

    • @BigNasouyi
      @BigNasouyi 2 дня назад

      ​​@@JorJorIvanovitchOnce you've calculated what's inside the parentheses is gone, then it goes back to left to right ÷x over +-, the sole reason why the + is calculated before is because of the parentheses, once that is done it's 6÷2x3 3x3=9.... The coefficient would only take priority if it was the one most on the left, or after +- for it's a multiplication, 6÷2(1+2) is written as such for ease, it's simply 6÷2x(1+2)...

    • @JorJorIvanovitch
      @JorJorIvanovitch День назад

      @BigNasouyi No. Because what's in the parenthesis can be expressed symbolically or algebraically as 'x' or anything else. Who would interpret 6÷2x or 6÷2a as 3x or 3a instead of 6/(2x) or 6/(2a)? No one.

  • @Raven_Ray1
    @Raven_Ray1 6 месяцев назад +3

    6/2(1+2) or 6/2 × (1+2)
    It's just the way they write it make it ambigu.

  • @cakeandicecream1582
    @cakeandicecream1582 8 месяцев назад +65

    That actually is a decent answer because you explain it with a very good analogy.

  • @bradroof9286
    @bradroof9286 Год назад +313

    Here's the thing. Multiplication and division are equal when discussing the order of operations. When they are equal it is exactly like reading a sentence. A sentence is read from left to right and the math needs to be done from left to right. This means division is first and then multiplication which gives the answer of nine. Otherwise, why did we bother with doing parentheses first?

    • @Jinsun202
      @Jinsun202 Год назад +103

      100% correct. The answer is 9.

    • @Joviex
      @Joviex Год назад

      They aren't equal the order is PEMDAS

    • @Joviex
      @Joviex Год назад

      Making up your own bullshit to solve the math

    • @RIK0-1
      @RIK0-1 Год назад +32

      That's not the correct reason though, multiplication and division can happen in any order with the same result just like addition and subtraction. When you think of division as a fraction there isn't a way divide by 2 and (1+2) because one is a numerator and one is a denominator. It would have to be 1/(1+2) instead. Another way to write the problem is 6/2 * (1+2)/1, both are fractions and now the reason is more obvious. You can also rewrite everything as multiplication between fractions, so 6/1 * 1/2 * (1+2)/1, and the order that you multiply them makes no difference. The result should always be 9 unless (1+2) is explicitly part of the denominator, otherwise it is assumed to be on top. So it's not the order that matters, it's the assumption that multiplying 2 by (1+2) is possible in the first place. There would need to be parenthesis around the whole thing, like (2(1+2))

    • @DavidBioformRains
      @DavidBioformRains Год назад +16

      Actually lookup mathematical order of operations: M is before D... Mixed division and multiplication
      Edit
      In some of the academic literature, multiplication denoted by juxtaposition (also known as implied multiplication) is interpreted as having higher precedence than division, so that 1 ÷ 2n equals 1 ÷ (2n), not (1 ÷ 2)n.[1] For example, the manuscript submission instructions for the Physical Review journals state that multiplication is of higher precedence than division,[20] and this is also the convention observed in prominent physics textbooks such as the Course of Theoretical Physics by Landau and Lifshitz and the Feynman Lectures on Physics.[d]

  • @methatis3013
    @methatis3013 6 месяцев назад +1

    People don't realise that this really isn't a maths question. Almost nothing about this is inherently mathematical. It's only a question about conventions. In reality, for example, there is no reason multiplication should have precedence over addition. 2+3*5 could be 25 in one world or 17 in another. We just generally agreed that multiplication should take precedence

  • @hi-sj7cu
    @hi-sj7cu 7 дней назад +1

    Easiest way to solve this without the ambiguity is to use reciprocal on the division, basically.
    6 ÷ 2(1+ 2) to 6 • 1/2(1 + 2)
    You change the division of 2 into a multiplication of 1/2.
    Therefore, regardless of the method (PEMDAS/BODMAS) you will still get the same answer, which is 9.

    • @v-chris156
      @v-chris156 7 дней назад

      You have to combine factors before doing that, otherwise you are flipping one factor and not the other.
      2x, where x is any function in parentheses is a monomial. You can't just flip one factor in a monomial and not the others.
      1÷2wxyz becomes 1 * (1/a), where a = 2wxyz (all the factors combined)

    • @GanonTEK
      @GanonTEK 7 дней назад

      No, both
      6÷2(1+2) and 6•1/2(1+2) are ambiguous for the same reason: they both have implicit multiplication after division on one line. That's the main problem.
      You need to write
      6•(1/2)•(1+2) or (6/2)•(1+2), for example, to be unambiguous there and something like
      6•(1/2)•1/(1+2) for 1

  • @serdar_k
    @serdar_k Год назад +1025

    I ran the telescope question through Chat GPT, interestingly, it stated the following: "The sentence "I saw a man with a telescope" implies that you saw a man who was holding or carrying a telescope. If you had seen the man through the telescope, the sentence would have been phrased differently, such as "I saw a man through the telescope."🙂

    • @3_pancakes767
      @3_pancakes767 Год назад +82

      Yeah just like how it would have been written differently to be equal to 1

    • @joelpww
      @joelpww Год назад +8

      How about switching with a telescope with using one

    • @stevejohn7459
      @stevejohn7459 Год назад +1

      The answer to the equation of the video is 12!

    • @artugert
      @artugert Год назад +81

      And.. Chat GPT was wrong. "Through" and "with" are both acceptable here, and have the same meaning.

    • @samuel9294
      @samuel9294 Год назад

      @@stevejohn7459 no its 16

  • @SlimThrull
    @SlimThrull Год назад +224

    Huzzah! Someone finally mentioned that the question is horribly ambiguous! THIS is the correct answer.

    • @jarredlucas4000
      @jarredlucas4000 Год назад +6

      Cringe

    • @artophile7777
      @artophile7777 Год назад +11

      ​@@jarredlucas4000ill mannered chap

    • @SuperWolfkin
      @SuperWolfkin Год назад +2

      But it's not ambiguous. Math has clear rules that give you the answer which is nine by the way. This is why Matt has rules to avoid this sort of ambiguity. This is like what middle school math was all about or remedial high school mat.

    • @signeCS
      @signeCS Год назад +9

      @@SuperWolfkin math is unambigous if you use the correct notations which this equation doesn't

    • @SuperWolfkin
      @SuperWolfkin Год назад +2

      @@signeCS I'd argue it's not ambiguous as it stands. You don't always need specific notations when it's covered by the conventions of the environment. Like you don't need to indicate which way to read the letters when you write a sentence because in English we have the convention of Left-to-Right. Likewise math has LTR/PEMDAS conventions that take any ambiguity out of this equation.

  • @7pz9
    @7pz9 4 месяца назад +1

    If we were to take the answer according to the laws of programming, the process of addition would be first, then multiplication, followed by division, which gives us one

  • @AdequateName.
    @AdequateName. 6 месяцев назад +3

    6÷2(1+2) parenthesis first
    6÷2×3 multiply/divide L-R
    3×3
    9

  • @ScoRPy22
    @ScoRPy22 Год назад +254

    I asked the same question to my professor. His answer was fairly simple and easy to understand. He said we never use ÷ sign for division in higher mathematics as it leads to a lot of confusion in complex calculations. Instead use / and you won't have any confusions against these type of problems.

    • @GanonTEK
      @GanonTEK Год назад +34

      Writing 6/2(1+2) is just as ambiguous.
      Never write multiplication by juxtaposition after division on one line.
      Modern international standards like ISO-80000-1 mentions about writing division on one line with multiplication or division directly after and that brackets are required to remove ambiguity.
      Follow that and there is no ambiguity.
      (6/2)(1+2) for 9
      6/(2(1+2)) for 1

    • @ScoRPy22
      @ScoRPy22 Год назад +46

      @@GanonTEK No it's not it's tough to put long / here. What I mean was try putting 6 as numerator and 2(1+2) in denominator. Now whatever way you solve it you'll get the right answer.

    • @GanonTEK
      @GanonTEK Год назад +18

      @@ScoRPy22 Ah, yes, using a viniculum, a horizontal fraction bar, does remove ambiguity. For example:
      6
      ---
      2(1+2)
      / is not a representation of the horizontal fraction bar though.
      The horizontal fraction bar implies grouping. / does not.
      / is the unicode Solidus but isn't the real Solidus.
      ½ is the real Solidus which shows a clear two line fraction but on one line by using a steeper line and sub and super script.
      1/2 is not as clear cut as the numbers are not offset so you get issues with 1/2(3).
      ½(3) is clear but 1/2(3) is not.

    • @stevejohn7459
      @stevejohn7459 Год назад +3

      Bruh it’s 12!

    • @KrutoiPersonazh
      @KrutoiPersonazh Год назад +1

      Bro he didn't answer the question

  • @Stu-dying1min
    @Stu-dying1min 8 месяцев назад +227

    As a 4rth grade Indian student i saw this as an absolute win
    Edit: Omg i got famous I wish I have same number of subscribers but it's ok

    • @Hester7410
      @Hester7410 7 месяцев назад

      I love watching cringe indian videos with cringe music, intro and voice

    • @anshnegi9519
      @anshnegi9519 7 месяцев назад +4

      9

    • @anshnegi9519
      @anshnegi9519 7 месяцев назад

      What else can it be

    • @anshnegi9519
      @anshnegi9519 7 месяцев назад +8

      Bodmas

    • @ltsKenzie
      @ltsKenzie 7 месяцев назад +13

      I can tell you are in 4th grade

  • @theclintevs9331
    @theclintevs9331 7 месяцев назад +3

    As 1 month year old Asian-Indian I see this as an absolute ez win

  • @andrewmcmillan8039
    @andrewmcmillan8039 Месяц назад +1

    Order of Operations
    1. Parentheses (Do first)
    2. Exponents
    3. M/D - whichever comes first left to right
    4. A/S - whichever comes first from left to right

  • @supermestre5042
    @supermestre5042 Год назад +41

    In Brazil, it is learned that the order of precedence is parentheses, followed by multiplication and division, but whichever of the two appears first on the left. But there has always been a confusion of which of the two is done first.

    • @SilverPh3nix
      @SilverPh3nix Год назад +11

      In the US we learn the same thing with the acronym PEMDAS, so yeah parenthesis are first and then after that is either multiplication or division whichever comes first left to right

    • @TheLifeLaVita
      @TheLifeLaVita Год назад +2

      they literally told you the order. You literally repeated it. From left to right ahaha

    • @SilverPh3nix
      @SilverPh3nix Год назад +4

      @@TheLifeLaVita no cause it’s more like
      P
      E
      MD (whichever comes first in the problem)
      AS (whichever comes first in the problem)

    • @TheLifeLaVita
      @TheLifeLaVita Год назад +1

      @@SilverPh3nix you wrote yes* wrong

    • @SilverPh3nix
      @SilverPh3nix Год назад

      @@TheLifeLaVita lmao I’m a dumbass whoops

  • @Kazutoification
    @Kazutoification 8 месяцев назад +241

    Part of the ambiguity here is not just from order of operations, but how people visualize ÷ in solving math equations. For instance, if someone were presented with 1÷2, that would be equal to 1/2. So, when one is presented with 6÷2(1+2), this could imply that 6 is the numerator and 2(1+2) is the denominator. In this case, the ambiguity of ÷ allows the solution to this math equation to be "yes".

    • @paulblart7378
      @paulblart7378 8 месяцев назад +9

      Division is division. Who tf would interpret it as one big fraction? That's not even a debate. The way you denote division doesn't change its precedence.

    • @whojoue0000
      @whojoue0000 8 месяцев назад +56

      ⁠@@paulblart7378just because u think it wouldnt be interpreted as a big fraction doesnt mean it would never be interpreted as such.

    • @paulblart7378
      @paulblart7378 8 месяцев назад +3

      @@whojoue0000 the point is that it's still wrong. It's not a big fraction, and you can't just choose to interpret is as such, it would be wrong.

    • @GanonTEK
      @GanonTEK 8 месяцев назад +22

      ​@@whojoue0000Very true, and if you use the academic interpretation of multiplication by juxtaposition, which implies grouping, it is a big fraction and commonly interpreted as such, even by many modern scientific calculators

    • @negativeharmoney
      @negativeharmoney 8 месяцев назад

      ​@@paulblart7378literally in any level of math beyond grade 10. Ex. The quotient law of logs

  • @jihadalsweed
    @jihadalsweed 6 месяцев назад +3

    Most people here are really lost and think mathematics is just simply blind calculations. It is more of a language in this sense, and using the man with telescope as in example is perfect. i could write 1+1 and the answer is not 2 if the system is binary meaning that every math question needs to be Clearfield and 'order of operation' is usually made for computers and calculators that needs more instructions on how to interpret the question not humans. It is upsetting for me to see that most people find these things as math problems not just silly word play.

  • @nathancate582
    @nathancate582 Год назад +17

    Mathematician: the answer is either
    Comments: here's the right answer..
    Never fails

    • @VoidHxnter
      @VoidHxnter 6 месяцев назад +1

      People on the internet with no qualifications when someone with all of the qualifications show up... and still call them wrong... are just so idiotic.

    • @lilium_lancifolium
      @lilium_lancifolium 4 месяца назад

      You can see this issue in their language. I've heard a bunch of people talking about how the other half can't do whatever grade maths. That's the problem! Most people are relying on elementary level maths without taking into account the other ways of doing things because their way is the right way, but it's only low level. Maths is unfortunately nuanced, despite us wanting to believe it's black and white.

  • @arshmalik8463
    @arshmalik8463 Год назад +6

    the ans would be 9 according to BODMAS and that is actual correct one

  • @arto3485
    @arto3485 6 месяцев назад +1

    That's one example of the many others that show why mathematicians basically never use ÷ symbol, it's way less ambiguous to use the fraction

  • @hotman718
    @hotman718 Месяц назад +1

    Because order of operations says multiplication and division first but this has both so it's ambiguous. I always distribute within a parentheses first before I tackle the division so this would be 1 if I solved it.

  • @alexandreman8601
    @alexandreman8601 Год назад +6

    Use fractions, they're never ambiguous.

  • @quedoom
    @quedoom Год назад +8

    We’re simple; Start with the numbers between the brackets; (1+2) which is 3 then we move on to the division; 6/2 which is, yes it’s three (3).
    Then we have left 3(3) or 3*(3) and that is 9.

  • @ElZedLoL
    @ElZedLoL 6 месяцев назад +2

    Unlucky, Ed said its both correct when actually the division instead of fraction is lacking clarity after using infix notation rather than prefix - so many reductions to terms that finally become ambiguous when used wrong like writing 6/2*(2+1)
    I mean, yes, its true, there is no axiom which makes one or the other correct. And if we wanted to write unprecise like this we have "conventions". But still this undersold math a bit like "aaah yes this is hard" rather that "thats incorrect usage of math"

  • @hardworkingslacker7233
    @hardworkingslacker7233 4 дня назад +1

    Nobody seriously uses the division sign beyond middle school anymore and this why.

  • @roberttran1114
    @roberttran1114 8 месяцев назад +8

    correct. in applied mathematics, a question is generally not written ambiguously like this.

    • @placeholderfornow4766
      @placeholderfornow4766 4 месяца назад

      Exactly. So many people are trying to pass themselves off as superior and so smart because they think it's a simple question... all they're doing is showing their failure to understand the topic.

  • @Jagdedge
    @Jagdedge Год назад +60

    So many people wonder what the right answer is that they forget to wonder if the question is right.

    • @GanonTEK
      @GanonTEK Год назад +3

      100%

    • @samshim3149
      @samshim3149 Год назад +2

      That's true for a lot of intentionally open-ended engineering/physics questions, but in this case, it's just a matter of remembering all the order of operations that we learned in grade school. In higher level math, we usually don't see things written this way because even though it's technically right, it's confusing, and some people can get the wrong answer (as made evident by this whole mess). This wasn't a trick question. It was a tricky one maybe. The answer is 9 btw.

    • @youravghuman5231
      @youravghuman5231 Год назад +5

      ​@@samshim3149 the writing is wrong. Without any context, this can be anything. Some calculators even said it 1. A fricking calculator!
      If this was a paragraph question, no doubt the answer will be wrong

    • @samshim3149
      @samshim3149 Год назад +3

      @@youravghuman5231 Again, I'd have to disagree. I'd argue that the question isn't wrong. Poorly written maybe, but that was intentionally done to cause confusion. The only part that people are confused about is the implied multiplication. I guess some people were taught that if you see number touching parentheses, you need multiply it immediately, no questions asked to get rid of the parentheses. Back when they taught me math, they also taught us that you can only do that if it doesn't affect the rest of the expression. Maybe I only know this stuff because I used to get points taken off when I showed my work like that back then, but this is how I do math in engineering today, and it works great. If you wanna read my full explanation, I left a comment.
      TL;DR is the question is only "wrong" if they meant to say 6/(2(1+2)), but since they didn't say that, you gotta assume they're trying to trick you, so you should read it literally and solve it literally, without making assumptions as to what it may have meant. Just curious... What kind of context were you talking about? Just like extra brackets or something? Because my first thought was the context is it's an internet challenge.

    • @youravghuman5231
      @youravghuman5231 Год назад +3

      @@samshim3149 im not good at English but it's poorly written. Intentional or not doesn't matter because it's a mistake in the question. Just read other comments they explain about juxtaposition.
      What i meant by context is like a question with a given scenario instead of giving an equation like this. That can be more understandable than this equation. If a student writes this equation like this in that question, no doubt he will be marked as wrong.

  • @saintlusso2907
    @saintlusso2907 5 месяцев назад +4

    The answer is 9 because multiplying first after solving the parentheses isn’t the correct order of operations which goes from left to right. For those of you who are currently saying “But division is just a fancy term for a fraction, and 6 over 2(1+2) equals 1” Which, while correct, isn’t the same equation, since that would’ve been written like 6÷[2(1+2)] because again math is solved from left to right unless it’s inside barracks or parentheses, then we solve what’s inside those from left to right first.
    The correct way to express the fraction inside the equation 6÷2(1+2) would be 6 over 2 as the fraction, which is multiplied by (1+2), or in other words 6÷2•3 which breaks down to 3•3=9,
    In summary
    9 = 6÷2•3 = 6÷2(1+2) ≠ 6÷[2(1+2)] = 1

    • @bigepicmanthatlovesfunands4477
      @bigepicmanthatlovesfunands4477 4 месяца назад +3

      Nope. Multiplication and division always go from left to right if in the same consecutive order unless one of the two is in brackets

  • @wailmoregd140
    @wailmoregd140 6 месяцев назад

    Where I’m from, we’re taught that 2(1 + 2) can also be written as 2 * (1 + 2), since 2(1 + 2) is, verbally, 2 of (1 + 2), which is mathematically written as multiplication. So that means the extended way to write this equation is 6 / 2 * (1 + 2). From there it’s standard PEDMAS, or BEDMAS where I’m from. You start with what’s in the brackets, so 1 + 2 = 3. And then, because division and multiplication are on the same tier in order of operations (addition and subtraction are also in the same tier order, being right below division and multiplication), you do both the division and multiplication at the same time from left to right. So 6 / 2 = 3, and then from there it becomes 3 * 3, which equals 9.
    6 / 2(1 + 2) = 9

    • @jiminverness
      @jiminverness 6 месяцев назад

      _"So that means the extended way to write this equation is 6 / 2 * (1 + 2)."_
      You can get away with 2 * (1+2) because it resolves to the same number in isolation, and where there is no preceding division in the expression.
      When you expand it the way you state, you are falling into a trap. 2 of (1+2) should become 6 over 2 of (1+2). but you are making it 6 over 2, of (1+2). See the difference? It should become 6 over (2 of (1+2)), not (6 over 2) of (1+2).

  • @killerwaspy1303
    @killerwaspy1303 Год назад +15

    I learned that to answer problems in mathematics, one would need context. Context is key to understanding and solving problems.

  • @orion6able
    @orion6able Год назад +54

    maybe the problem here is were using the arithmetic division sign, in algebra. So mixing two different types of math is causing something to break. Also, thats kind of fascinating, we mixed two different kinds of math and caused something to break! We have a place in math where there is no right answer! I mean we could define f(x)= 6÷2(x+1) and suddenly, we get a function with...

    • @DonPedro69
      @DonPedro69 Год назад +11

      I dont really know what you mean with two kinds of math, but i would agree in the sense that this is why fractions are superior. These are not so ambiguous. The arithmetic division sign is honestly just an inferior operator sign because you can just get confused with the order of operations rather quickly if you are not used to using this sign. But if you do exactly as the order of operations tells you, you are fine. Math itself is not breaking. It's the misinterpretation that makes it look like there is no right answer. Maybe I misunderstood what you mean by "different types of math"

    • @andreasibilla7855
      @andreasibilla7855 Год назад +6

      ​@@DonPedro69 idk if this is what Talla was talking about, but the way i see it is that that expression mixes two types of notations. it's not exactly a rule, but if you think about it it's more likely to see "÷" and "×"together in one expression, the same way as seeing "/" and " ⋅ " in the same expression. so when you mix the two notations it gets confusing.
      so if you write "6÷2×(1+2)" it's clear, as well as writing "6/2(1+2)".
      mixing the symbols makes stuff weird

    • @DonPedro69
      @DonPedro69 Год назад +1

      @@andreasibilla7855 maybe it was suppose to mean what you say, however that still makes no a big difference in the way you calculate. To make it clear.
      First of all, "÷" is never recommended to be used at all, but if you want to use it you can use it to show ratios between two numbers like 2÷3, even than it is prefered to use 2:3 or 2/3 (it's just a convention). If you have more than just a ratio between two numbers you should always use horizontal fraction bars like for example (5×6+2)/(5×3) (i cant write actual horizontal fraction bars but just imagine it) but also for algebra you should always use fraction bars. They are just much easier to understand and they also get rid of some parenthesis which makes it easier to calculate correctly. × and • have the same meaning tho and make no difference

    • @corneliahanimann2173
      @corneliahanimann2173 Год назад

      ​@@DonPedro69 the fun thing is that I believe this is mostly a mathematical debate because of the internet. I believe I watched a video once that explained that up ti a certain year people would prioritise the order from left to right, over the order of either ÷ or × having priority. This is a debate mostly because different generations and different countries get to look at this through the internet, and we can see that it really depends on how the rules of that country are, because in my case, if this was about a fraction, the second part would ned to be in brackets too. It is how I learned it, otherwise we just go from left to right. It's not that the math of me and other people is different, it's rhe way we have been taught to communicate it.

    • @DonPedro69
      @DonPedro69 Год назад

      @@corneliahanimann2173 yeah that's the main issue i think, you are right it really comes down to how you learn it at school ig, but at a certain level like university things become more unified...atleast to my knowledge

  • @redacted4ever-298
    @redacted4ever-298 5 дней назад +2

    Mathematicians created the BODMAS rule specifically to avoid this kind of confusion.

    • @crystalaustralia
      @crystalaustralia 5 дней назад +1

      But that alone doesn't help decide whether it's 1 or 9

    • @redacted4ever-298
      @redacted4ever-298 4 дня назад +1

      @@crystalaustralia Yes it does, According to the BODMAS rule, You solve the brackets first, then Division, Then Multiplication, Then addition, and finally subtraction. This is created to make sure every calculation is proper and sequential.

    • @GanonTEK
      @GanonTEK 3 дня назад

      Implicit notation must be interpreted before the order of operations can be used. So, BODMAS avoids nothing here since it's the implicit notation that is ambiguous.
      Academically, juxtaposition implies grouping and multiplication (1).
      Literally/programming-wise, juxtaposition implies only multiplication (9).
      Same order of operations used in both cases once the implicit notation is interpreted explicitly.

  • @yes-yogaearthstories1404
    @yes-yogaearthstories1404 Месяц назад +5

    In India, we had the BODMAS rule which is brackets of/orders (square roots or powers) division, multiplication, addition , subtraction. That'd mean B/brackets precedes divison and so on. =6/2*3=6/6=1

    • @Taffles-hh9cu
      @Taffles-hh9cu 11 дней назад +5

      no, the ‘brackets’ means whatever is INSIDE the brackets. the 2(3) is the EXACT same as 2x3 so its multiplication, not brackets. 6÷2x3, you go left to right because division and multiplication are paired in the order of bimdas, so its 3x3, then 9

    • @abcdefxyzzz
      @abcdefxyzzz 8 дней назад

      Bruh it's 9 you're supposed to do the division part before you multiply

  • @sleetyhurdle300
    @sleetyhurdle300 Год назад +4

    just follow bedmas
    6/2(1+2)
    brackets first (1+2) = 3
    since you only have division and multiplication now go from left to right.
    6/2 = 3
    3x3 = 9
    6/2(1+2) = 9

  • @Isometrix116
    @Isometrix116 8 месяцев назад +46

    This is why we do fractions for complex equations with division. Honestly, I’m not sure the last time I saw the division symbol in a formal equation for that exact reason. Also! When in doubt, use more parentheses 6/[2(1+3)] or (6/2)(1+3) are both valid. Also, I’d like to note that PEMDAS isn’t entirely accurate. It’s more PE M/D A/S since multiplication and division are the same thing, as are addition and subtraction. (Since 2*2 is the same as 2/(1/2) and 2+2 is the same as 2 - -2, we can say they are just different ways of writing the same concept).

    • @slamkam07
      @slamkam07 8 месяцев назад +1

      Parentheses come first.

    • @Isometrix116
      @Isometrix116 8 месяцев назад +2

      @@slamkam07 uh... Y...yeah? You're absolutely correct, but I just don't see how it connects to what I said

    • @Springroll65
      @Springroll65 8 месяцев назад

      I know it as BODMAS
      Brakette
      Off
      Division
      Multiplication
      Addition
      Substraction🎉

    • @Luizedu
      @Luizedu 6 месяцев назад

      I don't get it, i can just add parentheses in the equation if i want?

    • @proutjv
      @proutjv 6 месяцев назад +1

      @@Luizedu If it follows the initial order, yes, it can help avoid confusions.

  • @Vectordinate
    @Vectordinate 6 месяцев назад

    I’m sorry to have to inform everybody, but there is not a universally recognized convention for evaluating this expression. The three come up with different results. There are three common conventions currently in practice:
    PEMDAS/BODMAS:
    This is a set of rules for order of expressions that is taught to a large number of students at the advance arithmetic and early algebra phases of their schooling. For the expression given in the question it directs:
    6/2(1 + 2) = 6/2(3) -Do what is in the parentheses first.
    = 6/2(3) - No change because next come handling exponents, of which there are none.
    = 3(3) -Do multiplications and divisions in order from left to right.
    = 9. -Repeating previous step since there is one division and one multiplication.
    There are problems with this set of rules because they were designed for advanced arithmetic and early algebra. They do not handle more advanced expressions. For advanced arithmetic, typically all operations are expressed explicitly, so that 6/2(1 + 2) would not be given, but instead 6/2 × (1 + 2). We will see in the next convention how this distinction can be important, and standard PEMDAS/BODMAS do not distinguish the two expressions.
    Traditional practice of professional mathematicians and physicists (which excludes pre-university mathematics and science teachers):
    If we want to see how things are really done, let’s go to the professionals, rather than depending on overly simplified textbooks that cover only what you need to know now (which is what PEMDAS/BODMAS does). The basic rules are very similar to PEMDAS/BODMAS, with two exceptions: stacked exponentiation is regarded as to be done top-down (sometimes called right-associative), whereas PEMDAS/BODMAS usually does not specify a direction or, if they do, is left-to-right, which is backwards from professional practice; juxtaposed implicit multiplication has lower precedence than exponentiation (like PEMDAS/BODMAS) but higher precedence than all other multiplications and divisions (unlike PEMDAS/BODMAS). In other words, if you write 1/2a, the 2a is regarded as a tightly bound entity and to be treated as a single unit in the context of multiplications and divisions, so it means 1/(2a), not (1/2)a; PEMDAS/BODMAS would treat it as (1/2)a instead. It is necessary to distinguish juxtaposed multiplication from other expressions of multiplication to be able to handle properly formulas like:
    sin 4u = 2 sin 2u cos 2u
    as the first step in showing the expansion of sin 4u. Juxtaposed multiplications must be done before the trigonometric operators, which must be done before the non-juxtaposed multiplications. For the expression given in the question:
    6/2(1 + 2) = 6/2(3) -Do what is in the parentheses first.
    = 6/2(3) - No change because next come handling exponents, of which there are none.
    = 6/6 -The juxtaposed multiplication 2(3) is to be done next.
    = 1. -The only operation remaining.
    Clarity reigns:
    Because of the confusion that arises between methods 1 and 2, and confusion needs to be avoided, it has become in recent years standard practice among publishers of technical journals, the General Conference on Weights and Measures (responsible for defining the metric system), and several other standardization organizations to prohibit expressions that involve a division symbol followed on the right by a multiplication or another division within one term, unless explicit bracketing or use of vertical layout make it completely clear and explicit in which order the affected divisions and multiplications are to be done. For the expression given in the question, these rules regard 6/2(1 + 2) as undefined. We are not going to play some cutesy games like “I know PEMDAS/BODMAS and I’m going to see whether you do or I can trick you, so I am deliberately writing it hoping to confuse you.” For somebody who acts that way, you are being pretentious, acting like “I know more mathematics than you do and I am going to show you”, but in fact you are demonstrating that you know less mathematics, because you are showing that you do not realize that a key part of mathematics is to express your thoughts clearly and unambiguously without reliance on some convention not universally recognized. Therefore, the expression in the question cannot be validly evaluated unless it is rewritten in another form such as:
    (6/2)(1 + 2) [9], 6/(2(1 + 2)) [1], 62(1+2)
    6
    2
    (
    1
    +
    2
    )
    [9], 6(1+2)2
    6
    (
    1
    +
    2
    )
    2
    [9], 62(1+2)
    6
    2
    (
    1
    +
    2
    )
    [1]. [Brackets after each expression indicate the resulting value.]
    “Rules of mathematics” are not some stagnant ideas thought up once, written down, and never changed again. As technology changes, the modes of conveying ideas change as well, and the different modes have different new abilities never available before in some cases and more restrictions in other cases. This sometimes requires that the rules change. The rules for how multiplications and divisions are handled have changed several times in the last 120 years. They are changing again. Convention 3 (to be explicit as to intent) is rapidly becoming the new dominant convention. In this regard, PEDMAS/BODMAS that is so treasured by some people will soon become outmoded-even dead-if it is not changed to accommodate this prohibition of multiplications and other divisions immediately following a division.

  • @hiteshshekhawat3346
    @hiteshshekhawat3346 5 месяцев назад +2

    Americans = this is out of syllabus
    Indians = 🗿 यह बहुत आसान है 🍰

    • @BenB810
      @BenB810 5 месяцев назад

      Since when do they teach the material in the syllabus?

  • @piyushguptaji402
    @piyushguptaji402 Год назад +244

    According to BODMAS rule, the brackets have to be solved first followed by powers or roots (i.e. of), then Division, Multiplication, Addition, and at the end Subtraction.
    edit: GUYS BODMAS PEDMAS ASS-MAS ITS ALL THE SAME THING. You may abide by one or the other. Math doesn't change from country to country bruh y'all 💀

    • @derblaue
      @derblaue Год назад +28

      The problem here is the implicit multiplication (or juxtaposition) which makes it all ambigous and since implicit multiplication can only be used when it's not ambigous the whole expression is invalid.

    • @eliteteamkiller319
      @eliteteamkiller319 Год назад

      BODMAS is just a mnemonic device. Multiplication and division are literally the same operation. Regardless, this moronic expression is ambiguously written. You never see this is in grown up math because no one writes anything ambiguously.

    • @kryptoncrescent
      @kryptoncrescent Год назад +2

      @@derblaue well maths has a serious problem if its being ambiguous rather than concrete

    • @widevader
      @widevader Год назад +38

      ​​​@@kryptoncrescent that happens when people dont want to follow proper writing. If it was written properly it would either be 6/2*(1+2)
      Or 6/(2*(1+2)) in this case you dont need the *
      I think the biggest problem is that people dont even know how PEMDAS and simmilar stuff works. They think since addition is before subtraction it makes it a higher priority, luckly in my country we dont have such acronyms and we are just thought as it is.

    • @Cyril29a
      @Cyril29a Год назад +9

      @@kryptoncrescent Math doesn't have a problem, people who don't know how to write math do. There is a difference. This is a poorly written problem plain and simple. The fact that it is poorly written does not affect math itself only this problem and those who read it.

  • @kor3ancookie
    @kor3ancookie 7 месяцев назад +36

    The "man with a telescope" was such a brilliant comparison. I never thought of it that way

  • @vimalkumars4636
    @vimalkumars4636 Месяц назад +2

    Actually 5 ± 4

  • @Nine-nr1pe
    @Nine-nr1pe 6 месяцев назад

    Legend has it, the question is yet remains unanswered

  • @clehaxze
    @clehaxze Год назад +4

    The thing is. In a lot of higher math, especially calculus and other advanced subjects. Implicit multiplications have a higher precedence then all other operations. For example the expression ax/by is parsed as the following in high schools
    (Sorry for using LaTeX notation here)
    a \frac{x}/{b} y
    But in calculus. The differential equation ax/by=0 is parsed as
    \frac{ax}{by}=0.
    Like, it makes no sense to express it this way otherwise. If you really want the previous grouping, usually we follow the convention of putting variables last. So axy/b=0. Or \frac{a}{b} xy
    No one writes like that.

  • @TheoJay615
    @TheoJay615 Год назад +69

    Eddie DESTROYS misleading math questions with A TELESCOPE.

    • @RahulGupta-wn8xh
      @RahulGupta-wn8xh Год назад

      This will help you in your confusion
      ruclips.net/video/_HtJTPelgDo/видео.html

    • @ryankwok1021
      @ryankwok1021 Год назад +1

      Underrated comment

    • @medosfilms
      @medosfilms Год назад

      he fye 🔥

    • @_Nilu__
      @_Nilu__ Год назад

      9

    • @placeholderfornow4766
      @placeholderfornow4766 4 месяца назад

      @@_Nilu__ There is no multiplication in the question. It's juxtaposition. It functions the same as multiplication but it's undefined whether it has different priority or not.

  • @Samael3
    @Samael3 7 месяцев назад +1

    (6÷2)(1+2) =/= 6/(2(1+2))
    Probably why you don't see "÷" in higher level math generally. It's like a sentence with improperly placed or missing commas. (I guess like the video described.)
    "Let's eat, grandpa!" =/= "Let's eat grandpa!"

  • @Techy-Pirate
    @Techy-Pirate 6 месяцев назад +1

    BODMAS Rule brothers
    by bodmas you will first solve bracket then division then multiplication then addition then subtraction so by that answer is 9

  • @loganxavier
    @loganxavier Год назад +4

    The answer is simple, stop using the division sign and just use fractions

  • @rob1733
    @rob1733 Год назад +63

    Thank you, Eddie Woo! This is what I tried to explain to my Father AND my Son who both came up with different answers and both insisted they were right. It is not necessary to be this ambiguous. It's easy to be much clearer in your intentions in mathematics!

    • @grapeman8612
      @grapeman8612 Год назад +13

      Well tell whoever said 9 they are correct, and the other to go back to elementary school and learn order of operations

    • @SappinYourSentries
      @SappinYourSentries Год назад +4

      @@grapeman8612 order of operations is irrelevant. Multiplication and division have the same priority as they are the same operation (division is multiplication by the reciprocal). The only issue is that the problem is intentionally written poorly to cause arguments and generate engagement. Source: I have a math degree.

    • @grapeman8612
      @grapeman8612 Год назад +8

      @@SappinYourSentries order of operations also state you go left to right, and this problem is incredibly simple when you follow that. Also there is no reason to do 2*3 first because then the actual problem is 6/2/3 and that is not what this problem is. There is no parenthesis around 2*3 so you don’t do it first
      Also I know you’re not arguing but it isn’t really written that poorly
      Source: I have a brain and am not 1 year old

    • @hanmira
      @hanmira Год назад

      ​​@@grapeman8612
      Number 1 is correct because of three reasons:
      1)
      1. 6/2(1+2)
      2. 6/2(3)
      3. 6/2(3) ≠ 6/2×3, so you solve 2(3) first
      4. 6/6
      5. =1
      2)
      So you know in algebra if an equation is something like
      2×(2a+2b), you multiply the two with both factors in he brackets, making it 4a+4b
      Well, the same thing happens 6/2(1+2)
      1. 6/2(1+2)
      2. 6/(2+4)
      3. 6/6
      4. =1
      3)
      / is just the same as ÷, which means there is a fraction
      So that would mean that 6 is the dominator and 2(1+2) the nominator
      1.
      6
      ---
      2(1+2)
      2.
      (Solve 2(1+2) which way you like)
      6
      ---
      6
      3.
      =1
      UNLESS
      You interpret the 6 as the dominator and 2 as the nominator, which would then mean they both get multipled by (1+2).
      1.
      6
      -- × (1+2)
      2
      2.
      3 × (1+2)
      3.
      =9
      If that's how you solved the equation then that's fair. Anyways the answer is 1 and even any calculator says that
      And I realized I put way too much effort into my reply

    • @grapeman8612
      @grapeman8612 Год назад +8

      @@hanmira you didn’t put too much effort in, it’s all fine lol, but anyways here’s why your wrong
      1. Even if it is 6/2(3), it’s still be nine because you have to go left to right. (Parentheses rule does not matter because the 2 is not inside parentheses.)
      2. Again you are ABLE to distribute, but distributing at that time would be going out of order.
      3. And if you wrote it like an equation you would move the 2 to the denominator and the 6 and (1+2) (or 3) to the numerator. Still being 9 (18/2)
      I’ve done some more research since I’m confused as to how anybody gets this wrong, and apparently there is historical reasons.
      In the past the % (division symbol) would be differing from / (other division symbol)
      So a problem like this
      8%2Y, would turn into 8/(2Y).
      That symbol used to mean “divide everything that comes after” but it doesn’t anymore” so now % and / mean the same thing, and there is no version where this equals 1, unless you’re living in the early 1900s
      Also I realize that is a percent symbol but I couldn’t for the life of me find a division one like the one in the vid

  • @easylivinglife6284
    @easylivinglife6284 5 месяцев назад +1

    Whoever wrote the question needs fired.
    Its a notation error. Math is a language, not "just a fun challenge." Writing a sentence that makes no sense and then asking "Why doesn't this make sense?" Is the highest principle example of what is wrong with education today. Either write (6/2)X(1+2 ) or write 6/(2(1+2)). You cannot have it both ways. And you WOULDN'T have it both ways if you ever tried to think about this logically. 9 and 1 are very different answers, and not connected in any way. Its not like Sqrt(x) which can have both a positive and a negative number, there is just one correct answer here.

  • @ranphifer
    @ranphifer 6 месяцев назад +1

    people who studied chapter arithematic equations from ncert of class 10 can easily solve this within a second. the formula where 'sum of numbers = n/2 ( a + an)'

  • @kevinclark6681
    @kevinclark6681 10 месяцев назад +87

    THANK YOU!
    I've thought for some time that the whole question is meaningless, because if the point was to get the right answer, or even to *have* a right answer, greater clarity is needed.
    Also, been watching your videos off and on for awhile. I was a maths major, and I've done some tutoring here and there, so I can really appreciate both the depth of understanding and the enthusiasm you bring to the classroom.

    • @Rami-bi9xj
      @Rami-bi9xj 8 месяцев назад

      But what determines which way to get the result?

    • @ultrio325
      @ultrio325 8 месяцев назад +7

      ​@@Rami-bi9xjAsk whoever wrote the question to rewrite it as a fraction instead, or if that's not available just give up

    • @yourmommydotcommy2650
      @yourmommydotcommy2650 8 месяцев назад +5

      It’s not confusing, it’s not a special math problem, the answer is 9 and only 9.

    • @doughendrie5468
      @doughendrie5468 8 месяцев назад +1

      It’s a straight forward term divided by a term.
      The term 6 divided by the term 2(1+2) gives the answer of 1
      2(1+2) is one term containing 2 factors. The 2 and the (1+2). Factors multiplied, are a single term.

    • @rally7555
      @rally7555 8 месяцев назад

      ​@@yourmommydotcommy2650go back to school bro

  • @severinhilt3828
    @severinhilt3828 Год назад +4

    It is 9. And here’s why…
    It can be simplified to:
    6 / 2 • 3
    Order of operations states that division & multiplication are EQUALLY OPERATED so division is done first in this situation.
    6 / 2 = 3…. 3 • 3 = 9

    • @GanonTEK
      @GanonTEK Год назад

      The order of operations doesn't prove one answer over the other, unfortunately.
      It can't, because it's the *notation* that is ambiguous.
      If you interpret the implict multiplication literally, you convert
      6÷2(1+2) to 6÷2×(1+2) which is 9.
      If you interpret the implict multiplication academically, you convert:
      6÷2(1+2) to 6÷(2×(1+2)) which is 1.
      That's where the ambiguity is.
      There is no agreed upon convention on whether multiplication by juxtaposition implies grouping or not.
      Both are widely used and nothing to do with the order of operations used at all.
      It's also why anyone using the order of operations to prove one answer over the other is just making a circular argument and proving nothing.
      All they are doing is assuming a notation interpretation and saying the one they picked is the right one, when it's not the only right one.
      Mr. Woo is correct and multiple institutions and professors agree.

    • @413XUIFC
      @413XUIFC 6 месяцев назад +1

      ⁠@@GanonTEKThere is no ambiguity, you either come up with some parenthesis out of nowhere or just do math

    • @GanonTEK
      @GanonTEK 6 месяцев назад

      @@413XUIFC With ab/cd you get (a×b)/(c×d), so parentheses out of nowhere.
      With Sin²x you get (Sin x)², so parentheses out of nowhere.
      So, it's quite common and an integral part of maths.
      The issue here is the notation, which isn't maths. Notation is language. Language is used to describe the maths, but the language isn't the maths itself.
      Language is arbitrary, like our base 10 number system. You can use any number system you like, and all the rules and properties of maths still hold.
      Pythagoras theorem in base 10
      a² = b² + c²
      Pythagoras theorem in base 2
      a¹⁰ = b¹⁰ + c¹⁰
      Even indices notation is arbitrary.
      aa = bb + cc is valid.
      Notation and rules are completely separate from each other.

    • @413XUIFC
      @413XUIFC 6 месяцев назад

      @@GanonTEK Dude, you are just trying to mix the little knowledge you have about basic math just to try to show you know, when you don’t
      Having as an argument that you can invent parenthesis out of nowhere because of a trigonometry “shortcut” is the most ridiculous thing I’ve read in a while
      Copied comment:
      You are inventing a parenthesis out of nowhere, leading to this new creation:
      6/(2(1+2))
      Which would be 1
      BUT THAT IS NOT THE CASE
      So now read carefully because I will explain something you should have learnt at the age of five:
      There is something called “commutative property”, which only applies (in basic math) to sums and multiplications, but NOT DIVISIONS (turn /6 into 6^(-1) and see how you can now freely multiply), and that’s why you can’t do right side first.
      There are many different ways of demonstrating why 1 is simply NOT correct, but that is the most basic example I could come up with.
      You clearly have no idea mate, I don’t know what you are studying, but it is just being a waste of time

    • @GanonTEK
      @GanonTEK 6 месяцев назад

      @@413XUIFC All implicit notation conventions are shortcuts.
      That's the entire point of them.
      Don't you know that?
      2(1+2) is another form of implicit notation, like ab, or Sin²x.
      You just don't believe it is, with no evidence.
      Here is something you should know since you were 5:
      Notation is interpreted before any rules are used.
      Why? Notation is language and is arbitrary.
      6/2(1+2) using the academic interpretation of multiplication by juxtaposition convention means
      6/(2×(1+2)) which is 1
      Commutative property:
      6/(2×(2+1)) = 1
      6/((2+1)×2) = 1
      6/((1+2)×2) = 1
      Commutative property holds.
      Replacing division with multiplication of the inverse:
      6×½×1/(1+2) = 1
      For ease I'll write
      6×½×⅓ = 1
      Commutative property:
      6×⅓×½ = 1
      The multiplicitive inverse, commutative, distributive properties etc. all hold for 1 and 9.
      Why?
      1 and 9 are not determined by the rules here. They are determined by the notation convention applied.
      If you use tte more literal/programming-wise interpretation of multiplication by juxtaposition you get
      6/2×(1+2) instead and then, after you have removed all the implicit notation you can apply the rules which all give 9 in this case instead.
      The rules do not describe the language.
      The language describes the rules.
      So, you haven't demonstrated any way 1 isn't valid yet.
      Every way you can get 9, there is a way to get 1, without fail.
      It's impossible not to, since it comes down to notation conventions abs not rules at all.
      I've a lot more knowledge than you presume. You're the one with no idea, which is obvious when looking at the facts.
      Modern international standards like ISO-80000-1, the American Mathematical Society, calculator manufacturers, multiple professors and mathematicians all agree it's ambiguous. They are people and institutions with authority on the subject.
      If you think you know better than them, go ahead and take it up with them yourself.

  • @Goabnb94
    @Goabnb94 5 месяцев назад +1

    Its intentionally written to be confusing, not only by use of the division sign instead of a fraction line (or / in text form), but also with the knowledge that juxtaposition exists and is taught in some places and not others (leading to PEJMDAS). The writer knows some see "2(1+2)" and intuitively treat the lack of multiplication sign as it being "(2*(1+2))" but in such a way to remove unnecessary parentheses. 6/2x where x=1+2, and the answer is clear to anybody, but substitute in x and suddenly its meant to be treated differently? If somebody wanted half of pi, they write pi/2, but apparently 1/2pi is meant to be treated as half of pi as well? Any physics student would intuitively know that it would be 1 over 2pi, without needing parentheses.

  • @Youness324
    @Youness324 4 месяца назад +16

    First thing you solve (1+2)and it becomes 6÷2(3) which is 6÷2 x 3 then do the "left to right", now it's 3 x 3 = 9

    • @Gh05tt
      @Gh05tt 4 месяца назад

      He just said it can be 1 aswell

    • @Youness324
      @Youness324 3 месяца назад +1

      Only one answer and it's 9@@Gh05tt

    • @Gh05tt
      @Gh05tt 3 месяца назад

      @@Youness324 it can be 1 your wrong I take advanced mathematics

  • @Dravignor
    @Dravignor Год назад +8

    Moral of the story: Stop using the obelus and just write it in fractional form.

    • @GanonTEK
      @GanonTEK Год назад

      100%

    • @off3039
      @off3039 Год назад

      I would agree with you, but you can just use order of operations to solve and get 9. (1 + 2)=3, 6 divided by 2 = 3. Both threes are next to each other so you multiply them (3x3) to get 9

    • @doughendrie5468
      @doughendrie5468 11 месяцев назад +1

      It’s already in fractional form.
      6 divided by 2(1+2)
      Answer is 1
      6/2 cannot be the factor of the parentheses as factors must be whole numbers. Not fractions. And the term 6 is separated from the factor 2 by explicit division. So the factor 2 being juxtaposed with the parenthetical expression containing the factors 1 and 2, having a higher priority over explicit division and multiplication, must be simplified first.

  • @CatherineAaBb
    @CatherineAaBb Год назад +55

    When I was in school, my math teacher taught us that action within a brackets goes first and then all of the rest goes from left to right
    So, 6÷2(2+1) becomes (2+1) = 3, then 6÷2 = 3 and 3×3 as a result of previous actions

    • @BigFruity
      @BigFruity 8 месяцев назад +7

      No, no.......so 6/2 = 3 is just wrong. Where does the = come from? Sure, 2+1 = 3, but you don't put a = into the calculation. The way you wrote it, it would be 3=3 which doesn't make that much sense in that context. Even though you got the right answer. First, you solve the stuff inside the brackets, then you do the "point before line calculation" don't know if it is called that in English, what I mean is, you calculate multiplication and division before + and -.
      6/2(2+1) ---> 6/2(3) ----> 3*3 = 9

    • @jujucasar2003
      @jujucasar2003 8 месяцев назад +1

      but wut if u live in An Asian country where they write right to left?

    • @LaggPlxel
      @LaggPlxel 8 месяцев назад

      @@jujucasar2003 it doesnt matter. just use bodmas

    • @mariopluto6721
      @mariopluto6721 8 месяцев назад +4

      @@jujucasar2003 Math, is a language, if they speak their own language, they can write their own direction, but like english, math is ALWAYS written from left to right.

    • @chieflegend1729
      @chieflegend1729 8 месяцев назад

      ayo bro , here the question is not about using BODMAS, it is about whether the (2+1) is in numerator (answer = 9) or denominator (answer =1)

  • @colaxarsenal
    @colaxarsenal 5 месяцев назад

    The problem with his answer is that order of operations says that if there is a bracket you solve it first:
    1. 6/2(3)
    2. 6/6 as you still have solved the bracket so u must do 2x3
    3. 6/6 = 1

  • @N08ODY..
    @N08ODY.. 6 месяцев назад +1

    THE ANSWER OF THIS. QUES IS ACTUALLY NUMBER THAT COME AFTER = ... THATS THE ANSWER. .. AND IT IS CORRECT U CAN DEBATE ON THAT 🗿

  • @RoofWithAFloor
    @RoofWithAFloor Год назад +87

    "The great thing about maths is that there's always straight foward right or wrong answer"
    -parents to me in 8th grade

    • @monkeybusiness673
      @monkeybusiness673 Год назад +5

      LIIIEEES! I heard the same all the time.

    • @DonPedro69
      @DonPedro69 Год назад +7

      I mean to be fair it is very often the case

    • @andreadonato6210
      @andreadonato6210 Год назад +13

      There’s a right answer: 9.

    • @monkeybusiness673
      @monkeybusiness673 Год назад +2

      @@DonPedro69 Yeah, but as any mathematician will be quick to point out:" Well, it's not ALWAYS though, is it?!" x'D

    • @DonPedro69
      @DonPedro69 Год назад +2

      @Monkey Business good point...I say it the way I say because I'm really not sure xD

  • @beast7116
    @beast7116 Год назад +39

    The actual correct answer is 9, according to the very clear order of operations. That being said, I stopped using the “÷” symbol when learning algebra and if I saw an expression like that in my notes I would probably evaluate it as 1, because I implicitly accept a term before a “(“ as a coefficient for the term inside the “()”.
    I’ve personally found certain math notation makes no sense. For example, cos^2(x) is (cos(x))^2, yet cos^-1(x)≠(cos(x))^-1.
    A partial derivative uses “∂” but a partial integral does not.
    Order of operations doesn’t work perfectly for integrals; “dx” is technically being multiplied by the integral but if you have a variable just to the right of “dx” it’s considered outside the integral, violating the commutative property of multiplication. The same is true for the order of “dx” “dy” and “dz” at the end of double and triple integrals.
    Don’t even get me started on multiplication symbols, we have X used for cross products, • for dot products, * for convolution products, and an expression like y(x) could be the product of x and y or could be defining y as a function of x.
    Then as we start to apply math in other classes like physics, we run out of symbols despite already using two alphabets. So i for sqrt(-1) becomes j in circuit analysis so as not to be confused with current, i. Seeing V could mean a variable of voltage or the unit, volt.
    Basically math gets complicated enough where the meaning of an expression is dependent on context more than standardized rules of notation, which is why the analogy of “I saw a man with a telescope” is excellent despite order or operations providing a clear answer in theory.

    • @pineapplejuice3412
      @pineapplejuice3412 Год назад +7

      I read allat 🔥🔥that was fire

    • @bramvanduijn8086
      @bramvanduijn8086 8 месяцев назад +4

      I like how you disproved the clarity of the order of operations immediately after stating it is very clear.

    • @beast7116
      @beast7116 8 месяцев назад +5

      @@bramvanduijn8086 my thermodynamics homework the other day provided a gas constant in units “kPa·m^3/kg·K” which is wrong according to the literal rules outlined by order of operations. It technically should be kPa·m^3/(kg·K). You can never trust division symbols in place of fractions lol

    • @le4chehenry324
      @le4chehenry324 6 месяцев назад +7

      In my country, your method would be considered unacceptable

    • @jaycash4381
      @jaycash4381 6 месяцев назад +3

      YOU ARE INCORRECT. First of all you added algebra II and calc which are not very helpful for this problem. Brackets are first so we do (2+1). But here's everyone's mistake. Instead of multiplying (it's that because the number outside of the brackets is multiplied by the corresponding one.) And since it is also considered to be a part of the brackets expression because it's multiplying it by a constant then it becomes 6. Then you divide 6 by 6 and get 1 to be your answer. Try it on a calculator if you don't understand :]

  • @howtodrawwithpaint4648
    @howtodrawwithpaint4648 6 месяцев назад +1

    6 ÷ 2(1 + 2). So, we take 6 ÷ 2 first, is equal to 3. Then we take 1 + 2, is equal to 3. And take 3(3), is equal to 3 × 3 is 9.

    • @placeholderfornow4766
      @placeholderfornow4766 4 месяца назад

      There is no multiplication in the question. It's juxtaposition. It functions the same as multiplication but it's undefined whether it has different priority or not.

  • @UncringeGamingProductions
    @UncringeGamingProductions 6 месяцев назад +16

    i went from liking him to hating him within a span of 2 seconds

    • @naemek9675
      @naemek9675 5 месяцев назад +2

      ok, but why?

    • @ItsPro824
      @ItsPro824 4 месяца назад

      Because you are dumb?

    • @AyubHassan07
      @AyubHassan07 4 месяца назад

      answer is obviously 9 @@naemek9675

    • @pickleism253
      @pickleism253 4 месяца назад +1

      ​​@@AyubHassan07Bro he just explained why, this symbol ÷ is ambiguios and is replaced by fraction past 7th grade

  • @Dragonflies82
    @Dragonflies82 Год назад +67

    I'm confused cause I thought there was a math "law" that you have to solve was inside (the parentheses) first. 🤷‍♀️

    • @seanspreckelsen3496
      @seanspreckelsen3496 Год назад +63

      There is. Order of operations. The answer is 9. There is no ambiguity

    • @Dragonflies82
      @Dragonflies82 Год назад

      @@seanspreckelsen3496 In math there's an order to solve operations. Copy this from a webpage. "First, we solve any operation inside of parentheses or brackets. Second, we solve any exponents. Third, we solve all multiplication and division from left to right. Fourth, we solve all addition and subtraction from left to right."

    • @Dragonflies82
      @Dragonflies82 Год назад +17

      @@seanspreckelsen3496 If you follow the order is 1, but the calculator answer is 9. 🤷‍♀️🤷‍♀️

    • @austinaxley81
      @austinaxley81 Год назад +55

      @@Dragonflies82 that's not correct, you're misusing order of operations. PEMDAS is the acronym, but the order should be P>E>MD>AS, it is NOT P>E>M>D>A>S. You multiply AND divide in the order the problem is written (left to right, top to bottom) then you add AND subtract in the same order.
      6÷2(1+2)=x
      First the function inside the parentheses.
      6÷2×3=x
      Then, being no exponents, you multiply and divide in order from left to right. The left most function is division so in this case you divide BEFORE you multiply.
      3×3=x
      Then multiply SECOND.
      x=9
      The problem isn't designed to be ambiguous, it's designed to point out a common misunderstanding of order of operations.

    • @michaelmulla6178
      @michaelmulla6178 Год назад +18

      @@Dragonflies82 order says parantheses first, so you get 6:2(1+2)=6:2(3) which is 6:2*3. Now you need to follow the order from left to right. Youll get 9

  • @jacckkaboii3528
    @jacckkaboii3528 Год назад +8

    I absolutely agree with the fact that it’s ambiguous. But if there was an order of operations specified such as bodmas, then the answer would be clear. But all things aside I think Eddie did a good job acknowledging why the answer isn’t clear and didn’t feel the need to over complicate things by mentioning different orders of operations and what answers they would give you.

    • @GanonTEK
      @GanonTEK Год назад +1

      Funnily enough, there is a version of PEMDAS that does take multiplication by juxtaposition into account called PEJMDAS.
      Where J is for juxtaposition. It's above regular multiplication or division.
      Maybe BOJDMAS is the BODMAS variant? Hard to say it though!
      I agree with your comment completely.

    • @jacckkaboii3528
      @jacckkaboii3528 Год назад +1

      @@GanonTEK That's cool! I have never heard of variants with a J in them!
      Thanks for being so cool!

    • @GanonTEK
      @GanonTEK Год назад +4

      @@jacckkaboii3528 Thank you for being so kind!

    • @tjossai9302
      @tjossai9302 Год назад +1

      @@GanonTEK I never called it multiplication by juxtaposition but I always used it and thought it was part of the P or B in both version like, 2(5 + x), I always thought regardless of whatever is done to the 2, it will first become 10 + 2x first before anything else is done to it. So this 6/2(2+1) has always been 6 all divided by 2 into 2+1. It's the same as 5 x 8^2, because there is no bracket covering the 5 x 8 part of the equation, I would think that the thing being squared is the 8 and not 5 x 8.

    • @GanonTEK
      @GanonTEK Год назад +1

      @@tjossai9302 For the last example, exponents have higher priority than addition so that's why it's only the 8 being squared.
      Outside brackets are not part of the B/P step, only inside parentheses are.
      It's a notation convention, though, that puts implied brackets around expressions like that, so it's a perfectly valid interpretation but it's not the only one in use.
      That's the problem.
      It should be written properly as
      (6/2)(1+2) or
      6/(2(1+2)) to remove all ambiguity.

  • @highschoolhub1954
    @highschoolhub1954 6 месяцев назад +1

    Priority of solving: parenthesis and DMAS rule... So simple

  • @savageguy6709
    @savageguy6709 4 месяца назад +1

    in summary he told the answer of
    6÷2(1+2)= "I saw a man with a telescope"

  • @quietstorm0910
    @quietstorm0910 Год назад +37

    what i've learned here is that the ÷ symbol has a double meaning in mathematical proofs to reflect 2 fractions, but the clarity can be resolved by using a wider set of parentheses for the numerator and/or the denominator:
    6 6
    6 ÷ 2(1 + 2) = --- (1 + 2) = 9, while 6 ÷ _(2(1 + 2))_ = ---------- = 1, so i would still go with 9 based on order of operations or entering it into a calculator to fact check.
    2 2(1+2)

    • @enraqusbail6314
      @enraqusbail6314 Год назад +1

      the thing is, if we are already using brackets to make it clear that 1+2 must be done first, then it is obvious that if we leave the second brackets out of the divider 2 and the factor (1+2) that they must be seen seperately, otherwise i could doubt the means of the first brackets too

    • @JonGretarB
      @JonGretarB Год назад +3

      Oh calculators disagree depending on what convention they follow. Even calculators by the same company.

    • @lastyhopper2792
      @lastyhopper2792 Год назад +9

      ​@@enraqusbail6314 yeah,
      6 ÷ 2 (2 + 1) is
      6
      ---- (2 + 1) = 9
      2
      While, 6 ÷ (2 (2 + 1)) is
      6
      ----------------- = 1
      2 (2 + 1)

    • @gerrylaksono1222
      @gerrylaksono1222 Год назад +1

      Naaah. I still go with 1 for following logic in a sentence 🤣

    • @lolalola5757
      @lolalola5757 Год назад +2

      what are you talking about? the order of operations say that you solve the paranthesis first? so it's 2(3) = 6 and then 6/6 = 1. You have a multiplication between the 2(3) since you have a paranthesis and a multiplication it's going to be 6/6 = 1. The multiplication and division in the order of operations you find in PE(MD)AS while you find partanthesis in (P)EMDAS. Obviously since you have both M and P first before divsion the more dominant answer is 1. When you have a multiplication with a paranthesis it's like it's glued together in a sence, you can't just neglect that fact and take away the glue and divided 6 with 2 before you resolve the glue with 2(2+3)

  • @cuchinha
    @cuchinha Год назад +6

    I'm from Brazil so I don't know if the math there is different, but in my country when there's division and multiplication because both have the same priority, it goes in order from left to right

    • @batmirin35
      @batmirin35 Год назад

      Não exatamente exemplo:
      2 : 3x. (X=2)
      O resultado é 2/6 ou 1/3.
      Mas se vc fizesse na ordem que aparece estaria errado:
      2:3.2
      4/3
      Ou seja em alguns casos como 2x vc deve fazer multiplicação na direita e depois resolver a conta.

    • @vjollila96
      @vjollila96 6 месяцев назад

      order should go like this:
      ( )
      x^y √
      x /
      + -

    • @placeholderfornow4766
      @placeholderfornow4766 4 месяца назад +1

      There's an unestablished rule that might exist called juxtaposition (like a(b)), where it's like multiplication but takes priority above it and division.

  • @hammondvoodoo9555
    @hammondvoodoo9555 21 день назад

    For me, this problem is not ambiguous at all: 6÷(2×(1+2)) = 1 but 6÷2×(1+2) = 18÷2 = 9. The fractional notation would make things very clear and brackets really matter.

  • @gunfire_
    @gunfire_ 4 месяца назад +1

    firstly
    if there are() marks those are to be calculated first then everything else so it becomes
    and starbald3895 said
    1. Brackets
    2. Exponents
    3. Multiplication and divisions (left to right)
    4. Additions and substractions (left to right)
    which is right
    so by this logic
    6÷2(1+2)
    =6÷2x3
    =3x3
    =9
    CASE CLOSED

    • @placeholderfornow4766
      @placeholderfornow4766 4 месяца назад

      There is no multiplication in the question. It's juxtaposition. It functions the same as multiplication but it's undefined whether it has different priority or not.

    • @unbreakablebedrock2313
      @unbreakablebedrock2313 4 месяца назад

      ​@@placeholderfornow4766you are an idiot or just bad joking?

    • @GanonTEK
      @GanonTEK 4 месяца назад

      ​@@unbreakablebedrock2313They are correct.
      There is no juxtaposition in the regular order of operations since it is a notation convention.
      There are variants that include it like PEJMDAS and around half of scientific calculators effectively use that concept (you can see it in their manuals).
      Implicit notation needs to be interpreted before you use any rules unless you use a variant that includes it.

  • @mayankyadav1077
    @mayankyadav1077 8 месяцев назад +7

    BODMAS left the chat after hearing this

    • @placeholderfornow4766
      @placeholderfornow4766 4 месяца назад

      BODMAS is an acronym for helping you remember. It's not a rule by any means and isn't thorough at all.