There are 2 main reasons why people get 1 1. They think parenthesis takes priority no matter what. In reality, parenthesis no longer serves a purpose once everything inside it is at its simplest form. 2. Some people think that multiplication takes priority over division when in reality they have the same amount of priority. Meaning its from left to right instead of a specific order.
@CoolHandLouis
Жыл бұрын
There's a better reason. Because those who study higher levels of maths will interpret ab/cd as (ab)/(cd). Similarly 1/2x is properly interpreted as (1)/(2x). A strict PEMDAS evaluation would indicate that 1/2x = x/2, but that's not how higher level maths works. This problem simply demonstrates that PEMDAS is a flawed rule for explaining how expressions are interpreted at higher level maths.
@jordansimmons6530
8 ай бұрын
The problem could be asking a/bc or a/b x 3 it depends on how you interpreted it
@Valerius123
7 ай бұрын
@gunthegoldminer8119 No. The reason people get 1 is right in the title of this video. The question was 6÷2(1+2)=??? not 6/2(1+2)=???. 6/2(1+2) implies 6 is in the numerator and 2(1+2) is in the denominator which groups the the order of operations giving the answer 1. 6÷2(1+2) implies the whole thing is in the numerator which groups the order of operations to be 9. Division and fractions are functionally similar but syntactically different. The syntax of fractions gives a new way to group order of operations. You can group things in the numerator and you can group things in the denominator
@nithish9863
4 ай бұрын
@@Valerius123actually the division symbol (÷) and by symbol ( / ) both are meant for dividing the values right . Then why don't we have to change ÷ by / ? Can you explain to me ? Please actually i am so confused. Thus bodmas looks like a pain in the a&&. It is making a simple equation trickier to solve. At last why does we even have to use this system? Please explain me.
@Valerius123
4 ай бұрын
@@nithish9863 No one really uses (÷) past elementary school that I'm aware of. Because you can get away with fractions. So, I think a lot of us forgot the simple rules of bodmas/bedmas then we encounter these sort of questions and get confused. But really, at the end of the day mathematics is a sort of language and there are agreed upon rules in order for us to communicate effectively. If we didn't have standards like bodmas then everyone would be confused all of the time.
@allozovsky
3 ай бұрын
From Quora: “When writing mathematical formulas, what you are trying to do is _communicate._ That means that you should make it easy for your reader to understand what you’re trying to say“.
As a professional mathematician and a professional philosopher(both self proclaimed(i am 13)), the question is wrong as having two answers is failure at the side of the examinar and not the atudent.
@GanonTEK
Жыл бұрын
100%
@Failure_is_Cubing
8 ай бұрын
Totally agree. We shouldn’t argue over a math question that has a flaw in it.
@rishikeshnawathe3063
4 ай бұрын
There are no two answers.. It is 9
@allozovsky
4 ай бұрын
@rishikeshnawathe3063 Do you not believe a professional mathematician and a professional philosopher? 😂
@c.jishnu378
4 ай бұрын
@@rishikeshnawathe3063 I mean yes, it is 9. But the fact that this is being debated means the question was purposefully made tricky.
@Valerius123
7 ай бұрын
It's that people think division and fractions operators (÷ and /) are identical. When using a fraction you are splitting your expression into a numerator and denominator which groups the order of operations in a way like brackets. When only using ÷ it doesn't do this. This is where everyone is confused. So 6÷2(1+2) is all in the numerator and 6/2(1+2) has 6 in the numerator and 2(1+2) in the denominator. One of these gives the answer 9 and one of them gives the answer 1.
@grassytramtracks
3 ай бұрын
The fact that the brackets have no times sign can very easily be interpreted to mean that it's a single term because the multiplication is implicit. You wouldn't interpret 1÷2x as (1÷2)x now, would you? This is exactly why the division sign should be avoided like the plaque and if it can't be, then brackets should be used. It should be either (6÷2)(1+2) or 6÷[2(1+2)]
@davidduncan1362
4 ай бұрын
I would have to disagree upon PEMDAS being wrong. The problem we have is evaluating 6/2(1+2), which can also be written as 6÷2(1+2), 6÷2×(1+2) or 6/2×(1+2). Either way, it's still the same problem that we are arguing over. Of course, we can all agree that we take care of the parenthesis first, so 6/2(1+2) turns into 6/2(3). We basically have 6/2×3, which means we have a division and a multiplication to deal with. If both of these were multiplication, we would be evaluating from left to right. My side of the argument why we sometimes do division before multiplication is based on the fact that division is literally another form of multiplication. When you divide, you are multiplying times the reciprocal fraction of the number that is shown. 6/2 is the same as 6×(1/2). 6÷2 in fraction form is this: 6/1×1/2. When dividing in fraction form, we keep the first fraction, change the opperation to multiplication, and flip the second fraction. We can cancel out the 2 and reduce the 6 to 3, so we have 3/1×1/1, which we can simplify down to just 3, so we have third grade basic multiplication: 3×3=9, therefore, 6/2(1+2)=9. Note that the parenthesis is only grouping the 1+2 and nothing else, therefore, when we see 6/2(3), we are not multiplying 2×3 before taking care of the division. Instead, we are multiplying 6/2×3. 6/2 is a single factor in this multiplication that can be simplified as 3, therefore giving us 9 as the product. If you want to divide six by everything else to get one as the quotient, you would have to add more parenthesis or brackets to group everything together as the denominator like this: 6/[2(1+2)]. In this case, I would start with addition and work my way out like this: 6/[2(1+2)], 6/[2(3)], 6/6, which equals 1. Be careful with these problems because 6/2(1+2) does not equal 6/[2(1+2)]. We can also look at 6/2(1+2) this way: multiply 6/2×1, then 6/2×2 and add these products. Let's check to see if 6/2 can be simplified...yes, it can! 6/2=3, therefore we can multiply 3×1, which equals 3 and 3×2, which equals 6. Add these numbers up and we get 9. I actually would agree with your evaluation of juxtaposition multiplication except for this one thing: when we see 6/2(1+2), it's the fraction of 6/2 that we need to multiply, not the integer of 2 before doing division.
@allozovsky
4 ай бұрын
@davidduncan1362 > The problem we have is evaluating 6/2(1+2), which can also be written as 6÷2(1+2), 6÷2×(1+2) or 6/2×(1+2). Can it also be written as 6/xy, x=2, y=3 6/x(y), x=2, y=3 6/x(3), x=2 6/x(1+2), x=2 Should the results in all these cases be the same as with the initial 6/2(1+2) problem?
@DarellJsVlogz
Ай бұрын
Bro made a whole paragraph
@BoikiMaredi-md4im
23 күн бұрын
Nah we're just supposed to use BODMAS
@BoikiMaredi-md4im
23 күн бұрын
Nah we're just supposed to use BODMAS
@HardKn1ght
8 ай бұрын
Its 1. The multiplication sign has been removed between the 2 and the brackets the juxtaposition of the 2 to the brackets implies this is one term. 6÷(2(1+2)). If the multiplication sign was left explicitly in place. 6÷2×(1+2) then the answer is 9.
@frenchaviation
8 ай бұрын
yep, you're right
@l_poci_
7 ай бұрын
Its both. You proved it yourself. 6 ÷ (2(2+1)) is 1, while 6 ÷ 2 x (2+1) is 9. However that equation the way it is originally written is neither of those. And like he said, its written in an ambiguous way, to create this confusion. In an exam, research paper or anything with mathematical value this would have been written in a different way, one of the 2 above you specified yourself depending on the situation or example given. However, just using 6 ÷ 2(2+1) wont give you one determining answer. And more proof of that is that calculators, scientific ones at least will adjust it to either one of the 2 and then solve it. But whichever way you choose is dependent on the situation or example provided.
@MarcelliusT
6 ай бұрын
It's 9, there's a reason why we don't write 2*y we just write 2y same for the brackets 2(1+2) not 2*1+2) so it's 9
@TheRoyalGamingchannel
4 ай бұрын
P- parentheses E- exponents M- multiplication D- Division A- addition S- subtraction If you use your brain and then do the equation 6~2(2+1) First you do parentheses so 2+1=3 ok now it’s 6~2 3 And if you paid attention in school you would know that if an equation doesn’t have anything before parentheses it’s multiplication for example 6~2 3 changes to 6~2x3 6~2+3 if it has an exponent then don’t change So now this is where you go from left to right So you do 6~2=3 So now it’s 3x3=9
@carviz7199
4 ай бұрын
the operation is still multiplication so it is 9
@GanonTEK
Ай бұрын
100% It's ambiguous notation as there are two common interpretations for juxtaposition. Academically, juxtaposition implies grouping and multiplication (1). Literally/programming-wise, juxtaposition implies multiplication only (9) The division symbol doesn't matter. It's ambiguous either way with ÷ or /. ÷ and / are synonymous in most cases. Both are one line division operators. Not fraction notation. ½ and 1 -- 2 are fraction operators. Two different symbols to ÷ and /. Even over in America, the American Mathematical Society stated it was ambiguous notation and 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. Even scientific calculators don't agree on one answer. It's obvious it's ambiguous notation but there seems to be a lot of stubborn people out there wanting their opinion to be the only correct one, which won't happen as their opinion doesn't change the evidence of what's in use.
@bakonandsonicfamily2930
6 ай бұрын
Well, here in Vietnam, from Secondary education forward, we no longer have to put a times sign? “x” to refer to the equation as a multiplication. For example, (a+b)c is (a+b)xc, so my answer is 9 :)
@marafty3776
3 ай бұрын
That's universal not just in vietnam
@peterthomas5792
2 ай бұрын
@@marafty3776 It's not universal. Google "Math textbook PDF". Pick any one. Read it. Learn that PEMDAS is wrong.
@lucasbusselen9137
Жыл бұрын
There are rules you have to follow and according to the rules 2( 2+1) = 2×(2+1) and the answer to the question is 9
@AddisonKavanagh
Жыл бұрын
Exactly! I'm going to 8th grade and for some reason adults wont understand this?
@X3GoldenOfficial
11 ай бұрын
@@AddisonKavanagh This leads to the right answer BUT you're ignoring the fact that in both PEMDAS and BODMAS you have to calculate what is inside the brackets or parenthases FIRST.
@AddisonKavanagh
10 ай бұрын
@@X3GoldenOfficialyep, that's what I did. 1+2=3 and 6÷2=3, 3×3=9.
@X3GoldenOfficial
10 ай бұрын
@@AddisonKavanagh oh ok never mind then xd
@AddisonKavanagh
10 ай бұрын
@X3GoldenOfficial it's alright dude 👍
@BoikiMaredi-md4im
23 күн бұрын
Ans is 1
@GanonTEK
16 күн бұрын
It depends on which interpretation of multiplication by juxtaposition you use. Academically, juxtaposition implies grouping and multiplication (1). Literally, juxtaposition implies multiplication only (9). Both use the same order of operations after the implicit notation is interpreted.
@ogostrich
7 күн бұрын
This guy is trying to say that division comes before parenthesis lmao
@GanonTEK
3 күн бұрын
The two answers depend on which interpretation of multiplication by juxtaposition you use. Academically, juxtaposition implies grouping and multiplication (1). Literally, juxtaposition implies multiplication only (9). Both use the same order of operations after the implicit notation is interpreted.
@andrewmcmillan8039
2 ай бұрын
Wrong. This problem takes the form of a/b*c; that's why the Commutative Property works. We can flip the order of the operands and still maintain the same solution.
@JackieRodriguez-ui3gp
3 ай бұрын
Let me tell you why I know it's 9 1+2=3 then we have 23 so we do 23+23=46 now we add 6 bc it's there and that's 52 and then we add 2 bc it's there it's 54 and 54 ÷ 6 = 9 so that's how I got 9
@andrewmcmillan8039
2 ай бұрын
The problem is separated by multiplication
@Bhautiki123
Жыл бұрын
Bodmas
@c.jishnu378
8 ай бұрын
Bodmas is flawed and is absolutely useless in higher levels of mathematics.
@AmritGrewal31
Жыл бұрын
Because it doesn’t use brackets properly.
@meiter4515
5 ай бұрын
If you got 4/2x you do the 2x part first right? Then why does it have to be different with 2(1+2) Answer is 1.
@NieTykajLekarza
5 ай бұрын
Cuz 6 and 6:2(1+2) are two different --- equations 2(1+2)
@NieTykajLekarza
5 ай бұрын
So the answer is 9
@grassytramtracks
3 ай бұрын
@@NieTykajLekarza the answer is not to use lazy, ambiguous notation
@nicfedz
29 күн бұрын
6
@MANIK_COMIC
Ай бұрын
9
@andrewmcmillan8039
2 ай бұрын
It's a binary operation
@kmusic5944
Ай бұрын
Pemdas.... 9.. i dont get what so confusing..growing up. We wouldnt even give this equation a second thought...ir did they chnage math over the 3 decades
@GanonTEK
16 күн бұрын
It depends on which interpretation of multiplication by juxtaposition you use. Academically, juxtaposition implies grouping and multiplication (1). Literally, juxtaposition implies multiplication only (9). Both use the same order of operations after the implicit notation is interpreted.
@BAMBOOMBLACK
8 ай бұрын
As a calculator and is 9😂
@ItsPro824
6 ай бұрын
Download a scientific calculator get implicit multiplication on and then check your ans Correct ans is both
@pandu2129
Ай бұрын
Answer is 1 It's just simple arithmetic problem where we have to give first preference to bracket a÷b(c+d) = a÷(bc+cd) So, 6÷2(1+2) = 6÷2(3) =6÷6=1 Mathematicians always write like this
@reminderIknows
Ай бұрын
5±4
@100gnews
3 ай бұрын
It’s 27
@andrewmcmillan8039
2 ай бұрын
This problem is just like saying 2 × 3 = 6 or 3 × 2 = 6
@cyberagua
2 ай бұрын
It's rather like saying: *aᵐ/ₙ ÷ bᵘ/ᵥ = (a + ᵐ/ₙ) ÷ (b + ᵘ/ᵥ)* or *aᵐ/ₙ ÷ bᵘ/ᵥ = (a × ᵐ/ₙ) ÷ (b × ᵘ/ᵥ)*
@cyberagua
2 ай бұрын
Or maybe *aᵐ/ₙ ÷ bᵘ/ᵥ = (a + ᵐ/ₙ) ÷ (b × ᵘ/ᵥ)* 😮🥺😱😧
@imacarguy4065
7 ай бұрын
People in this comment section fail to realize that many of the rules in Math are contradictory.
@andrewmcmillan8039
2 ай бұрын
a/b * c
@ankitgokhare2620
7 ай бұрын
6÷2×3
@rusluck6620
5 ай бұрын
its not as simple as that, because the problem uses implicit multiplication. it could be interpreted as 6/(2*3)
@ankitgokhare2620
5 ай бұрын
@@rusluck6620 so 6÷×6
@rishikeshnawathe3063
4 ай бұрын
@@rusluck6620the Rules say slove the bracket first.. Then go for any cubes or squares if there are any -- then Division -- then multiplication.. So it is 6/2 x 3
@rusluck6620
4 ай бұрын
@@rishikeshnawathe3063its not rules, its a convention. another convention which i personally use involves juxtaposition. bascially its pejmdas.
@Midtan
10 ай бұрын
This is not actually suprising because people before 1917 thought the answrr would be 1
@ebiebanzhaf4971
Жыл бұрын
👍👍👍👍👍👍
@kaplada22
5 ай бұрын
🤓
@rusluck6620
5 ай бұрын
get a life instead of commenting 🤓 on anybody who has more intellect than you
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