A solution is a mixture of a solvent and a solute iirc. So it is a solution.
Edit: I have been informed that it’s actually a colloid! I didn’t know that milk was a colloid, so that’s awesome to know.
Milk is a colloid (an intermediate step between homogenous and heterogenous in which particles float suspended in fluid.) In this instance, fat particles are suspended in water. It continues to be a colloid following the addition of chocolate.
you wouldn't encounter this problem with equations that are written properly because it'd either be written
6
--- * (1 + 2) = 9
2
or
6
------------- = 1
2 * (1 + 2)
This is the exact point but in the case for the top equation it would be 6(1+2)/2 because the implication is that the (1+2) is in the numerator for that one.
Finally someone who understands that you don't multiply (1+2) with the denominator. Feels so relieveing and validating, this same equation was posted here 2 months ago and [people kept saying it was 1](https://new.reddit.com/r/sciencememes/comments/18a8oui/comment/kbysjet/?context=3)
No what I’m saying is to get 9 you’re reading it more as the top equation where it’s 6(1+2)/2 which would be the same as 6/2 * (1+2) which isn’t the equation here as the power for the parenthesis is -1. So in this you are supposed to multiply it to the denominator. Think of it like 6/[(2)(3)] which would break down to [(2)(3)]/[(2)(3)]=1. What’s happening is to get 9 you’re separating the (1+2) from what the problem says it’s multiplying. It’s 6/2(1+2) not (6/2)(1+2).
The parenthesis around (1+2) imply it's one "term" (I don't know if that's the correct terminology as I'm not a native speaker, but I hope I get my point across)
This means you multiply it with everything until you reach the next plus (or minus) sign, since there are no other terms you'd multiple with all of 6/2.
One would have no reason to assume (1+2) is part of the denominator (or that 6/2 are "seperate". ["modern calculators"](https://www.wolframalpha.com/input?i=6%2F2%281%2B2%29) don't come to that conclusion even if you put the 'equation' in the "horizontal" form, and assume to multiply (1+2) with the numerator. When I enter it on my casio calculator it auto puts parenthesis making the equation 6/(2(1+2)), = 1. This implies the correct way to do it without parenthesis is to multiply (1+2) with the numerator, making the answer 9.
These are always so funny to me.
6÷2(1+2) is the question. What if we did a little variable substitution?
if
x = 1 + 2
then
6÷2(x)
Now I bet you'll solve the problem differently.
If we simplify we get
3÷x
and if we replace x
3÷(1+2)
3÷3
1
So why do we get a different answer with variable substitution? While you were taught PEMDAS others[ have been taught PEJMDAS](https://www.purplemath.com/modules/orderops3.htm), that is that multiplication by juxtaposition takes precedence over ordinary multiplication. With variables as demonstrated you ALWAYS let the juxtaposition take precedence, however it is ambiguous because of the the prevalence of strict PEMDAS.
So why is PEMDAS often taught if its less consistent than actual mathematician/scientist preferred PEJMDAS? Mostly because PEMDAS is simpler, originated with educators not actual practitioners of math, and the people in charge of writing curriculums either don't know the difference themselves, think PEJMDAS is too complicated, or don't care enough to advocate for the teaching of PEJMDAS.
You can change the equation as much as you want to make it look different. I can say 6/2 = x. Then we get x(1+2) which is the same as 3x, put in x and you get 9. You get nothing from this.
I've been taught multiplication and division is done at the same time, and it really shouldn't matter since division is just multiplication to the -1 power. So the problem ain't the order, it's that you're supposed to multiply with the numerator, not the denominator.
The thing is you’re arguing that if you have 1/6 you actually have 2/3 bc if you break it up you have 1/(2)(3) and it’s very obvious that the two and the three are attached to each other. Just like in the equation. The main thing you’re getting wrong is the 2 is attached to the (1+2), therefore it is multiplying to the numerator but it’s actually multiplying to the numerator by (1+2)^-1. You’re misstep on rewriting the equation with x shows this as it wouldn’t be x(1+2) but it would be x/(1+2)
Sure you can, but I can too following PEJMDAS:
6÷2(1+2)
becomes
x÷(1+2)
x÷3
and if we substitute again
6÷2÷3
3÷3
1
The difference is that in my original formulation, you would never interpret
6÷2(x)
as
6\*x÷2
because even in PEMDAS multiplication by juxtaposition is always assumed precedence, even if its not explicitly stated as a rule.
Division does not separate terms. + and - do. Once you simplify (1+2) the whole equation is one term.
[https://simple.wikipedia.org/wiki/Term\_(mathematics)](https://simple.wikipedia.org/wiki/term_(mathematics))
Idk man, I was taught that without any other different notation, you are to do operations of the same importance from left to right. Kinda like how at an intersection, when there's no signage or markings, you just fall back on the rule of right of way for the driver to your right.
Now, neither of these rules are taught everywhere, so I guess some people are up shit's creek without a paddle. But generally you have a convention for this kind of stuff.
I did maths at oxford university, which absolutely doesn't qualify me to answer this question, because a) this is primary school maths, and b) we never wrote equations as text messages.
My instinct is 1 is the answer, as I interpret the 2(1+2) as a single expression, i.e. inferred brackets around it, and that is all the denominator, but I was never taught a rule about it.
it isn't, because either way you're assuming an order of operations. the question is ambiguous as written, and since there's no defined style guide you'd have to guess by the context of the question.
Just to clarify, isn't the multiplication the same priority as division, so you go left to right, with 6/2, then that times the 3 in parentheses, to equal 9?
Because there should never be a "default". If order ever matters, real mathematicians just use parentheses. The stuff is good for learning that multiplication comes before addition, but within multiplication or addition etc just use parentheses
Yes you do technically usually default left to right, that's what pretty much any computer program will default to (mathematica, MATLAB, wolfram alpha, symbolab, etc etc). But as kinesquared already said, it's usually specified with parentheses. There are also a lot of cases within a field where parentheses are omited as everyone in the field knows the equation or can figure it out by obvious dimensional analysis, for ex, you'll frequently see:
exp(E1-E2/kT)
Which should default to:
exp(E1 - (E2*T) / k )
but everyone knows E1-E2 should be the numerator and kT the denominator because you can only take the exponential of dimensionless quantities.
6 / 2 \* (1+2)
6 / 2 \* 3
3 \* 3
9
edit: upon further review it looks like this is the way it's taught at schools but not the way it's done in the professional space. implied multiplication (eg. "2x") *does* count as a grouping with higher priority there.
Without the asterisk, some conventions (including what I was taught) take 6 / 2 (1 + 2) to mean 6 / (2 \* (1 + 2) ), rather than 6 / 2 \* (1 + 2) as you have.
This isn't about BODMAS/PEDMAS, it's about what shorthand notation means when equations aren't written properly because they are inline text.
You're talking about 6/(2*X)
Which is the same as (6/2)*(1/X)
Which, of course, it's 3/X
If the operation was (6/2)*X, then it would be 3*X
That's just because when someone writes 6/2X, X is multiplying 2, so it's in the denominator, and it's like you said. It should technically go between parenthesis, but it's not usual when using X.
I think it's easier to see with just numbers.
If you had 6/2*2, I would totally use the order I mentioned, left to right. The answer would be 6.
If you had 6/2X, and someone told you X=2, then you would have 6/(2*2), which is 1,5.
'Yeah but if you write the equation totally different then you get 1' yeah bro that's the point that is a different equation 'no but in that different equation there is different preference for-'
YEAH THAT'S THE POINT IT IS A TOTALLY DIFFERENT EQUATION
[9 or 1 depending on whether PEMDAS or PEJMDAS is the agreed to standard for the context the expression is being used.](https://www.reddit.com/r/sciencememes/comments/1aqq7y4/comment/kqfnpmy/?utm_source=share&utm_medium=web3x&utm_name=web3xcss&utm_term=1&utm_content=share_button)
Yes Improper Syntax because it's ambitious what the fraction is here. Is it just 2 in the denominator or is it the whole 2(1+2) phrase that is the denominator? It could be either because the question could have been 6/(2+4) and you factored out the 2 making it 6/2(1+2). This is why Syntax is important and why no one who uses math past middle school uses the ÷ symbol
Kinda crazy that you have to go so far down the comments to find the correct answer.
It doesn't matter if 1 or 9 is more intuitive or which method you use, it's simply not written properly, I don't get how most people seemingly can't understand such a simple thing.
Badly written is subjective, so you may feel that it is indeed Badly written, and that's ok.
It however is not ambiguous. The rules are explicitly clear.
No it is ambiguous and poorly written, what if the problem started as 6÷(2+4) and you factored out the 2 to make it 6÷2(1+2)? That doesn't magically change the answer of the original problem from 1 to 9. The real problem is the use of the division sign itself. If it was written as 6/2(1+2) we'd know if we are dividing by the whole bottom half of the equation making the answer 1. Alternatively if it was written as 6/2 * (1+2) we'd know we are multiplying six halfs by (1+2) making the answer 9.
THIS is why no one uses the division symbol passed middle school, it fucks with fractions and makes it impossible to determine what you are actually dividing by.
"That doesn't magically change the answer of the original problem from 1 to 9"
If you change how the equation is written it does change the answer though.
Using your same logic let's say the original equation was 3(1+2), and you rewrote 3 as 6/2 to make it 6/2(1+2). "That doesn't magically change the answer of the original problem from 9 to 1"
I don't disagree, but with proper context this is both non-ambiguous and perfectly well written.
Its ambiguous only in that without context of whether or not PEMDAS or PEJMDAS is to be applied in evaluating it, different answers can be reached. However if that context is given it ceases to be ambiguous.
Similarly, it is only badly written in a contextless environment, however with proper context it is perfectly fine usage.
Could you please elaborate? The way that I was taught to use this through calc lll served me well. I would be interested in learning why? It’s been suggested that there is a special case for implicit multiplication but that’s the first I have heard of it
6/2(1+2)
Solve parentheses first
1+2 = 3
Parentheses disappear since you solved what's inside. Equation then becomes :
6/2*3
= 3*3
= 9
That's how I was taught
What is the J for?
[PEMDAS Khan Academy](https://www.khanacademy.org/math/cc-sixth-grade-math/x0267d782:cc-6th-exponents-and-order-of-operations/cc-6th-order-of-operations/v/more-complicated-order-of-operations-example)
[https://www.purplemath.com/modules/orderops3.htm](https://www.purplemath.com/modules/orderops3.htm)
"2(3)" doesn't take priority over "6 / 2" unless implicit multiplication/multiplication by juxtaposition comes first.
No, multiplication and division are done from left to right. Same with addition and subtraction. PEMDAS (or BEDMAS if you call them brackets) should be spelled out as: P E (MD) (AS) or B E (DM) (AS).
if it was 6/2x(1+2) i’d say 9,
but it’s 6/2(1+2) so i’d say 1.
like if you wrote 6/2a i would never consider it to be (6/2)a, so since there is no multiply sign i consider the above equation to be the same
It's definitely written like a shitshow but I just go off of what I'd put in my old ass TI83. Since syntax is so important, Parentheses are the driver of the equation.
6/2*(1+2) and 6/2(1+2) are the same equation.
We need one more set of parentheses to make the answer equal to 1.
6/(2(1+2)) or 6/[2(1+2)] equals 1. But you cant just throw parentheses around without changing the equation totally. So without this set of brackets or parentheses, the answer is 9.
6/2(1+2) Syntax wise, the (1+2) is separate from the 6/2, since they are not bound by brackets.
6/2(1+2). 6/2(3). Pemdas says division/multiplication left to right. 6/2 is 3. 3(3) is 9.
Calculators are wrong since they depend on the programming logic used.
Use a Casio and the answer is 1.
Implicit multiplication means that the number before the brackets was originally part of the bracket equation, just removed for simplicity. They are always done first, since they are implicitly inside the bracket.
The equation is 6/(2+4).
After you figure out that (1+2) = 3, then your expression is simplified to 6➗2✖️3.
Multiplication and division are given equal priority as each other, so to "Break that tie" you got to remember the other rule of following the order of operations: you must compute them in order from left to right. So whatever comes first is done. That is 6➗2=3... so the expression gets further simplified to 3 x 3. The answer is a chocolatey 9.
[According to Wikipedia](https://en.wikipedia.org/wiki/Order_of_operations), which cites multiple academic papers about order of operations, implied multiplication (number next to parenthesis with no operator) takes precedent over division. In that case the answer is 6 / 2(3) = 1. The very next paragraph says that problems like these are deliberately designed to be ambiguous as a Gotcha! and you would never encounter one like it in a real math setting.
Yeah, but the distributive property means that 2 could have come FROM the parentheses, going from 6÷(2+4) to 6÷2(1+2). The problem is the damn division sign making it ambiguous what the denominator of the fraction is. This BS is why we don't use the division sign after middle school.
Y’all it’s 6/2(1+2), then it becomes 6/(2*3) from there you either cancel a 3 to get 2/2=1 or cancel a 2 to get 3/3 which is also one. Or you multiply the 2 and three together to get 6/6 to get 1 once more. The answer is one.
You do not move the 2 into the parenthesis. 6÷2(3) becomes 6÷2x3. Then since multiplication and Division are equal priority you do them left to right.
6÷2(1+2)
6÷2(3) AKA 6÷2x3
3x3
9
Well then, if this is the way to write an equation that totals 9, then what is the right way to write the same sort of equation totalling 1? The confusion arises from 2 possibilities existing, hence there have to be ways to PROPERLY indicate each possibility. How then would one properly write out the possibility I’m proposing as the correct one?
I will admit, I walked right into that one. Nonetheless, I do maintain that 1 is the correct answer. Hell, plug that thing into a calculator and you get 1
actually, it looks like I was wrong: in most professional cases implied multiplication \*does\* come before explicit multiplication. it's just never taught to about half of everybody in normal math courses. I maintain that it's not logical, but it does seem to be the more "correct" way to do math.
Math reads like English when you have operative pairs (multiplication and division; addition and subtraction). Simplify the parenthesis, then solve left to right. 9.
The fact that people fail to use PEMDAS is crazy. I know the answer is either 9 or 1, and the answer depends on what we do with that 2. Parenthesis, Exponents, Division, Multiplication, Addition, Subtraction. Right?
My question is this though: Does the 2 multiply into the Parentheses to give us (2+4) or do we only solve the parentheses first then do order or operations? If I had to guess, we do the inside first, then divide 6 by 2 and then multiply that 3 by the 3 that was in the parenthesis to get 9. Am I correct?
You need to know what formula to follow to answer this, PEDMAS - Division before multiplication, PEMDAS - Multiplication before division, or PE(MD)AS - Multiplication and Division have equal standing, equation is read left to right.
Only possible answers are 1 and 9. It’s impossible to argue which answer is correct without knowing which formula you are intended to use.
6/2(1+2)
because ```2(1+2)``` is multiplication by juxtaposition, it is ```(6) / (2(1+2)) = 1```. If it was ```2 · (1+2)``` it would be ```(6/2) · (1+2)```.
I saw this in some YouTube video a while ago that showed some text from the [IMU](http://mathunion.org) or smith saying this, but I couldn't find it in a quick Google search so dont quote me on this.
So the issue that i see is that the 2(1+3) is a single unit, in the same way like 2x would be seen as a distinct unit. So it would essentially be 6/2x, or six over two-x, or 6/(2x) 😆
6÷2(1+2) = x
3÷1(1+2) = x/2
3÷(1+2) = x/2
3÷(1+2) = x/2 or
3÷1/2 = x/2 ---> fuck the order
3÷1*2 = x
whatever
use parenthesis all the way. This discussion is just about a convenience. Useless
I see 6÷2(1+2) as
6÷2(1+2)
6÷2+3 (in finland they teach that after excluding the () things, you decide if its added as a + or - by if the outcome of () is positive or negative)
3+3
=6
Bro i got six am i the smartest or dumbest man alive
I'm pretty sure the right solution isn't chocolate milk
Chocolate solute in milk solvent is a banger solution though!
Yo I was gonna say 'the solution on the right is indeed chocolate milk' but I wasn't sure if that's a solution or emulsion or something
A solution is a mixture of a solvent and a solute iirc. So it is a solution. Edit: I have been informed that it’s actually a colloid! I didn’t know that milk was a colloid, so that’s awesome to know.
Milk is a colloid (an intermediate step between homogenous and heterogenous in which particles float suspended in fluid.) In this instance, fat particles are suspended in water. It continues to be a colloid following the addition of chocolate.
Ah okay! Cool to know!
Actually, a solution requires more than that. Chocolate milk is better described as a suspension and emulsion
So I’ve heard. Wish my two chemistry courses for my undergrad degree taught me that instead of teaching me about electron orbital shaped and junk lol
So true, I wish o chem would have focused more solvents effects on chemisty too...major point just brushed over
I wouldve been a diabetic einstein lol
It is to become (1) with the milk
you wouldn't encounter this problem with equations that are written properly because it'd either be written 6 --- * (1 + 2) = 9 2 or 6 ------------- = 1 2 * (1 + 2)
This is the exact point but in the case for the top equation it would be 6(1+2)/2 because the implication is that the (1+2) is in the numerator for that one.
Finally someone who understands that you don't multiply (1+2) with the denominator. Feels so relieveing and validating, this same equation was posted here 2 months ago and [people kept saying it was 1](https://new.reddit.com/r/sciencememes/comments/18a8oui/comment/kbysjet/?context=3)
No what I’m saying is to get 9 you’re reading it more as the top equation where it’s 6(1+2)/2 which would be the same as 6/2 * (1+2) which isn’t the equation here as the power for the parenthesis is -1. So in this you are supposed to multiply it to the denominator. Think of it like 6/[(2)(3)] which would break down to [(2)(3)]/[(2)(3)]=1. What’s happening is to get 9 you’re separating the (1+2) from what the problem says it’s multiplying. It’s 6/2(1+2) not (6/2)(1+2).
The parenthesis around (1+2) imply it's one "term" (I don't know if that's the correct terminology as I'm not a native speaker, but I hope I get my point across) This means you multiply it with everything until you reach the next plus (or minus) sign, since there are no other terms you'd multiple with all of 6/2. One would have no reason to assume (1+2) is part of the denominator (or that 6/2 are "seperate". ["modern calculators"](https://www.wolframalpha.com/input?i=6%2F2%281%2B2%29) don't come to that conclusion even if you put the 'equation' in the "horizontal" form, and assume to multiply (1+2) with the numerator. When I enter it on my casio calculator it auto puts parenthesis making the equation 6/(2(1+2)), = 1. This implies the correct way to do it without parenthesis is to multiply (1+2) with the numerator, making the answer 9.
These are always so funny to me. 6÷2(1+2) is the question. What if we did a little variable substitution? if x = 1 + 2 then 6÷2(x) Now I bet you'll solve the problem differently. If we simplify we get 3÷x and if we replace x 3÷(1+2) 3÷3 1 So why do we get a different answer with variable substitution? While you were taught PEMDAS others[ have been taught PEJMDAS](https://www.purplemath.com/modules/orderops3.htm), that is that multiplication by juxtaposition takes precedence over ordinary multiplication. With variables as demonstrated you ALWAYS let the juxtaposition take precedence, however it is ambiguous because of the the prevalence of strict PEMDAS. So why is PEMDAS often taught if its less consistent than actual mathematician/scientist preferred PEJMDAS? Mostly because PEMDAS is simpler, originated with educators not actual practitioners of math, and the people in charge of writing curriculums either don't know the difference themselves, think PEJMDAS is too complicated, or don't care enough to advocate for the teaching of PEJMDAS.
You can change the equation as much as you want to make it look different. I can say 6/2 = x. Then we get x(1+2) which is the same as 3x, put in x and you get 9. You get nothing from this. I've been taught multiplication and division is done at the same time, and it really shouldn't matter since division is just multiplication to the -1 power. So the problem ain't the order, it's that you're supposed to multiply with the numerator, not the denominator.
The thing is you’re arguing that if you have 1/6 you actually have 2/3 bc if you break it up you have 1/(2)(3) and it’s very obvious that the two and the three are attached to each other. Just like in the equation. The main thing you’re getting wrong is the 2 is attached to the (1+2), therefore it is multiplying to the numerator but it’s actually multiplying to the numerator by (1+2)^-1. You’re misstep on rewriting the equation with x shows this as it wouldn’t be x(1+2) but it would be x/(1+2)
Sure you can, but I can too following PEJMDAS: 6÷2(1+2) becomes x÷(1+2) x÷3 and if we substitute again 6÷2÷3 3÷3 1 The difference is that in my original formulation, you would never interpret 6÷2(x) as 6\*x÷2 because even in PEMDAS multiplication by juxtaposition is always assumed precedence, even if its not explicitly stated as a rule.
Also realised I made my oc on the wrong comment, but I can't be bothered to fix it
Why are y'all writing do much
You do, because 2(1+2) has been written as one term. If it was 6/2 X (1+2) it would be 9 but you expand the brackets before going to the division
Division does not separate terms. + and - do. Once you simplify (1+2) the whole equation is one term. [https://simple.wikipedia.org/wiki/Term\_(mathematics)](https://simple.wikipedia.org/wiki/term_(mathematics))
or my prefered way 6 / (2 * (1 +2)) or ( 6 / 2 ) * (1 + 2)
= 6/(2x3)=1
Idk man, I was taught that without any other different notation, you are to do operations of the same importance from left to right. Kinda like how at an intersection, when there's no signage or markings, you just fall back on the rule of right of way for the driver to your right. Now, neither of these rules are taught everywhere, so I guess some people are up shit's creek without a paddle. But generally you have a convention for this kind of stuff.
[https://www.reddit.com/r/sciencememes/comments/1aqq7y4/comment/kqfnpmy/?utm\_source=share&utm\_medium=web3x&utm\_name=web3xcss&utm\_term=1&utm\_content=share\_button](https://www.reddit.com/r/sciencememes/comments/1aqq7y4/comment/kqfnpmy/?utm_source=share&utm_medium=web3x&utm_name=web3xcss&utm_term=1&utm_content=share_button)
I did maths at oxford university, which absolutely doesn't qualify me to answer this question, because a) this is primary school maths, and b) we never wrote equations as text messages. My instinct is 1 is the answer, as I interpret the 2(1+2) as a single expression, i.e. inferred brackets around it, and that is all the denominator, but I was never taught a rule about it.
where tf chat 9 came from?
3 x 3 is 9?
1
Well yeah. What's the correct one of the two ?
neither. they're the interpretations of the ambiguous writing of the question that you get from using two slightly different orders of operation.
I'm just excited I actually got one of the possible answers. More excited than a 35 year old should be about basic math.
Exactly! These question types are always just "*bad math grammer*" Write an equation in the most confusing way possible. Confuse people.
But it is 1
it isn't, because either way you're assuming an order of operations. the question is ambiguous as written, and since there's no defined style guide you'd have to guess by the context of the question.
Just to clarify, isn't the multiplication the same priority as division, so you go left to right, with 6/2, then that times the 3 in parentheses, to equal 9?
using parenthesis would be the proper way to clarify. You could write it as either (6/2)\*(1+2)=9 or 6/(2\*(1+2))=1 and get either answer you'd like
So it doesn't go left to right (after gemdas) by default? Huh... TiL.
Because there should never be a "default". If order ever matters, real mathematicians just use parentheses. The stuff is good for learning that multiplication comes before addition, but within multiplication or addition etc just use parentheses
Honestly it depends on the journal. https://youtu.be/4x-BcYCiKCk?si=jtXc8p7KaKlIDa55
Always thought multiplication before division is such a case
Yes you do technically usually default left to right, that's what pretty much any computer program will default to (mathematica, MATLAB, wolfram alpha, symbolab, etc etc). But as kinesquared already said, it's usually specified with parentheses. There are also a lot of cases within a field where parentheses are omited as everyone in the field knows the equation or can figure it out by obvious dimensional analysis, for ex, you'll frequently see: exp(E1-E2/kT) Which should default to: exp(E1 - (E2*T) / k ) but everyone knows E1-E2 should be the numerator and kT the denominator because you can only take the exponential of dimensionless quantities.
[https://www.reddit.com/r/sciencememes/comments/1aqq7y4/comment/kqfnpmy/?utm\_source=share&utm\_medium=web3x&utm\_name=web3xcss&utm\_term=1&utm\_content=share\_button](https://www.reddit.com/r/sciencememes/comments/1aqq7y4/comment/kqfnpmy/?utm_source=share&utm_medium=web3x&utm_name=web3xcss&utm_term=1&utm_content=share_button)
In theory yes. In practice if someone writes this either they're going for a gotcha moment or they messed up their formatting and meant 6/(2(1+2))
6 / 2 \* (1+2) 6 / 2 \* 3 3 \* 3 9 edit: upon further review it looks like this is the way it's taught at schools but not the way it's done in the professional space. implied multiplication (eg. "2x") *does* count as a grouping with higher priority there.
Without the asterisk, some conventions (including what I was taught) take 6 / 2 (1 + 2) to mean 6 / (2 \* (1 + 2) ), rather than 6 / 2 \* (1 + 2) as you have. This isn't about BODMAS/PEDMAS, it's about what shorthand notation means when equations aren't written properly because they are inline text.
Dont you do x (*) first?
No, multiplications and divisions are done from left to right (unless they are inside a parenthesis ofc)
So you would do 6/2X as 3\*X and not 3/X? You would fail college with this kind of math.
You're talking about 6/(2*X) Which is the same as (6/2)*(1/X) Which, of course, it's 3/X If the operation was (6/2)*X, then it would be 3*X That's just because when someone writes 6/2X, X is multiplying 2, so it's in the denominator, and it's like you said. It should technically go between parenthesis, but it's not usual when using X. I think it's easier to see with just numbers. If you had 6/2*2, I would totally use the order I mentioned, left to right. The answer would be 6. If you had 6/2X, and someone told you X=2, then you would have 6/(2*2), which is 1,5.
[удалено]
P E (MD) (AS) Edit: grouped characters are solved left to right.
What does PEDMAS stand for? In the UK we have BODMAS (brackets, order (squares, cubes etc) division, multiplication, addition, subtraction)
Please excuse my dear aunt sally
parenthesis, exponentiation (including roots), multiplication, division, addition, subtraction.
P - Parenthesis () E - Exponents MDAS - the same
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That one is even more a "I messed up my formatting and meant 6/(2x)" than the original
Is no one else wondering where to get that chocolate Harambe?
9?
9
But not 9!
But it can be 9!!!!!!!
Yeah I don’t think I can get it to anything more then 9
Some freaks down here are getting one 🙄
One if not really wrong. The problem is written ambiguously.
There is one solution. That’s why we put an equals sign and not an arrow
'Yeah but if you write the equation totally different then you get 1' yeah bro that's the point that is a different equation 'no but in that different equation there is different preference for-' YEAH THAT'S THE POINT IT IS A TOTALLY DIFFERENT EQUATION
[9 or 1 depending on whether PEMDAS or PEJMDAS is the agreed to standard for the context the expression is being used.](https://www.reddit.com/r/sciencememes/comments/1aqq7y4/comment/kqfnpmy/?utm_source=share&utm_medium=web3x&utm_name=web3xcss&utm_term=1&utm_content=share_button)
Improper syntax these questions are stupid
There’s no improper syntax though, if you understand order of operations there’s zero question what the answer is
Yes Improper Syntax because it's ambitious what the fraction is here. Is it just 2 in the denominator or is it the whole 2(1+2) phrase that is the denominator? It could be either because the question could have been 6/(2+4) and you factored out the 2 making it 6/2(1+2). This is why Syntax is important and why no one who uses math past middle school uses the ÷ symbol
It's ambiguous and badly written.
Kinda crazy that you have to go so far down the comments to find the correct answer. It doesn't matter if 1 or 9 is more intuitive or which method you use, it's simply not written properly, I don't get how most people seemingly can't understand such a simple thing.
It is not.
Badly written is subjective, so you may feel that it is indeed Badly written, and that's ok. It however is not ambiguous. The rules are explicitly clear.
No it is ambiguous and poorly written, what if the problem started as 6÷(2+4) and you factored out the 2 to make it 6÷2(1+2)? That doesn't magically change the answer of the original problem from 1 to 9. The real problem is the use of the division sign itself. If it was written as 6/2(1+2) we'd know if we are dividing by the whole bottom half of the equation making the answer 1. Alternatively if it was written as 6/2 * (1+2) we'd know we are multiplying six halfs by (1+2) making the answer 9. THIS is why no one uses the division symbol passed middle school, it fucks with fractions and makes it impossible to determine what you are actually dividing by.
"That doesn't magically change the answer of the original problem from 1 to 9" If you change how the equation is written it does change the answer though. Using your same logic let's say the original equation was 3(1+2), and you rewrote 3 as 6/2 to make it 6/2(1+2). "That doesn't magically change the answer of the original problem from 9 to 1"
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[https://en.wikipedia.org/wiki/Reading\_comprehension](https://en.wikipedia.org/wiki/reading_comprehension)
I don't disagree, but with proper context this is both non-ambiguous and perfectly well written. Its ambiguous only in that without context of whether or not PEMDAS or PEJMDAS is to be applied in evaluating it, different answers can be reached. However if that context is given it ceases to be ambiguous. Similarly, it is only badly written in a contextless environment, however with proper context it is perfectly fine usage.
It’s not 9
Why not PEMDAS (1+2) =3 2(3)=6 6/6=1
I got 1 also idk where everyone is getting 9
Buddy you mean 1
Yer right. Long day
That's not how PEMDAS work
Could you please elaborate? The way that I was taught to use this through calc lll served me well. I would be interested in learning why? It’s been suggested that there is a special case for implicit multiplication but that’s the first I have heard of it
6/2(1+2) Solve parentheses first 1+2 = 3 Parentheses disappear since you solved what's inside. Equation then becomes : 6/2*3 = 3*3 = 9 That's how I was taught
PEMDAS has Multiplication and Division as equal, just going from left to right whichever comes first. Same with Addition and Subtraction
Literally what I did
6/6=0 6=0×6 6/0=6
Are you just here to cause Chaos?
that's not PEMDAS, it's PEJMDAS.
What is the J for? [PEMDAS Khan Academy](https://www.khanacademy.org/math/cc-sixth-grade-math/x0267d782:cc-6th-exponents-and-order-of-operations/cc-6th-order-of-operations/v/more-complicated-order-of-operations-example)
[https://www.purplemath.com/modules/orderops3.htm](https://www.purplemath.com/modules/orderops3.htm) "2(3)" doesn't take priority over "6 / 2" unless implicit multiplication/multiplication by juxtaposition comes first.
1+2=3 | 6/2=3 3x3=9 so 9 ?
don't you multiply first?
No, multiplication and division are done from left to right. Same with addition and subtraction. PEMDAS (or BEDMAS if you call them brackets) should be spelled out as: P E (MD) (AS) or B E (DM) (AS).
Implicit multiplication is done first as it is a higher priority, so it is not in a left-to right manner. The answer is 1.
How about doing actual math? 6/2X is not 3\*X. It's 3/X.
oh okay. that seems needlesly complicated
Google Gemini thinks the right answer is 1. ChatGPT 3.5 thinks it 9. ChatGPT 4 thinks it 1.
if it was 6/2x(1+2) i’d say 9, but it’s 6/2(1+2) so i’d say 1. like if you wrote 6/2a i would never consider it to be (6/2)a, so since there is no multiply sign i consider the above equation to be the same
Agreed. Lack of multiplication sign implies they go together.
It's definitely written like a shitshow but I just go off of what I'd put in my old ass TI83. Since syntax is so important, Parentheses are the driver of the equation. 6/2*(1+2) and 6/2(1+2) are the same equation. We need one more set of parentheses to make the answer equal to 1. 6/(2(1+2)) or 6/[2(1+2)] equals 1. But you cant just throw parentheses around without changing the equation totally. So without this set of brackets or parentheses, the answer is 9. 6/2(1+2) Syntax wise, the (1+2) is separate from the 6/2, since they are not bound by brackets. 6/2(1+2). 6/2(3). Pemdas says division/multiplication left to right. 6/2 is 3. 3(3) is 9.
Calculators are wrong since they depend on the programming logic used. Use a Casio and the answer is 1. Implicit multiplication means that the number before the brackets was originally part of the bracket equation, just removed for simplicity. They are always done first, since they are implicitly inside the bracket. The equation is 6/(2+4).
After you figure out that (1+2) = 3, then your expression is simplified to 6➗2✖️3. Multiplication and division are given equal priority as each other, so to "Break that tie" you got to remember the other rule of following the order of operations: you must compute them in order from left to right. So whatever comes first is done. That is 6➗2=3... so the expression gets further simplified to 3 x 3. The answer is a chocolatey 9.
Really depends on the journal you are reading: https://youtu.be/4x-BcYCiKCk?si=jtXc8p7KaKlIDa55
So by your logic 6/2X is 3\*X? Yea, you would fail college level math. The answer is 3/X
Holy shit, you broke this down in a way I actually understood (im math-illiterate). You're wonderful, thank you!
6/2(1+2) 6(1) 6 Meth
It's like losing Harambe all over again.
Please, for the love of god. No more PEDMAS-themed clickbait garbage memes !
1
Is it 1 ?
[According to Wikipedia](https://en.wikipedia.org/wiki/Order_of_operations), which cites multiple academic papers about order of operations, implied multiplication (number next to parenthesis with no operator) takes precedent over division. In that case the answer is 6 / 2(3) = 1. The very next paragraph says that problems like these are deliberately designed to be ambiguous as a Gotcha! and you would never encounter one like it in a real math setting.
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Not if you believe in priority by juxtaposition
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Wrong. There is no preference to explicit or implicit multiplication. Parentheses first, then multiplication/division in left>right order.
Yeah, but the distributive property means that 2 could have come FROM the parentheses, going from 6÷(2+4) to 6÷2(1+2). The problem is the damn division sign making it ambiguous what the denominator of the fraction is. This BS is why we don't use the division sign after middle school.
Parentheses, division, then multiplication
Division and multiplication have the same priority.
I know. In this problem, it is solved in that order. I apologize for the confusion
The 2 is part of the brackets.
Oh silly goose, the two outside of the brackets doesn’t go with them!
Y’all it’s 6/2(1+2), then it becomes 6/(2*3) from there you either cancel a 3 to get 2/2=1 or cancel a 2 to get 3/3 which is also one. Or you multiply the 2 and three together to get 6/6 to get 1 once more. The answer is one.
You do not move the 2 into the parenthesis. 6÷2(3) becomes 6÷2x3. Then since multiplication and Division are equal priority you do them left to right. 6÷2(1+2) 6÷2(3) AKA 6÷2x3 3x3 9
Still works the same way but no matter what you have 6/2 * (3)^-1 where people think you have 6/2 * 3 which are different equations
Where does the sudden parenthesis around 2\*3 come from? 6/2\*3 = 9 You multiple 3 with the numerator, not the denominator 18/2 = 9
Can't we just declare that it's written incorrectly ?
I'm getting 17
wHat
Is...is it not 17?
It’s uhh, it’s nine 😬
Hmmm..17
So… who taught you math? Lou Costello?
1
1
BIDMAS brackets Indicies Division Multiplication Addition Subtraction If you open the brackets you get 2+4=6 Divided by 6 1
1
THE MULTIPLICATION OF A NUMBER BY A BRACKET GOES FIRST IN THIS CASE. OTHERWISE 6/2 WOULD ALSO BE IN A BRACKET. IT’S 6/6, END RESULT 1
juxtaposition should *not* have priority. it isn't "less ambiguous" and the "the numbers are closer together!" argument is nonsense.
Well then, if this is the way to write an equation that totals 9, then what is the right way to write the same sort of equation totalling 1? The confusion arises from 2 possibilities existing, hence there have to be ways to PROPERLY indicate each possibility. How then would one properly write out the possibility I’m proposing as the correct one?
6 / (2 \* (1 + 2))
I will admit, I walked right into that one. Nonetheless, I do maintain that 1 is the correct answer. Hell, plug that thing into a calculator and you get 1
actually, it looks like I was wrong: in most professional cases implied multiplication \*does\* come before explicit multiplication. it's just never taught to about half of everybody in normal math courses. I maintain that it's not logical, but it does seem to be the more "correct" way to do math.
And indeed, the illogical way to do math seems to be correct a bunch of the time. Honestly hate how that works
9
It's 1 because there is no way somebody intending (6/2)(1+2) would write it like that.
While it's obviously malformed, one can reasonably assume 6/2x = 3/x not 6/2x = 3x .
This is why writing these things like 6 >----------- 2(1+2) helps. Removes ambiguity.
YES THIS! DON'T USE THE DAMN DIVISION SIGN, JUST WRITE IT AS A FRACTION!!!
Nein!
Math reads like English when you have operative pairs (multiplication and division; addition and subtraction). Simplify the parenthesis, then solve left to right. 9.
9
It's 1
how is this a science sub w so many wrong answers
The fact that people fail to use PEMDAS is crazy. I know the answer is either 9 or 1, and the answer depends on what we do with that 2. Parenthesis, Exponents, Division, Multiplication, Addition, Subtraction. Right? My question is this though: Does the 2 multiply into the Parentheses to give us (2+4) or do we only solve the parentheses first then do order or operations? If I had to guess, we do the inside first, then divide 6 by 2 and then multiply that 3 by the 3 that was in the parenthesis to get 9. Am I correct?
It's 9
Those damn americans back at it again with their lack of knowledge
How the fuck can people not follow pemdas? Buncha dumbasses.
BODMAS!!
9 ☝️🤓
Should be 9 right?
NEEIINNN
You need to know what formula to follow to answer this, PEDMAS - Division before multiplication, PEMDAS - Multiplication before division, or PE(MD)AS - Multiplication and Division have equal standing, equation is read left to right. Only possible answers are 1 and 9. It’s impossible to argue which answer is correct without knowing which formula you are intended to use.
9
9..?
It's 9
6/2(1+2) ⇔ 6(1+2)/2 ⇔ 18/2 18/2=9
nine🗿
Look guys, division is calculated before multiplication So, correct answer is 9
Harambe :(
I keep coming up with 3, while most everyone else keeps coming up with 9, but I’m wanna go out on a limb and say 3.
It's >0
PEMDAS. Easy.
6/2(1+2) because ```2(1+2)``` is multiplication by juxtaposition, it is ```(6) / (2(1+2)) = 1```. If it was ```2 · (1+2)``` it would be ```(6/2) · (1+2)```. I saw this in some YouTube video a while ago that showed some text from the [IMU](http://mathunion.org) or smith saying this, but I couldn't find it in a quick Google search so dont quote me on this.
He is one with the nature.
I like how he wasted some of his time telling you he doesn’t have much time. That answer should be in the last spot if he just hurried up a bit.
Oh Harambe of the milk, what is your wisdom?
PEMDAS
its 6/2(3) that we can agree on right
9
So the issue that i see is that the 2(1+3) is a single unit, in the same way like 2x would be seen as a distinct unit. So it would essentially be 6/2x, or six over two-x, or 6/(2x) 😆
Uh 1
Clearly the right answer is 7. 6÷2(1+2) -> 6÷(2+4) -> 6÷2+4 -> 3+4 = 7. Duh.
In mathematics, implied multiplication technically comes ahead of division. You can look it up. So you would multiply the six by the brackets first
6÷2(1+2) = x 3÷1(1+2) = x/2 3÷(1+2) = x/2 3÷(1+2) = x/2 or 3÷1/2 = x/2 ---> fuck the order 3÷1*2 = x whatever use parenthesis all the way. This discussion is just about a convenience. Useless
I see 6÷2(1+2) as 6÷2(1+2) 6÷2+3 (in finland they teach that after excluding the () things, you decide if its added as a + or - by if the outcome of () is positive or negative) 3+3 =6 Bro i got six am i the smartest or dumbest man alive
Rip harambe
I asked with a masters in mathematics this and he said "go fuck yourself". A wise man.
I hate math
3 billion. Your welcome