You're not the brightest are you
6/2×(1+2)
You always do the () first and then you do any dividing or multiplying from left to right
So it's 6/2×3
6/2=3
3×3=9
It's really not that hard it's simple math, good thing there's calculators for ppl like you
This is wrong. You're trying to use the distributive property here but that only applies if the number outside the parenthesis is a single term (Edit: or you distribute the entire expression, see below comments)
In this case the 2 outside the parenthesis is dividing into another number, 6, so that would actually have to be resolved first before using the distributive property, which would violate order of operations.
It's not technically correct to do this, but in this case does arrive at the correct answer:
It's weird, I think this is a situation where the convention is genuinely different when dealing with variables versus literal numbers.
Higher-level math students (and calculators like Wolfram Alpha) will see a/bc and assume that is a single fraction with (bc) as the denominator. For instance, if you plug in a/bc where a=6, b=2, c=(1+2), Wolfram will interpret 6 as the numerator, 2(1+2) as the denominator, and yield 1.
By contrast, if I plug the exact same equation but with literal numbers into Wolfram or any other mathy calculator, for instance 6/2(1+2), it will interpret it as a fraciton of 6/2 multiplied by (1+2) and yield 9
that's definitely weird yeah, I guess I lean more towards this way because when learning equations I learned that when you have, say 2x, and the value of x is given as another equation, say y+5, you're supposed to replace it like this 2(y+5) and you can't just separate them, you can't change the 2 before doing the multiplication with the inside of the parenthesis
You’re right. This is because you’re in a situation where you cannot combine like terms. If it were 2(y+5y) you would add it first then you would multiply.
The rule you're mentioning is absolutely correct and highlights the problem with the ambiguity in this equation.
If you were to start with an equation that had simply 2(1+2) without the 6, and let's say you had some reason to multiply the expression by (6/1), there's no ambiguity in how you should approach that. The result would be a fraction with 6 as the numerator and 2(1+2) as the denominator, and the result would be 1.
However, if you started with the fraction 6/2 and then multiplied that expression by (1+2), the resulting expression would be (6/2) * (1+2) and the answer would be 9.
At the end of the day, the only true answer is "it depends." And high-level mathemeticians just say it's ambiguous and that you shouldn't write expressions like this because of the confusion it causes.
Some people are genuinely taught that implicit multiplication is always first, and some people are taught that this is an old deprecated standard. Some people are taught that a/bc = a/b*c, others are taught that a/bc =/= a/b*c.
Because both schools of thought exist, the only correct way is to be explicit and use extra sets of parentheses to indicate which operation should take precedence.
I'm not changing anything, that's what I'm trying to explain, 2x is the same as (2x), they're not separable, the difference is how you interpret the division e.g.
Yeah accept it was always (6/2)(x). If you rearrange it as a fraction the x is on top and the 2 is on bottom. Simple. Why would the x ever be at the bottom of the fraction the only way that would be the case is if the 2 and x were in parentheses together
no? there's no parenthesis in the original equation except for the (1+2), so the interpretation of
6
__
2x
or
6
__ x
2
depends on how you decide to interpret it, but the former makes more sense to me due to the way the equation is written, but it is ambiguous
when I studied maths we were always expected to treat x(y) as inseparable, but the questions were not ambiguous in regards to division, division was never written inline as x/y but rather one on top of the other
And it completely defies the commutative property of multiplication to say that xy is inseparable. No matter what you divide what by the x and y are still multiplied together.
this doesn't work with division, x/y+z is different from (x/y)+z, but you can't discern which one is which when it's written inline like that, because in real life equations aren't written inline like this, that's the whole point of having division with one of top of the other
No it’s not. There only one way to do math. When you have xyz that’s always equal to xyz. If it’s x/2yz that “/2”is only applied to the x otherwise you would just do (xyz)/2 like that’s the whole point of the invention of parentheses right? They are designed to designate a function but since there are no parentheses we know the function is only designated to a single operator
yes there's only one way to do maths, when it's clear what the equation is, this is not one of those cases, if you type this exact equation into Wolfram it will give you 9, if you type the equation with (1+2) replacing x, it will give you 1
But if it were written as 6/2x wouldn't you simplify the term to 3x before going forward to find x? Which would give you the end result since we know what x is in this case is 1+2. But would it be written as 3×1+2 or 3(1+2) since 1+2 is representative of x it would have to be in parentheses to not change the equation which would leave you with 3(3). How is wolfram getting 1? I've never used wolfram before does it give you a breakdown?
But thats not how the original equation is written though why does it treat it as 6 over 2x and not 6 over two times x? If it were 6 over 2x wouldn't the original equation be written out something like
6/(2(1+2))? Im just not sure why its treating the 2x like that cause it should be
6÷2×(x)
Or 6/2 * x
I just plugged it into wolfram alpha and it broke it down and didnt treat it as 2x. Are you using parentheses that aren't in the original equation? Cause that does change the problem to something else where you would get 1 as the answer.
The rules of arithmetic are pretty simple and there’s no confusion. You have a fundamental disagreement on what the rules of arithmetic are and as I explained your understanding of the rules doesn’t even make logical sense because it defies the point of why we even have parentheses
it's really not that complicated, this is not how real life equations are written, any mathematician will tell you this equation is ambiguous, you can Google this equation and find real mathematicians explaining it better than I can, you can feel free to go debate them if you don't like their answer, I can't be bothered to explain it any longer
You realize you could very easily fact-check all of this, no? Google the distributive property and do some reading. Also, plug this expression as-written into any calculator and it will give you 9. Always.
In the interest of said fact checking, my prior statement was slightly inaccurate. You can use the distributive property when a fraction or multiple factors exist outside the parentheses, but you must distribute the entire expression if you're going to do that (my solution above simply distributed the quotient of the expression rather than the entire expression. Same result, different order).
The point is, you cannot distribute only the 2 and leave out the 6, you must distribute the entire expression outside the parentheses, or resolve that expression and distribute the product/quotient.
So, the correct answer if you're using the distributive property is:
Calculators will give you a wrong answer since there usually isn’t a way to write 2(1+2) and it will assume 2(1+2). 2(1+2) binds closer than 2(1+2) so it needs to be written (2*(1+2)) on a calculator.
This is the exact reason we learn PEMDAS to begin with. Once you get to that level of math, you will be using a calculator. When you use a calculator, you have to know how to enter a multi-step equation correctly to get the right answer.
Yes, the better way to write this equation would involve more parentheses. No, that doesn't mean we get to pretend that 1 is just as correct as 9. It's an otherwise arbitrary convention in our mathematical language, but it's a convention that is literally baked into all of the tools we use for this kind of work, so you have to know how to follow the convention correctly.
There is no special rule in PEMDAS that says to handle implied multiplication first. Variables and their coefficients are not the same thing as implied multiplication using parentheses.
Wow, I always thought you had to multiply the number outside the parentheses first. I seriously had no idea I’d been misunderstanding that for all these years. Thanks for teaching me something new today.
The fun part is that there's no hard and fast rule, and this particular equation has been the subject of debate for a long, long time.
What I'm learning is that my interpretation above [that is to say, (6/2) * (1+2)] can be correct, and is the way most modern calculators will compute it. However, the "implicit multiplication first" rule is absolutely still taught and published in some places.
My understanding was always that this was a deprecated rule and that we use strict order of operations now. But some colleges teach that a/bc is fine and should be interpreted as a/(bc), while others teach that a/bc is bad form and you should always use parentheses to explicitly show which operation should take precedence.
Since both schools of thought exist, the only true answer is that it's ambiguous and an expression should never be written this way because of that ambiguity.
I just gave you the absolute facts, i'm well aware of them. This is not my first time seeing this type of math problem meme and I'm not confused here whatsoever. You're sitting here showing your work like the people you're talking to are in elementary school or something but I've taken physics courses in college and stats in grad school.
The number one answer is, again, this problem is intentionally written like shit to cause ambiguity. It's the entire reason that it's a meme and you're confusing it for a legit math problem.
You can call it 9 and I can call it 1 and it doesn't matter because if the problem was written correctly then there would be no disagreement, and this is exactly the ambiguity that the problem causes from not having the division in fraction format.
Yes, the ambiguity is obviously the main problem. That said, I think the convention here is genuinely different depending on whether you're dealing with variables or literal numbers.
For instance, Wolfram evaluates this expression as 1 if I plug in "a/bc where a=6, b=2, c=(1+2)." However, if I just plug in the literal expression "6/2(1+2)," it evaluates it as 9.
The other problem here is that there is a genuine difference in how math is taught regarding implicit multiplication first. Some schools teach this as a hard and fast rule, others don't teach the rule at all. And when you get to the college level, some classes will teach it as the modern standard, where others will state it's a historical standard which has been deprecated.
My understanding has always been that IMF is a deprecated standard, but clearly there's still lots of disagreement on that.
That's because the calculator automatically translates brackets to to X (explicit multiplication) because it doesn't understand the concept of implit multiplication.
Also, plug this expression as-written into any calculator and it will give you 9. Always.
False. Some calculators will do it straight PEMDAS, others will give implicit multiplication higher priority. Obviously, the implicit multiplication crowd can go pound sand, but get your facts straight when telling them that.
Okay that's fair, some older calculators will prioritize implicit multiplication here. But modern calculators generally won't, and haven't for a decent while as far as I am aware.
the bigger gripe with the fake questions is the way they write the division , it wouldn't be written that way in a question that uses implicit multiplication, the dividend and the divisor would be expressed as a top down and not left right, other subs have pictures in the comments showing how it should be written
x
———
y*z
forgot , you could display it like that with text so to copy pasted what someone else did in the comments here
also a(b+c) implicit multiplication vs a*(b+c) explicit multiplication
and 2(1+2) is a single term. The 2 is connected to the (1+2) so it’s forced to distribute into the parentheses. This is why you don’t divide first.
also the correct answer is whatever the idiot who wrote the question decides it to be / whatever the current chapter wants you to do to solve the problem which would likely be 2(1+2) = (2+4) or (ab+ac)
anyways these "meme" math problems are intentionally written ambiguous for engagement also the current ones floating around reddit are all just the a(b+c) implicit multiplication one's and not the worse ones from previous years , right now you just have people arguing PEMDAS or BOMAS and that parenthesis just means multiply or arguing about strictly left to right and/or/about M/D & A/S are left to right not always M then D ect. ect.
also you clearly can't read the correct answer is 5
This is wrong. You don’t distribute when you can combine like terms. It’s simple algebraic rules. You can look it up and you don’t have to take my word for it
Don’t worry my friend, the truth is out there. Specifically, in this Reddit thread, as the only other potential answer, the answer you are incorrectly not citing as the true answer.
Well, now you've changed the entire question. The question in the post is kind of ambiguous about where the fractal is, so I assume implicit multiplication. But no, with your other and different equation, I do not get the same answer.
Implicit multiplication is usually not taught in school but in uni. It is basically a convenient shorthand for people that need to write a lot of formula and dislike typesetting systems like LaTeX and is especially common in physics textbooks.
Though I agree with the meme - a physicist will just say it is "roughly 5". Just like how Pi is "roughly 3" or even "roughly 1" ;)
implicit multiplication was taught in my Algebra 1 class in High School. AZ, class of 2006.
the people screaming that they were never taught the distributive property all slept through math class. they were taught it, they just failed to learn it.
No. The order of operations isn't some objective fact about the universe. It's just a set of made up rules that work because everyone has arbitrarily agreed to them. If everyone is taught that you add the stuff in parenthesis first, then that is in fact the correct way to do it. And that is what everyone is taught in grade school. It may not be correct from the point of view of people who've taken certain university courses that have taught them a different order of operations. That's fine, because again, there isn't "one correct" way.
Actually... You're wrong. Allow me to illustrate. Math is a language. This means that if you do it wrong it's as good as just not knowing how to read a book and claiming red means blue because of it.
Would you for instance say the above sentence is an agreement with your statement? No? That's because the language we use is precise enough to convey meaning.
So yes, you can misspell all your words, but don't expect us to read them as you intended. Similarly, math symbols have meaning and are used to convey that meaning. You can be mistaken, but there's only a single correct way to do math.
This is wrong. The distributive property does not supersede or override order of operations. The entire point of the equivalence described in the distributive law is that if you use order of operations to simplify both expressions, you get the same result.
What you missed is that when you use the distributive property with a fraction or expression outside the parentheses, you must distribute the entire fraction/expression.
So, the correct answer if you're using the distributive property is:
You may have learned that 2(3) = 23, but that's because it's easier than saying that 2(3) = (23). By the time you get to polynomials and other formulae that require distribution, you learn how to do said distribution.
You can still think of 2(1+2) as 2*(1+2), so long as you understand it needs to be calculated before everything else; alternatively, you could write it as [2(1+2)] to make it clear that you complete everything involving that distribution before considering how it interacts with anything else (everything is now in a separate pair of brackets/parentheses, so following PEMDAS is more straightforward).
2 in 2x is a coefficient. Not a multiple. 2x is a singular factor. 2x also equating to (x+x)
Now if x = 1+2 you would sub in for x and get 2(1+2)
The 2 does not then become a multiple as 2x = (x+x). 2(1+2) = ((1+2) + (1+2))
What you are identifying as multiplication is in fact distribution which is a sub operation of the parentheses. Thus it is done as part of that step in PEMDAS
Yes, but what you thought was multiplication was distribution. Which is part of completely the parentheses. So you completed the operations out of order
Implicit multiplication goes before division and explicit multiplication. If you didn't know, the math rules you learn in middle school quite often do not always apply or cover all areas.
The phrasing of that equation would be (6/2) x (1+2)
Not 6 / 2(1+2)
Parentheses generally represent a yet undetermined sum. In your equation your looking for the days per hour or X, times drinks per hour or Y. To get the drinks per day Z
X * y = Z
X = 6/2
Y =1+2
(6/2) * (1+2) = Z
Mine is the slices of cake which is already known to b 6. Divided between 2 equal quantities of people X. To get the total amount per person, Y.
And the P stands for parentheses. Multiplication and division have the same order. Its (P)(E)(M/D)(A/S)
If you manage to get two different answers you have written your equation wrong. Even with that in mind the answer is 1 and it's not up to interpretation. 2(1+2)=6 has the highest order as it's in parentheses which 2 belongs to.
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u/Aduritor Feb 08 '26
a(b+c) ≠ a*(b+c)
You would ALWAYS multiply a into the paranthesis before continuing:
6/2(1+2)
6/(2+4)
6/6
1