Maths professor reveals the correct answer to the viral maths equation ‘8 ÷ 2(2 + 2)’
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- เผยแพร่เมื่อ 19 พ.ย. 2019
- The entire internet has been divided over the answer to the viral maths question '8 ÷ 2(2 + 2)' because of the two apparently 'correct' answers that can be calculated, 16 or 1. The equation went viral with millions of people around the world arguing over which answer was more correct than the other. Maths expert Professor Keith Devlin, originally from California's Stanford University, is based at the University of Huddersfield while he completes a Leverhulme Visiting Professorship and we quizzed him about the equation. He reveals that in actual fact both calculations, 16 and 1, are both incorrect. Find out why in the video.
Finally, we asked him for his thoughts on current mathematics education and he told us how the skills he learnt as a mathematics student have now become obsolete due to advancements in technology and explained what needs to happen to mathematics education in order to keep up with the modern world. Watch this video here: • Traditional maths skil... .
Professor Keith Devlin also delivered a public lecture entitled "What do mathematicians do now, that machines can do all the maths?". View the lecture in full: • Video .
My friends think it's 8 and it's honestly just sad 😂
If you never learned it you don't know any better 🙏🏼
like fresh air.... I knew it now... Thank you, professor!
Indeed!
Amusing to see so many commenters doubling down on a "correct" answer....
The fact is, there is diversity of opinion on what the expression actually means (or whether it's nonsense), even among academics and STEM professionals and insisting that there is an objectively correct answer is akin to bigotry...
This would have been better if he had shown the correct mathematical grammar for both answers. His answer is vague.
Can mathematicians just clearly define how to solve this problem, so we can end rhis debate!
😂😂😂
There is no answer it’s not a math question
8÷2(2+2) ?= 16
x=2+2=4
8÷2x ?= 16
-------- ------
8÷2 8÷2
x ?= 16 / 8÷2
a ÷ b/c = a × c/b
x ?= 16 × 2/8
x ?= 16 × 1/4
a × 1/b = a/b
x ?= 16/4
x = 4
8÷2(2+2) ?= 1
x=2+2=4
8÷2x ?= 1
-------- ----
8÷2 8÷2
a ÷ b/c = a × c/b
x ?= 1 2
--- × ---
1 8
x ?= 2/8
x =/= 1/4
@@lanzibangli1259 Is 6 the coefficient of your x in this equation below?
8÷2x ? 16
-------- = ------
8÷2 8÷2
Then if it is, your algebra is wrong. I know what your trying to do but the Professor is right, the equation is wrong.
The solution is: don't write ambiguous expressions. There is no single answer. It's bad notation.
Yes! Thank you Professor! I knew it!
So the question is, how is this not an equation?
Respect.
But what's the correct form of it?
People are still trying to answer the question, just give up people lmao. The question was intentionally poorly written to cause a debate, and you guys certainly made it viral, it's not a serious problem whatsoever. It's ambiguous by definition so let's just move on.
Its not ambiguous. It's just people do not know how to handle parenthesis with common factor removed. Or how to split an equation into segments either.
If in the US, math teachers can't give a precise response to this question, in France they can and the answer is 16
I also feel like in Poland is a common understanding that the answer is 16, however i didn't make any poll or anything. The problem arises on the internet where people from various countries meet.
@@jarlfenrir in Canada it is widely understood by those fluent in math that it is sixteen
the missing multiplication symbol makes it ambiguous, but you can solve with algebra
a / b(c+d)
a / (bc+bd)
Come to gods of mathematics.. Indian.. its 1 not 16.
Now we have the English opinion. Engineering shorthand in the US when I attended engineering classes. Not ambiguous.
Yeah well ... when you propose an mathematics objects as an Abelian Groups how to do it ? Division aren't commutative and might not have an inverse element.
Tf why do people need a math prof to tell them the answer to a simple equation
Because people are incredibly stupid
the long lasting convention for 8/2(2+2) is that it is
8
________
2(2+2)
but that is implied, to make it explicit it should be 8/(2(2+2))
and for those that think it is 16, it should be (8/2)(2+2)
The correct answer is 1, because according to the commutation law, multiplication takes priority over addition. However, it does not apply for the division which in this case is only the conventional version of the fraction. It is also necessary to pay attention to the fact that the distributive law takes priority over the commutative law. It goes from left to right for the "2 × (2 + 2)" part
8 ÷ (2 × (2 + 2))
= 8 ÷ (2 × 2 + 2 × 2)
= 8 ÷ (4 + 4)
= 8 ÷ 8
= 1
But as the professor already said, the way as the question is written, is false.
You already made an assumption in your very first step, why would you put the parentheses around the 2(2+2) for and not anywhere else? You obviously simplify the parentheses first which gives you 8/2(4), then this is where the problem occurs, multiplication and division has the same priority, but there is no mathematical axiom that mentions the "left to right" method here, because we're lacking parentheses we can't evaluate the problem, we get different results depending on which we do first.
1 is correct m.th-cam.com/video/Yf8njlNRFMQ/w-d-xo.html
The correct answer is 16.
Distributive property *of multiplication* is the property of multiplication so it has the same order as multiplication.
www.mathgoodies.com/glossary/term/Distributive%20Property%20%20of%20Multiplication
Distributive Property of Multiplication
www.aaamath.com/ac43.htm
Multiplication Properties -> Distributive property (It's just a property of multiplication.)
www.mathwarehouse.com/dictionary/D-words/distributive-property-definition-and-examples.php
The distributive property is one of the most frequently used properties in math. In general, this term refers to the distributive property of multiplication.
www.themathpage.com/arith/mental-arithmetic-multiplication-2.htm
Decomposing the multiplicand: The distributive property of multiplication
There is also distributive property of exponent.
www.solving-math-problems.com/exponent-rules-distributive.html
Distributive Property of Exponents: (xy)^b = (x^b)(y^b)
www.sparknotes.com/math/algebra1/exponents/section3.rhtml
If an exponent acts on single term in parentheses, we can distribute the exponent over the term.
And here is also distribution of division.
(a+b)/x = (a/x + b/x)
teachmath.openschoolnetwork.ca/grade-5/division/distributive-property-for-division/
Distributive Property for Division
www.khanacademy.org/math/pre-algebra/pre-algebra-arith-prop/pre-algebra-ditributive-property/a/distributive-property-explained
The distributive property is sometimes called the distributive law of multiplication *and division*.
mathforum.org/library/drmath/view/69813.html
But you can only distribute division over addition (or subtraction) in one direction: (a + b)/c = a/c + b/c is true
en.wikipedia.org/wiki/Distributive_property
In practice, the distributive property of multiplication (*and division*) over addition ....
1/3 + 1/3 + 1/3 = (1 + 1 + 1)/3
4/2 + 4/2 = (4 + 4)/2
(4/2 + 4/2)(4) = (4 + 4)/2(4)
(4)(4) = 8/2(4)
8/2(4) = 16
@@HDitzzDH It does matter because when solving the brackets we are also remember the priorities that left to right and multiplication has higher priority over addition in bedmas you are forgetting the critical meta thinking that bedmas still applies when solving the bracket
It's 1 to me because 2(2+2) still a factorization of 8. If you have an operación like 8÷2(2+2) Is not the same as 8÷2*(2+2) .
The correct answer is 16.
8÷2(2+2) Is not the same as 8÷2÷(2+2).
@@Araqius _"8÷2(2+2) Is not the same as 8÷2÷(2+2)"_
Well, duh. Of course not. LOL.
The * is implied. Because of pemdas you have to solve the parentheses first. Meaning you get (4) and because it’s solved that means you get rid of it. So now that the parentheses are gone the equation will look like this 8/2*2. Not 8/22 or 8/2(4).
Nah ur bad at maths. How is 8÷2(2+2) not the same as 8÷2*(2+2) ? They are LITERALLY the same equation.
And the correct way to solve this is 8÷2(2+2) = 8÷2(4) = 4(4) = 4*(4) = 16
the "2*" is not in the parenthesis
My take on it.
Mathway definitions of Term and
Quotient
Term
Any expression written as a product or quotient.
Example: 2xy, 4m²,
Quotient
The answer to a division problem.
8/2 cannot be used as the factor of (2+2)
As it is not a quotient. 4/1 or 4 is a quotient.
And the answer to 8/2.
So 8/2(2+2)
By the Distributive Law we get -
“The product of a multinomial by a monomial is obtained by multiplying each term of the multinomial by the monomial and adding algebraically the resulting products.”
2(2+2) 2 (mono) (2+2)(multi)
(2*2+2*2) Multiply
(4+4) Add
8 is the product of 8/2(2+2)
In accordance with Distributive Law
And Order of Operations.
8/8 Answer can only be 1
there is a way to solve the problem that is why the distributive property exists.. 8/2(2+2) Use the DISTRIBUTIVE property and the equation becomes 8/(4+4) ... 8/8 = 1.. if the distributive property did not exist then this equation would be problematic BUT since the DISTRIBUTIVE property does exist it makes this a solvable problem..
You just assumed that the (2+2) part was a part of the denominator, which doesn't have to be the case, thus the ambiguity.
The order of operations or the distributive property aren't the issue and can't prove anything here.
The problem is with the notation itself and what the question actually is.
The academic interpretation gives multiplication by juxtaposition higher priority so you distribute the 2 and get (4+4) which leads to 8/8 = 1.
The modern programming interpretation gives multiplication by juxtaposition equal priority so distributes the 8÷2 leading to (8÷2×2 + 8÷2×2) = 16.
Both are valid interpretations and both use the distributive property.
The question is ambiguous and nothing can change that except writing it out properly.
8/2 is 2 factors separated by an explicit division. So it’s
8
---- = 1
2(2+2)
In addition to that, 8/2 has not been simplified.
2 is the only factor that can be distributed.
The only problem with that evaluation of this problem is that calculators and computers will give 16 as the answer. So what does that tell us? It tells us that there is a convention for correcting bad mathematical grammar - the left to right rule.
That's not the problem here.
Computers don't care too much about left to right, it's more about brackets. It used to be that 8 / 2(2+2) = 8 / (2(2+2)) = 1. That's because of two reasons:
1. Typewriters weren't able to portray fractions, so the automatically interpreted fractions to the said equations.
2. It is easier to code "this part is part of the fraction" than "this part of the part is part of the fraction", so we chose to just add extra brackets to get a bigger fraction.
Why the man is saying that this is, indeed, a poorly handwritten equation... is because it should be a fraction. Computers and modern interpretations say it is 16, because we see (8/2)(2+2). So 16 is most definitely correct in this case (that's the professor's mistake in this).
But others may interpret this as 8 / (2(2+2)) instead, because it is no clear fraction. That's why the equation itself is just stupid, you won't see it like this very often due to this reason.
Instead, teachers say:
- (8/2)(2+2), but (8/2) in a fraction.
- 4(2+2)
- 8/(2(2+2))
- (8/2)(2+2), like this.
It tells us that man-made machines like computers and calculators has been programmed to perform things in a certain way, in almost all cases we have told a computer to go left-to-right when evaluating expressions including multiplication and division, but there is no mathematical rigor or logic behind this "rule", it's just an agree-upon convention to make things easy.
Some calculators and some computer programs will give 16 as the answer. Others will give 1 as the answer. th-cam.com/video/4x-BcYCiKCk/w-d-xo.html
A + B + C or C + A + B. Which way gives you the right answer I'll wait
My scientific calculator gave me an answer of 1
Haha
Ok if I do like this. 8/2(2+2)=8/4+4=2+4=6 ????? Correct or no. And. Why
That’s wrong because you distributed 2 in the parentheses and then dropped the parentheses before adding the 2’s. It should be like this 8/2(2+2)= 8/(4+4)= 8/8=1. This is sort of how people are getting 1 and this is the point of this video. If it was written as a fraction with 8 OVER 2(2+2) it would undoubtedly be 1. As it’s written it is most likely 16. That’s this guys point that the equation isn’t precise so the answer isn’t precise. In math you don’t just write down random equations, you try to solve a problem. Depending on the problem you’d use precise mathematical language. Hope this helps.
this evaluation of the problem is wrong, because you make the assumption while solving that after you distribute the 2 onto (2+2) the parentheses disappear. after distributing, the equation would remain 8/(4+4). you still have to address the (4+4), and so after it would be 8/8 thus equaling 16. it honestly doesn’t even matter tho tbh, because the Professor Devlin explains in the video that the equation is left too ambiguous to solve correctly.
It’s wrong because 8/2(2+2) is equal to 16 if you calculate from left to right 8/2(2+2)= 8/2x4= 4x4= 16 or it can also be equal to 1 if you follow the old maths rules 8/(2(2+2))= 8/(2x4)= 8/8= 1 but nowadays 16 would be the right answer.
Because you assume that the 2 was in the numerator when it might as well could have been a part in the denominator, in that case you obviously can not just distribute the 2 into (2+2).
By PEMDAS it is 1 or 16
But by BODMAS it is only 1
Bodmas its definitely 16 because brackets come first
1 is the answerm.th-cam.com/video/Yf8njlNRFMQ/w-d-xo.html
BODMAS = 16
A bodmas/bidmas is actually 1
Because the brackets 2(2+2) actually equate to 2x2 + 2x2 so 8
8/8 is 1
@@GamerBoy_Legend 16 is the answer
With all due respect to Prof Keith Devlin, his view that the expression is illegitimate is just one of many and in fact singularly his own (idiosyncratic). Most will consider the expression a legitimate math expression. BIDMAS plus the modern left to right convention DOES give an unambiguous answer and it is 16. It gives the answer 1 only when you disregard this rule and insist that × ALWAYS comes before ÷ (which was a 100 years ago). It is irrational and inefficient to have no rule and to place brackets all over the place such as (8÷2)(2+2) to yield 16 unquestioningly or 8÷(2(2+2)) to yield 1 unquestioningly. Instead of eliminating the controversy, I'm afraid Prof Devlin by disclaiming the BIDMAS rule will himself become the subject of a controversy. In maths no one is King. It is the widely accepted practice of mathematicians that reigns. For an antidote to Prof Devlin's false assertion view this video which explains the use of PEMDAS long beloved in the US as "Please Excuse My Dear Aunt Sally" which is identical to the British BIDMAS. Prov Devlin would have us just dump Aunt Sally into the river. th-cam.com/video/BKXxaEMPPWs/w-d-xo.html
The ”left to right” method is not a mathematical axiom whatsoever, it’s a made up procedure to make it easier for students to understand. The problem is ambiguous in every sense of the word. I can link plenty of sites in which multiple professors of mathematics will agree that it’s an ambiguous problem, the lack of parentheses is what’s causing the issue.
@@HDitzzDH 100%
Answer is 16
It’s indeed 16.
Always start with the parentheses ()=2x2=4
Then divide. 8/2=4 */ is mainly used for the division symbol because the symbol is not on the keyboard just a disclaimer*
Now, ik what your thinking, there’s no symbol to add or multiply wtf do we do?? Well, when this happens, you multiply because Multiplication comes before Division, look, PEMDAS. M which is multiplication comes before D which is division. “Please Excuse Multiplication (My) Division (Dear) Aunt Sally”. I let ‘em rats talk, so if y’all rats wanna talk in my reply section, go ahead, I ain’t stopping you.
So, 4x4=16!
Like this comment if you got 16 a different way and please explain it by replying. Thank you!
Pemdas m is multiplication not division 8=2(2+2) right first you do prenthis witch is (4) no exponent so you multiply 2x4 witch is 8 the divide 8÷8÷1
you are wrong 16 is the wrong answer because of the very first step of the equation which eliminates the possibility of having 16 as the answer 8/2(2+2) should not be 8/2x4 yes it is a correct answer but we only made that because it is easier for ourselves to be lazy but the proper order was not used correctly
brackets have the highest priority but what has higher priority among what can be applied to the bracket? multiplication or addition?
it's multiplication and to support that 8/2(2+2) should be 8/(4+4) because we are solving the bracket from left to right another reason why it should be prioritized
so it goes like this
8/2(2+2)
8/(4+4) we are solving the bracket with the priority that we are going left to right and multitiplication before addition
8/8 we solved the bracket
=1
no where with this proper ruleset and proper thinking does it show a hint that 16 can be a possible answer you must always remember not do each rule 1 by 1 because all rules applies to what you are doing
brackets
exponents
division
multiplication
addition
subtraction
Bedmas the bracket solving als0 relies on bedmas this is the critical meta thinking we should remember
Yes
It is one
Its funny but if you put the equation into any calculator it says 16 😳. Its almost as if theres rules in math... one we learned in elementary school... called PEMDAS
The answer is 16 no mater what order of operations you use bedmas is the easier one which is self explanatory. pemdas has a special rule that I’m guessing everyone doesn’t know about not even most Americans or where ever else is used… which is if division and multiplication are in the same equation you go from LEFT to RIGHT, the same thing applies for addition and subtraction. the correct way to write pemdas is like P E M or D A or S or to put it easier PE(M or D)(A or S) that “or” means the special rule….. fun fact back in the 1900 pemdas was used without this rule and the answer would have been 1 but then later on it was corrected/developed. So the answer is 16. Unless the people that say 1 are over 100 years old because the only way to get 1 is by using the old way of order of operations 😂💀… idk I could be wrong 💀
There is a very easy way to do this.
There are several paths to 1 as the only correct answer. But this is the easiest.
For those long and difficult equations we normally break them into segments.
Splitting this terribly complicated equation into segments, is a method that is INCONTROVERTIBLE.
[Look for explicit operators not enclosed in brackets, then put brackets around each segment.]
There is only the divisor. This simplifies and clarifies this long and tedious equation.
i.e. 8 / 2(2+2) -> [8] / [2(2+2)]
Now we clearly see it is 8 / 8 = 1
For people who do not understand parenthesis, this avoids the silly question of what to do 1st.