No video :(

Maths professor reveals the correct answer to the viral maths equation ‘8 ÷ 2(2 + 2)’

University of Huddersfield News & Research

Подписаться 2,6 тыс.

Просмотров 40 тыс.

50% 1

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 .

Опубликовано:

26 авг 2024

Ссылка:

Скачать:

Готовим ссылку...

Добавить в:

Мой плейлист

Посмотреть позже

Комментарии : 97

@seadrown6252 3 года назад

My friends think it's 8 and it's honestly just sad 😂

@Lilkfc3500 Год назад

If you never learned it you don't know any better 🙏🏼

@RealMesaMike 2 года назад

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...

@RazerSCYNescafe 4 года назад

like fresh air.... I knew it now... Thank you, professor!

@HDitzzDH 4 года назад

Indeed!

@mickmaidens2183 Год назад

This would have been better if he had shown the correct mathematical grammar for both answers. His answer is vague.

@ssbsnb1200 3 года назад

Can mathematicians just clearly define how to solve this problem, so we can end rhis debate!

@imjustalilkitty 3 года назад

😂😂😂

@maximilianmusgotwaves9188 3 года назад

There is no answer it’s not a math question

@lanzibangli1259 3 года назад

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

@mikkodetorres2936 3 года назад

@@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.

@GanonTEK 3 года назад

The solution is: don't write ambiguous expressions. There is no single answer. It's bad notation.

@JolanXBL 3 года назад

So the question is, how is this not an equation?

@robson_leao Год назад

But what's the correct form of it?

@robertomoreno7877 4 года назад

Yes! Thank you Professor! I knew it!

@yassinelouchi2024 4 года назад

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.

@HDitzzDH 4 года назад

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.

@GamerBoy_Legend 4 года назад

1 is correct m.ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-Yf8njlNRFMQ.html

@Araqius 4 года назад

The correct answer is 16.

@Araqius 4 года назад

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

@reactionlessssbu-clips2723 3 года назад

@@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

@HDitzzDH 4 года назад

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.

@mikestuart7674 Год назад

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.

@johng.1703 Год назад

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)

@fernandolino6493 4 года назад

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) .

@Araqius 4 года назад

The correct answer is 16.

@Araqius 4 года назад

8÷2(2+2) Is not the same as 8÷2÷(2+2).

@jiminverness 3 года назад

@@Araqius _"8÷2(2+2) Is not the same as 8÷2÷(2+2)"_ Well, duh. Of course not. LOL.

@tannereubanks9353 3 года назад

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).

@autistipoika54 2 года назад

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

@doughendrie5468 Год назад

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

@daijirokatoh3769 4 года назад

If in the US, math teachers can't give a precise response to this question, in France they can and the answer is 16

@jarlfenrir 4 года назад

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.

@spencerholman9137 3 года назад

@@jarlfenrir in Canada it is widely understood by those fluent in math that it is sixteen

@90AlmostFamous Год назад

the missing multiplication symbol makes it ambiguous, but you can solve with algebra a / b(c+d) a / (bc+bd)

@sufiyanshaikh7735 Год назад

Come to gods of mathematics.. Indian.. its 1 not 16.

@Nunya_Business_ 3 года назад

Now we have the English opinion. Engineering shorthand in the US when I attended engineering classes. Not ambiguous.

@Sean-ve2zt 3 года назад

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..

@HDitzzDH 3 года назад

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.

@GanonTEK 3 года назад

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.

@doughendrie5468 Год назад

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.

@steelea3122 3 года назад

Tf why do people need a math prof to tell them the answer to a simple equation

@TensedOut 3 года назад

Because people are incredibly stupid

@onlykaramellah2868 4 года назад

Respect.

@Atistatic Год назад

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.

@ginoalvear2512 Год назад

Answer is 16

@reactionlessssbu-clips2723 3 года назад

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

@williamarrington245 Год назад

Yes

@williamarrington245 Год назад

It is one

@dennis5130 2 года назад

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 💀

@GodofBigots 4 года назад

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.

@WritingGeekNL 4 года назад

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.

@HDitzzDH 4 года назад

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.

@jiminverness 3 года назад

Some calculators and some computer programs will give 16 as the answer. Others will give 1 as the answer. ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-4x-BcYCiKCk.html

@Tekrow 3 года назад

A + B + C or C + A + B. Which way gives you the right answer I'll wait

@Megan-gs4si 3 года назад

My scientific calculator gave me an answer of 1

@trineeluv5071 3 года назад

Haha

@mikestuart7674 Год назад

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.

@sambeetrath7328 4 года назад

By PEMDAS it is 1 or 16 But by BODMAS it is only 1

@user-vr3nb3bt7q 4 года назад

Bodmas its definitely 16 because brackets come first

@GamerBoy_Legend 4 года назад

1 is the answerm.ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-Yf8njlNRFMQ.html

@Araqius 4 года назад

BODMAS = 16

@sophiebrown4315 3 года назад

A bodmas/bidmas is actually 1 Because the brackets 2(2+2) actually equate to 2x2 + 2x2 so 8 8/8 is 1

@miserquemiguel2144 3 года назад

@@GamerBoy_Legend 16 is the answer

@dylans_vibeschannel Год назад

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!

@williamarrington245 Год назад

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

@ameermuhsen2430 4 года назад

Ok if I do like this. 8/2(2+2)=8/4+4=2+4=6 ????? Correct or no. And. Why

@jordanseawalker178 4 года назад

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.

@brookesteelman320 4 года назад

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.

@xshenyu_x1100 4 года назад

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.

@HDitzzDH 4 года назад

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).

@stefentan8847 4 года назад

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. ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-BKXxaEMPPWs.html

@HDitzzDH 4 года назад

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.

@GanonTEK 3 года назад

@@HDitzzDH 100%

@quaklessduck Год назад

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