8÷2(2+2) = ? Mathematician Explains The Correct Answer 

My problem with this is that we have PEMDAS, and the way the problem is written doesn’t allow you to say the parentheses is solved if it is still on the equation. (2) is on parenthesis and is implied that you should get rid of this before going to the next order on the pemdas.

This is crazy you didn't even show the way I was taught, but then again I did always refer to my algebra teacher as a dummy that only knew the answer because she had the teachers guide. I was taught to take the 2 that is outside the parentheses and multiply with the first 2 within the parentheses then use that same 2 outside the parentheses and multiply by the 2nd two within the parentheses, this would leave 8÷(4+4) then add the two 4's to get 8, then divide 8 by 8 and get 1. What a weird way now that I think about it, and evidently incorrect as well. Thanks for the clarification now i just have to deal with the cognitive dissonance that my whole life has been a lie!

@@ernestonoiran1852 You made up a fgalse rule. scholar.harvard.edu/files/contrastingcases/files/chapter_1.pdf 1. First, simplify expressions ***in*** parentheses. 2. Second, apply exponents. 3. Third, do all multiplication and division from left to right. 4. Fourth, do all addition and subtraction from left to right. fsw01.bcc.cuny.edu/mathdepartment/Courses/Math/MTH01/allmath01.pdf Page 36: 1. operations ***within*** grouping symbols first; 2. exponents and roots next; 3. multiplications and divisions (in order of appearance) next; 4. additions and subtractions (in order of appearance) last. www.wallace.ccfaculty.org/book/0.3%20Order%20of%20Operations.pdf Page 2: When we want to do something out of order and make it come first, we will put it ***in*** parenthesis (or grouping symbols). Order of Operations Parenthesis (Grouping) Exponents Multiply and Divide (Left to Right) Add and Subtract (Left to Right) www.mathlearningcenter.org/sites/default/files/pdfs/B5PB-B_0110bw_0.pdf Page 11: Anything ***inside*** parenthesis Multiplication and division from left to right Addition and subtraction from left to right www.mathsisfun.com/operation-order-bodmas.html First part of an equation is start solving *inside* the 'Brackets'. B Brackets first O Orders (i.e. Powers and Square Roots, etc.) DM Division and Multiplication (left-to-right) AS Addition and Subtraction (left-to-right) www.math-only-math.com/bodmas-rule.html Do things *in* Brackets First B ¨ Brackets first (parentheses) O ¨ Of (orders i.e. Powers and Square Roots, Cube Roots, etc.) DM ¨ Division and Multiplication (start from left to right) AS ¨ Addition and Subtraction (start from left to right) www.skillsyouneed.com/num/bodmas.html Brackets (parts of a calculation *inside* brackets always come first). Orders (numbers involving powers or square roots). Division. Multiplication. Addition. Subtraction. (In the lower section: Multiplication and division rank equally, so you go from left to right in the sum, doing each operation in the order in which it appears.) www.thecalculatorsite.com/articles/units/pemdas-bodmas-order-of-operations.php Step 1: Brackets The highest level order is defined by anything *contained in* brackets Step 2: Order or Index The terms Order or Index all relate to operations containing powers or indices such as squaring or square rooting. Steps 3 and 4: Divide and Multiply The third and fourth steps, division and multiplication, have equal weight and so form a third level order of operations that are carried out at the same time. Importantly, when two or more operations of the same order appear one-after-another, the operations should be carried out from left to right. Steps 5 and 6: Add and Subtract study.com/academy/lesson/grouping-symbols-in-math-definition-equations-quiz.html Whenever numbers or variables and a math operation are *contained within* grouping symbols, it is like that part of the problem is saying, 'Do me first!' www.dummies.com/education/math/algebra/grouping-symbols-in-algebra/ Terms *inside* a grouping symbol have to be operated upon before they can be acted upon by anything outside the grouping symbol. www.cliffsnotes.com/study-guides/algebra/algebra-i/preliminaries-and-basic-operations/grouping-symbols Parentheses are used to group numbers or variables. Everything *inside* parentheses must be done before any other operations. bconline.broward.edu/shared/CollegeReadiness/Math/U02_L08_OrdOpInt/U02_L08_OrdOpInt4.html Perform all operations *within* grouping symbol first.

@@BraveNewWorld-1984 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

Araqius I don’t think I made up any false rule. I do think I misunderstood the rule of parentheses first, and I also thank very much all the effort you took for the explanation, now I won’t make that mistake again! 🙌🏽

X frikin D

Lol

At least they're not arguing about the blue or gold dress anymore.

1

Right on right on....

Ur not funny

OPTIX PREACH I thought he was hilarious

They didn’t teach us the right way it’s not your fault

Nah it's people getting answers wrong and changing math cuz one nerdy kid named albert said I gotta diff anwser and the rest of em just went along with it. It's 1 it will always be 1 we don't needs change math.

@@cordeliaclaire1960 Ah come on, things change and they have. Otherwise you'd still be using middle English spellings. Things evolve when we know better - or we just decide things need to be simplified or clarified. The rules now state this equals 16. I was taught this would equal 1, and that was only but 20-30 years ago. I was taught using century-old information...!

Depends on the scientific calculator but here are some that give one or the other: These give 1: Casio FX 83GTX, Casio FX 85GT Plus, Casio 991ES Plus, Casio 991MS, Casio FX 570MS, Casio 9860GII, Sharp EL-546X, Sharp EL-520X, TI 82, TI 85 These give 16: Casio FX 50FH, Casio FX 82ES, Casio FX 83ES, Casio 991ES, Casio 570ES, TI 86, TI 83 Plus, TI 84 Plus, TI 30X, TI 89. Online calculators don't agree either. WolframAlpha & Google don't give implicit multiplication grouping so give 9. Microsoft Math gives both answers on screen. The notation is ambiguous. There is no agreed upon convention on whether multiplication by juxtaposition implies grouping or not. It's just terribly written.

Not a math guy at all, but it takes almost no extra effort to write "(8÷2)(2+2)=" and alleviate all potential ambiguity.

100% on board with this, this is my exact feeling on the issue. The intentional ambiguity of the question is what caused controversy, and I think the difference based on settings is what causes the issues.

@@sanguine8963well if it were (8/2)(2+2) we could then rewrite it as 8(2+2)/2 which I think is pretty neat and shows why we use 8/2(2+2) to indicate 8/(2(2+2)) instead

This! The fact that anyone can confidently say that this expression is "well-defined" is beyond me.

ur answer is right

You still should do brackets first. But it's everything *inside* the brackets, not just next to them. There should be another set of brackets in this question to eliminate confusion. If there are 2 ways of doing it like this you should follow the bidmas rules then solve from left to right

I agree. Old school math, that answer is 1. Also, it helps to understand algebra better.

Same here. That was my automatic first thought.

The answer looks like 1, because you instinctually feel the ÷ symbol means "Everything before the symbol divided by everything after it" In reality it just means one number divided by one number. That symbol isn't really used in real algebraic equations, and I was taught in school not to use it.

What rules do you use to determine parenthesis placement? (Yes, this questions is asked ironically)

You’re doing it correctly.

@@UrbanNilssonOssian parentheses around each term I am assuming

@@UrbanNilssonOssian sincere answer to ironic question: if I am writing the equation, *I* know how the terms are related and it is up to me to make sure my intentions are clear when I write it down.

Example (8/2)(2+2) = 8/(2(2+2)) = Makes life easier doesn’t it?

I studied in France and was taught the answer is 16 😭

When I was in high school in the seventies we did implied multiplication first. So we would have gotten 1. The right way to do it still seems wrong to me.

Another reason why Europe is inferior

Division will always be division, left to right man makes no sense. It's 1

This bothered me all weekend, I guess when you have operations of the same precedence you calculate left to right. So parentheses first (2+2)=4. Next, 8÷2 = 4. Finally 4x4=16. Apparently the problem is within the problem itself. They say no one writes equations like this.

What modern international standards like ISO-80000-1 say to do is (8/2)(2+2) for 16 and 8/(2(2+2)) for 1. No issues then. Scientific calculators don't even agree on what 8/2(2+2) is.

Highly correct. Truth is that there's no rule that forces 8/2(4) to mean (8/2)*4 and not 8/(2*4). Traditionally if we were even to assume. We should assume the latter and get 1 as answer

@@opeadewuyi exactly and that's how we would solve a linear equation too. If there's equation a÷b(c+d), it would be solved as would be a÷(bc+bd) or a/(bc+bd) and not as (a/b)(c+d). If someone does the second thing, then its definitely a problem unless there was × symbol like this a÷b×(c+d).

@@dhruvkaushik8329 i don't understand how they don't understand! 😂 Basic standard traditional maths. The kids today have ruined things by getting to uni at 17😂

@@opeadewuyi yes lol and imagine a text a÷2b. Can you ever interpret that as a/2×b or ab/2. No you can't. That messes up the whole expression. It is supposed to be a/2b

Exactly

I like the fact that they're saying people like Newton, Airy, Pascal, etc. would be wrong today.

yeah same

In computer science papers I'm pretty sure everybody implies the special rule when not writing the operator. In math papers the full notation is given to avoid the problem.

@@Eddie42023 Actually not. Because those people worket excessively with brackets. If you read some of their papers, you will see it. Just because they were so smart, they already knew back then that this would cause problems.

@@bowlchamps37 Well they would be wrong on this ambiguous problem.

you are right

@@rickabick1982 No they are not. The answer is 16

@@MrGreensweightHist you explain to me this. 1(1+7)=4(1+1)=16(0.25+0.25) = 8 you are right with this ? SO HOW COME, in the way I calculate, the answer of each of these math sentences are all 1 if you add 8/ at first as the mathematical sentence you first see. When you calculate your way bud, you will have 4 answers (in this case) ( or an infinite possibilities of answer depending of the sentences) . SO IMO, maybe those who created PEMDAS wanted to create a certain ethic to follow, but IMO, this way to calculate is wrong. I didn't have my degree in mech. engineering calculating the way the answer is 16. I also asked one of my teacher that I still email sometimes for questions or just to know how he is, and he answered the same exact answer I gave you I mean 1. so Answer for me is 1 and will only be 1 until I die.

@@rickabick1982 "1(1+7)=4(1+1)=16(0.25+0.25) = 8" 1(1+7) = 8 4(1+1) = 8 16(0.25+0.25) = 8 These are ALL correct, and ALL have nothing to do with the problem presented because NONE of your examples included division. Any other off topic problems you would like me to confirm? " SO HOW COME, in the way I calculate, the answer of each of these math sentences are all 1" Because you are doing it wrong. 8÷2(2+2) does not = ANY of your above samples. Let's put 8/ in front of them. 8/1(1+7) 8/1(8) 8*8 = 64 8/4(1+10) 8/4(11) 2*11= 22 8/16(0.25+0.25) 8/16(0.5) 0.5(0.5) = 25 Why do they have differnt answers/ Ebcause 8/1 = 8 8/4 = 2 8/16=0.5 Ad in the origional proble, 8/2=4 They have different answer because you FUNDAMENTALLY changed the problem Your insane example is like saying... 1+5=6 2+4=6 3+3= 6 Then why, if I put 12/ in front I get different answer. 12/1+5 =17 12/2+4 = 10 12/3+3 = 7 OMG, stop the madness 🙄 "When you calculate your way bud, you will have 4 answers" "so Answer for me is 1 and will only be 1 until I die." And you will remain wrong until the day you die. Your inability to learn from your mistakes is your own problem, not mine. Your OPINION is irrelevant. The fact is, the answer is 16.

@@MrGreensweightHist this explains it really easy. ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-lLCDca6dYpA.html

I was part of that 51 percent... haha

I got 16 lol

I clicked 1 too fast!

51 got 16 now

Yes

No. As a fraction, it would read as 8/2(2+2). Simplifying the fraction would be 4(2+2), because eight halves is four.

​@MrGreensweightHist but would the fraction format look read put like this: 8 -- 2(2+2)

@@zachseidle1171 No, like this... 8 ------ (2+2) 2 The way you wrote it would only be if the original problem were 8/(2(2+2)), thus grouping it ALL as the denominator.

Solve for x 8÷2(x+2)=16 tell me why it isn't 2

It’s obvious once you set (2+2) = x then you sub it back in later

To be honest that is not wrong written to begin with. The answer is one . No discussion here.

I agree The writing conventions enforce the answer And in this case It clearly writes 8/(2(2+2))

so, (8÷2)(2+2) pull out a 2 from the first set, we get 2(4*(1/4)(4) [since 8÷2 is just 8*1/2, dividing out a 2 would give use 4*(1/4)] this gives us 2(1)(4), not saying it's correct, but by the left to right convention some people go for it gives a 3rd answer, which would tell me their method is flawed. especially when using 8/(2(2+2)) we can pull out a 2, and get 2[(4/2(2+2)) and arrive at the same answer we would if we just solved it.

@@aladinkejkubat8227 The ONLY ANSWER is 16 - and no discussion or debate.

I had teachers in school over 50 years ago that would red-pencil anything turned in that wasn't explicit with operation precedence. I've seen professional papers rejected for rewrite for exactly what you've cited.

It isn't about doing the 1917 version that you should be ashamed of, it's that nobody corrected you. You are not at fault, the people who taught you wrong/didn't correct you are.

Hey at least you know that it is outdated and don't just argue with people without knowing the facts

@@shaahidghoor9143 Incorrect. 8 ÷ 2(2+2) = 16 The Calculator is notoriously programmed poorly.

@@MrGreensweightHist But the answer 1 lines up with the distributive law and algebra too. Unless I'm mistaken, distributive law falls under Parenthesis/Brackets in order of operations, meaning it can be done first. Let's take the distributive law: 8 ÷ 2(2 + 2) = 8 ÷ (4 + 4) (by distributing the 2) =8 ÷ 8 =1 Similarly if I write 2x, that is treated as a single number. So is xy. These variables multiplied together are treated as one unit/number. So if I wrote: 8 ÷ xy. The xy is treated as a single number. Or if I wrote 8÷ 2x, it simplifies to 4 ÷ x.

don't be fooled. 4ab ÷ 2ab = 2, not 2(a^2)(b^2).

To add on to that, this is also how math papers would interpret such expressions - by juxtaposition - the PEMDAS method, while technically true, is impractical to write, and isn't even used in higher level math. I don't care what the technically correct answer is, the majority of mathematicians would treat the expression a/bc as (a)/(bc), and never as (a/b)c. In PEMDAS: (a)/(bc) is written as: a/(bc) (a/b)c is written as: a/bc In Juxtaposition: (a)/(bc) is written as: a/bc (a/b)c is written as: ac/b One requires brackets, the other does not. Juxtaposition is what should be taught, and not PEMDAS.

@@gapple1733Thank you. But it won't penetrate. The pragmatic answer programmatically is DO NOT ASSUME what the computer is going to do... Tell it explicitly... But His video worked. HE GOT US TO COMMENT>

@@lu0z9_the_I Yeah, the sooner we bin off the obelus for good, the better.

"multiplication by juxtaposition" Does not apply here. "For any equation, a/b(c+d), I would interpret it as (a)/(b(c+d))." You would be incorrect. The Correct way would be (a/b)(c+d)

Well you wasted a lot of time

EXACTLY

Yup

You still get it sometimes when you have to use / when writing text. because if I wrote something like 8/2(2+2) you get the same issue. is this 1 or 16. If I threw this into a calculator or some programming language, the answer would be 16.

@@eragon78 The answer is unambiguously 1. I don't know what planet Presh is living on to think the answer is 16 when he apparently has a degree in mathematics. Parenthesis is a distributive operation, NOT a multiplication. a(b+c) = ab + ac. a(b+c) is NOT a * (b+c). Therefore, it is simply wrong to write 8/2(2+2) as 8/2 * (2+2) as Presh is trying to do.

@@godtrader6102 Except for thats not true. Many calculators, online software, and even coding languages, will interpret a(b+c) = a*(b+c). This isnt a mistake. Software could interpret it differently without too much difficulty but it doesnt. The reason is because its its more generally accepted using this format. Unless you really think google doesnt know how to program a simple calculator to read a(b+c) as ab+ac. They could and would if that was the correct way to read it.

And it would appear that I did, in fact, waste 12 years of math classes

I still cannot pass algabra which has prevented me from getti g my college degree FOR THIS VERY REASON! I AM 62 YRS OLD!

Just got a degree in mathematics 3 days ago.. I got 1 as a answer.. They should have added more ( ) for clarification. If it would of said (8/2)(2+2) then duh it’s 16 If it would of said 8/(2(2+2)) then duh it’s 1 But no, we got people that are chaotic neutral writing math problems.

@@-Clueless- While it would be nice to add more (), it isn't needed. As is, the answer is 16 based on orders of operations. That's all there is to it.

Luckily, many people don't waste their maths classes😅 I study biology and so far I had "Maths for biologists", "Physics for biologists", and now I have "Mathematical biology". The first two were similar to school maths, but the thing we have now is so different😣 It's actually mostly very easy if you know how to solve the problems, but the exercises we have are pretty confusing, so I just think "Wait, that's not what we talked about in the lectures?".

correct. We need to unite to stop Americans from inventing American Math

The answer I came up with, is 16. That's because I am 59. The year I learned the was 1976. I was in 7th grade. That was 36 years ago. That was the year that the answer of 16 was correct.Since then, the devils math has changed according to scholars. Because mathematical equations now have debatable answers, I have decided that I have been correct all along. Algebra is inconsistent and untrustworthy to critical thinking, thus making it nonsense. 😂😂😂

8 is divided by the group 2(2 + 2).

8 / 2(2+2) is the *reason* so many people get this wrong. The actual problem is mixing of the dividing sign with the missing multiplication operator. If they put a * or an x or a dot at the mid-line, the order of operations becomes immediately obvious. Simply turning it into a fraction increases the "illusion".

To avoid that I simply write down thw expression like this: [8÷2] * (2+2)

@@Mapledpa That's incorrect, you have to multiply the two by parentheses two plus two. this is why @Carlos Eduardo VT says everyone uses fractions. This equation isn't dividing eight by two, it's dividing 8 by 2(2+2)

@@leahjoyner4696 have you even watched the video yet? Andres is correct

Buddy, you didn’t even watch the video.. Your mathematics is outdated too.

@@jurajudic2734 I'm sorry I can't answer your question, I barely know myself.

Ikr, our education system is so bad

@947 The US. Maybe my teacher was behind the times🤷

Same

No the people that write programming today are not the same ones that would write an academic paper. This is an improperly written academic problem that programmers say has a correct answer. The programmers also imply that you would not need to follow the order of operations, even though Pash that solves the equation claims he needs to follow, to get the correct answer. The answer they get you can also acquire by dividing before solving parenthesis and get the answer of 16. They justify their solution by since you can change 8÷2 to the equation 8*.5 then they interpret the equation as 8*.5(2+2). They interpret it as you want half of what is in parenthesis multiplied by the first number. An academic paper would have it written as 8 numerator / 2(2+2) denominator. Academic papers will teach that 2(a+b) is short hand for (2a+2b) or [(a+b)+(a+b)] keeping the parenthesis or brackets. That is would be interpreted as you want the first number (8) divided by 2 of the equations of (2+2). They would infer that if you are able to divide first to get the answer then (8÷2)(2+2) is how the equation should be properly written.

100%

I have come across youtube videos from Germany, Brazil, and India for sure -- and I think France and Great Britain too, if I remember correctly -- that do NOT give multiplication of the form 2(4) a higher precedence. So, no, it is not a regional difference. And the programming languages that I have used, C, Fortran, perl, python, and R all work the same way world-wide for expressions like this.

@@donmacqueen Take a look at theset two then: ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-S3R4r2xvVYQ.html ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-4x-BcYCiKCk.html

@@DavidCookeZ80 As I said, it's not a regional difference, because there are people from outside North America who hold the same interpretation as the supposedly North American version. See, for example, ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-Xw3PgAbsxng.html (for that matter, both interpretations can be found within North America).

British Commonwealth people's answer is 1. Who crashed the Mars lander because calculation were wrong.

Here's the right method for you: Don't write things like this... 8÷2(2+2) Write it in a way that everybody will know exactly what you intended.

I use bodmas in other countries it might me bedmas or pedmas

@@rekhav4842 I use DUMBASS, which I find super helpful. :)

@@rekhav4842 theyre all the same.

8÷2(2+2) is a poorly structured equation and should be implied as 8÷(2(2+2)) not implied (8÷2)(2+2), otherwise your world is gonna be shook come algebra. I would fist fight a teacher who tried to teach my child this nonsense

lmao feels bad man

Lol it's not a lie. You sucessfully used the principles that were taught you at the time.

NA education OMEGALUL

What is the distributive property

Me too

correct. bodmas is primary school. 1 afterwards for higher education

@@jamescollier3 I'm sorry, but that implies that math is different between grade school and high school. It's not. It's that people aren't using PEMDAS/BODMAS incorrectly.

@@jamescollier3 why would order of operations stop applying after primary school? rewrite the equation as 8 * 1/2 * (2+2) and there's only one clear answer

@@koifish528 exactly

@@DanODea It is not that it is taught differently. It is that you must first learn simple parenthesis before you learn to remove the common factor from them. Everything is done in steps and if you miss a step it can be hard to recover. Like (2x2+2x2)=2(2+2) that the leading 2 is not a term but a mnemonic telling us that every element inside the parenthesis has a x2 attached. Rather than 2*(2+2) Only after we have learned simple parenthesis do we learn this.

​@@SomeRandomGtaDude-zl3us it isnt 16 no matter what order u do it in. there is no multiplication symbol between 2 and (2+2), which would lead some calculators to presume that 2 and (2+2) are as ONE whole factor/variable, and if they're one who variable, it would look like 8/2(2+2) = 8/8. for example, its like saying 8/2a. i personally would always first find what 2a is, as theyre seen as ONE whole variable, just like 2(2+2), so i still interpret the answer as 1. i dont see how u can think of it as 8 * 1/2 * 4, or 8/2 * (2+2), bcuz the original equation never had a multiplication sign in between 2 and (2+2) however, if the original question looked like this: 8/2 * (2+2), i would no doubt agree the answer would be 16, but that isn't the case. adding the multiplication symbol makes it a whole 'nother equation just my opinion

Now u know hahaha

2(2) is multiplying...... type it into any calculator and you will get 4.

@@Kuro-bh8mr 2(2+2) has always been 8 on its own

@@cbjones82 you have to calculate the brackets first dude

This is a problem with people misinterpreting sloppy notation. It's NOT a problem with Mathematics.

@@UTU49, I think they're referring to the part of the video where the "mathematician" goes wrong and tries to say that the answer is 16. ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-4x-BcYCiKCk.html

Fr

*reality

@Miloš Đošić correct

Division and multiplication are of the same order, so solving left to right 8/2x4 becomes 4x4=16. You got the equation right, solve the parenthesis to get rid of the brackets, then move onto the next order of operations.

@@shadowrador I disagree (not regarding order of operations) if all the numbers were different, you cannot solve the problem the way you described. A/b(c+d)

That's actually really cool.

same i don't remember direction playing a part in maths but inherently in a case like 1 + 2 - 1, you'd solve this from left to right

@@OAS15 so you do know it! Now that kinda contradicts your first sentence now doesn't it?

YOU'RE IGNORANT

Ricky Bloss right

@@StepwaveMusic But you don't have to actually solve the equation he mentioned by going left to right. -1+2+1 would still be the same answer.

That's the case when you actually do this 20 levels up in school almost everyday

ikr

You can not get less funny

@@asgrid9938 I easily solved it as 1, using the PEJMDAS system

This is me lolol

Except that he is missing a key point. Academically, multiplication by juxtaposition implies grouping. So that makes 1 just as valid today. Nothing to do with the old meaning of ÷. Presh himself doesn't use implicit multiplication to imply grouping in any case, even in the form a/bc which the majority agree is interpreted as a/(b×c) and not (a/b)×c. You can see Presh's post on the Harvard maths ambiguity page where the professor, and their students, disagree with how he interprets the form a/bc. Wolfram Alpha's Solidus article mentions the a/bc ambiguity and modern international standards like ISO-80000-1 mention about division on one line with multiplication or division directly after and that brackets are required to remove ambiguity. Even over in America where the programming interpretation is more popular, the American Mathematical Society stated it was ambiguous notation too. Multiple professors and mathematicians have said so also like: Prof. Steven Strogatz, Dr. Trevor Bazett, Dr. Jared Antrobus, Prof. Keith Devlin, Prof. Anita O'Mellan (an award winning mathematics professor no less), Prof. Jordan Ellenberg, David Darling, Matt Parker, David Linkletter, Eddie Woo etc. Even scientific calculators don't agree on one interpretation or the other. Calculator manufacturers like CASIO have said they took expertise from the educational community in choosing how to implement multiplication by juxtaposition and mostly use the academic interpretation. Just like Sharp does. TI who said implicit multiplication has higher priority to allow users to enter expressions in the same manner as they would be written (TI knowledge base 11773) so also used the academic interpretation. TI later changed to the programming interpretation but when I asked them were unable to find the reason why. A recent example from another commenter: Intermediate Algebra, 4th edition (Roland Larson and Robert Hostetler) c. 2005 that while giving the order of operations, includes a sidebar study tip saying the order of operations applies when multiplication is indicated by × or • When the multiplication is implied by parenthesis it has a higher priority than the Left-to-Right rule. It then gives the example 8 ÷ 4(2) = 8 ÷ 8 = 1 but 8 ÷ 4 • 2 = 2 • 2 = 4 Presh neglected all of this evidence. Having creditials is one thing, but you have to back up claims with evidence. Presh is very biased on this topic unfortunately.

Exactly I am 13 and I got the right answer right away just by seeing the thumbnail

@@abheeshtan8794 I also

@@abheeshtan8794 which is?

@@idontcare7197 16 ofc It's 8÷2(2+2) We have to solve the brackets first (2+2) = 8÷2(4) Now we have to do division = 8÷2= 4 So we r left with = 4(4) So that's 4x4 that's 16 = 16 :)

I know them but I also know that 8÷2x≠4x or that's at least what they have taught to me so I was still confused

Except that 8/2(2+2) is the same as 8/(2*(2+2)) because there is no separation between the 2 and the 2+2. Had they thrown in a multiplication symbol, then it would possibly be ambiguous. 8 / 2a = 4/a, not 4a.

It's not intentionally ambiguous, it's just ambiguous. Whether or not it's intentional is also ambiguous. In the case of the problem, the division symbol is rarely used because it's ambiguous in most cases. For most schools, that division symbol disappears when you start worrying about the order of operations.

It's not intentionally ambiguous (it's math not English) people like you who can't solve these problems blame everyone but themselves for their failures. PEMDAS exists exactly for the purpose of resolving any ambiguity. If you knew how to use it you wouldn't be confused.

@@Strikerfm1 I know how to use PEMDAS perfectly and I knew the answer to this before watching the video. That’s not the point. The point is that a mathematician or engineer would never write it this way in case someone makes a mistake while calculating it. Math is about making things simpler to compute, not more difficult.

@@christophermccann1218 Well no, the multiplication is assumed. 8/2(2+2) is (8/2)*(2+2). But OP has it right. It should be less ambiguous.

Yea exactly why is no one talking about this option 8/2(2+2) = 6 because dissolve “()” so 8/2(2+2) = 8/4+4 = 2+4 = 6

@@Ace-zu2st If you dissolve the "()" the equation becomes 8 / 2 * 2 + 2 = 10. The reason why no one is talking about the option of removing (), is because is a completely different equation. I'm not sure how you arrived at 8/4+4.

I learned this in Australia in the 1970s, and it was the old method, where you would deal with anything connected to the brackets first, and then move to multiplication/division operations.

@@barryschwarz Then that means your first step was 2+2, at which point you arrive at 8 / 2 * 4, arriving at 16. It was not an "old method". It was the correct method 🙂(once you deal with 2+2, the brackets are gone)

@@erich6860 By 'everything connected to the brackets first", I mean everything connected to them, including the 2 to the left, sitting snugly against it, not separated by a mathematical function. So do inside the brackets first, = 4, and then multiply that by the 2 = 8. My old method yields the answer 1.

ok and

@@RetroStuff Nothing. Just some food for thought.

Ya i am a 6th grader and its so easy its 16

I learned this when i was grade 3

@@asp3ct665 Same lol, but i wanted it to relate some ppl, bc some might be learning this in gr. 6.

This, exactly. A lot of us are taught to treat statements like y(y+y) as a monomial, which is where the confusion lies. There is a way to write it so that the clear answer is 16, like (8÷2)(2+2). This is also such an age-old problem by now, and I find it funny that there are folks insisting on one true answer "because calculators"-which I find insufficient as there are calculators that DO consider the y(y+y) statement as a monomial as well and some that don't. Search for the "Your guide to solving the next online viral maths problem" article and you'll find the exact same problem written differently from 2 years ago. It's cropped up time and again before then, and it'll probably go "viral" again in the near future. TL;DR using more brackets wastes less time.

Shoulda said (mad) genius just in case some people think you have anger management issues.

Gpsi861 ((8)/(2))(2+2) ;)

It was not written with a parenthesis, you are changing the problem.

Mrs_pinky85 I understand, I thought it was made abundantly obvious that the example I provided would be the way *I would* write the problem, *had I'd been the one who initially presented the problem.* Apparently not.

New math has failed the younger generation

@@epsteinsghost7247Wdym

The rule is that you should get rid of the parentheses first

solve this question by my process 👻 🤪 my mind has seen future I mean I m came back from 2117 So u have to do is 8/2=4 first step Now, 4(2+2) So, 4×2=8, 4×2=8 Now 8+8=16......

same lol

@@fgwrts your mind also left behind 1917🤔🤔

@@adityarajput8337 yeah

@@adityarajput8337, explain how you decided to separate the term "2(2+2)"?

Same, maybe it has to do with country. I'm from Australia

Same im from austria and we were taught that 1 is the correct answer and the other way is wrong

im from jamaica and im getting 1

I'm from the UK and always been taught the way that makes the answer 16

I'm 15, answer is 1. I'm from Germany btw

British calculators (mine) calculated it to be 1 since UK learns BIDMAS (BODMAS for another name). But on USA calculators, it gives 16 because of PEMDAS.

Mine also says 1 lol

@@wolframtan176 me too bro

@@k0ana889 they are the same thing with different synonyms

@@k0ana889 PEMDAS vs BODMAS dose not change answers. Your calculator is just wrong.

Of course it IS very disappointing when the answer isn't 'banana'

Banana? I GOT GRAPE JUICE :(

I got strawberry smoothie

I got 2

I got the sunglasses emoji

It is. The video neglects to address multiplication by juxtaposition. It may impliy grouping. This makes the notation ambiguous then, depending on context (E.g. academic or programming). It's just really poorly written and has two valid interpretations as a result. This is backed up by Wolfram Alpha's Solidus article (mentions the a/bc ambiguity) and international standards, like ISO-80000-1, which mentions that brackets are required to remove ambiguity if you use division on one line with multiplication or division directly after it. The American Mathematical Society's official spokesperson literally says "the way it's written, it's ambiguous". The AMS blog Viral Equations confirms this also. Many calculators, even from the same manufacturer like Casio, TI etc., have no consensus on the notation. Online calculators don't agree either. WolframAlpha & Google don't give implicit multiplication grouping while Mathway, Geogebra & Desmos do give implicit multiplication grouping. Microsoft Math gives both answers on screen. Other references are: Entry 242 in Florian Cajori's book "A History of Mathematical Notation (1928)" (page 274) - says brackets should be used when using × and ÷ together. "The American Mathematical Monthly, Vol 24, No. 2 pp 93-95" mentions there was multiplication by juxtaposition ambiguity even in 1917 (and not the old ÷ issue) "Common Core Math For Parents For Dummies" p109-110 addresses this problem, states it is ambiguous. "Twenty Years Before the Blackboard" (1998) p115 footnote says "note that implied multiplication is done before division". "Research on technology and teaching and learning of Mathematics: Volume 2: Cases and Perspectives" (2008) p335 mentions about implicit and explicit multiplication and the different interpretations they cause. "The Primes Contain Arbitrarily Long Arithmetic Progressions" (2007), Green & Tao, p36 uses multiplication by juxtaposition with brackets to imply grouping for e_k. This can be checked as a couple paragraphs down they say e_k < 1/k and that only works if interpreted as implied grouping. Other credible sources are: - The PEMDAS Paradox (a paper by a PhD student on this ambiguity) - The Failure of PEMDAS (the writer has a PhD in maths) - Harvard Math Ambiguity - Berkeley Arithmetic Operations Ambiguity - PopularMechanics Viral Ambiguity (AMS's statement is here) - Slate Maths Ambiguity - Education Week Maths Ambiguity - The Math Doctors - Implicit Multiplication - YSU Viral Question (Highly decorated maths professor says it's ambiguous) - hmmdaily viral maths (Another maths professor says it's ambiguous) The sheer volume of evidence highly suggests it's ambiguous.

@@GanonTEK damn , this was legit an interesting read, ive also read thorugh some of the sources you gave and yeah it is, without a doubt, ambiguous. cheers my friend

@@RoyalJester17 You're very welcome

I think you do 8/2 instead of 8/8

That's the pemdas rule, and it is correct but the acronym is misleading. Division and multiplication are equivalent and go from left to right, and addition and subtraction work the same way. It goes Parentheses Exponents Multiplication and division, left to right Addition and subtraction, left to right.

Because this dude got the answer wrong... 🤦‍♂️

@@philpie2998 It atually got it right from European Standard

@@philpie2998 Europe#1

The issue isn't the division symbol, whether you use / or ÷ the problem exists. It's about the elevated priority of implied multiplication. From my memory of being taught 8÷2(2+2) and 8÷2*(2+2) would have different answers.

James Golz no he didnt

Yes😭

Yep 😭💀

yeah

16 bruh

HAHAHAH YESSIR

There is no agreed upon convention on whether multiplication by juxtaposition implies grouping or not. Academically, yes it does, so writing 8÷2(2+2) explicitly using that notation convention is 8÷(2×(2+2)) Using distribution then gives 8÷(4+4) = 1 Literally/programming-wise, multiplication by juxtaposition implies only multiplication so writing 8÷2(2+2) explicitly is 8÷2×(2+2) using that notion convention instead. Distribution then gives (8÷2×2 + 8÷2×2) = 8+8 = 16 So, distribution makes no difference. It can't because it's just a way to rewrite an expression. Like the associative and commutative properties too. There is no agreement on what the explicit version of this expression is. That'the entire problem. It is a notational ambiguity, the mathematical language is unclear. The rules of maths cannot resolve it then. If I said "I saw a man with a stick" that means a man had a stick in his possession and you saw that man. What if instead I said, "I hit a man with a stick". I just changed the verb. Nothing else. Does that mean you used a stick to hit the man or you hit a man who had a stick in his possession, like the first example? It's not very clear and is ambiguous as a result of the poor writing.

You are correct. Because the parentheses do not denote multiplication but distribution.

What calculator are you using because you aren't correct

@@wxbrainiac my calculator also says its 1 used casio here

its because you put fraction mode on your calculator

The () are gone when you add 2+2 and get the 4. 8÷2(2+2) 8÷2(4) 8÷2*4 4*4 16 This is the proper way to do this problem

The is why I teach it as PE(MD)(AS)

Is this the American version or something? Because in my school we did either BIDMAS (brackets, indices,division, multiplication, addition and subtraction) Or BODMAS (brackets,other,division, multiplication, addition and subtraction)

@@izuurokii6068 Yes In the U.S. Brackets = Parentheses. Indicies = Exponents And since M and D share the same priority they just happen to be listed opposite

@@MrGreensweightHist oh that's cool- I guess I learned something new- Thanks

@@izuurokii6068 ik this is an old comment but I’ve gathered every place has a slightly different one. In Canada we use BEDMAS.

It's not just Americans dumazz

@@RS-fg5mf mainly americans

@@carlotacmv391 Wrong... Plenty of non Americans get the wrong answer... FYI... the correct answer is 16

@@RS-fg5mf We watched the video, we know the answer. Also he said it’s mainly americans, not only americans.

@@tolerk1303 mainly would suggest a majority which unless you have specific data to back that statement up I can tell you that it's not mainly Americans because I work with people all over the world that get this wrong.

these people are here to ruin maths learned by everyone soo far

Watch this RU-vid Video to know the correct answer of this puzzle. ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-HGxQp2Yf6cg.html

Right. Math isn't supposed to be tricky or misleading. This expression is deliberately written to mislead. It's bogus

@@nicholasschroeder3678 true. People these days enjoy trolling more than they enjoy science.

@@nicholasschroeder3678 Nothing wrong with the way it is written

It's just people who got the answer wrong that are now trying to make us do it their way.

Me too😪😭.. Already in my PHD and I realise Ive been doing worng what the heck🤣✋🏻 But at least My line is not maths anymore from Grade 12 except some few easy calculation otherwise when I though Im right I'll be told Im wrong n will got embrassed in public😂

Or you possibly didn't pay attention in middle school.

@@Kevin-di6ef nah i remember my teachers from elementary untill highschool exactly teach us to do the calculations in order of (×) > (÷) > (+) > (-) :")

@@Kevin-di6ef my teachers only taught bedmas and that's it

You're right. The internet must be infested with six graders.

@@artsietopology wai... FBI OPEN UP

No second graders

I know, right?

@@Machodave2020 preschoolers !

so me

if you are convinced, you are not smart enough. that said, you become smarter after figuring out why the answer is actually 1 instead of 16.

@@jeremysun7365 Ikr the answer is freakin 1. How come no one in the comments understands this?

Couldn’t be me

@@jeremysun7365 "you become smarter after figuring out why the answer is actually 1 instead of 16." You're wrong. The answer is 16

PEMDAS IS FOR THOSE IN PRIMARY SCHOOL....ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-lLCDca6dYpA.htmlsi=npBrCRKQARRi71k0

8÷2(2+2)= 8÷2×2+8÷2×2 Expanded

True, that's what we were taught too and the fact that we are indians, it sounds ironic.(India is renowned for producing some of the greatest mathematicians)

I am a math teacher... I also explained like this👍

Same

I mean all indian teachers taught us like this didn't they.....now im wondering if they really should be called as teachers they had been teaching us the wrong thing lol😂

No they are right because the answer is 1 if the question is 8÷2(2+2) and is 16 if the question is (8÷2)(2+2) go back to the video from 5:10 where it's mentioned how calculators change the question to get 16

Don't feel bad. This so called "math" problem has nothing to do with actual math. It's just notation and convention.

I’m in middle school and got 16 instantly there is no thinking needed to be done

Probably because you over thought ti and treated the 2 outside the () as a coefficient when it isn't. The correct answer is 16

@Jéster He got the right answer at least

Taddik. You're probably in the habit of writing fractions and divisions with a full fraction bar, which always makes it crystal clear what is and is not in the denominator. This is the habit of someone taking a serious math course.

The TI is the better calculator... CASIO has admitted to programming different models for different markets based on popularity and opinion not the rule of math.

@@RS-fg5mf yeah i never said it was correct, it was a calculator from the early 80s so i did also just assume maybe it was using the older method

@@amarkendale2230 you're demonstrating your ignorance... 2(4) is not a parenthetical priority and is exactly the same as 2×4 Parentheses only group and give priority to operations INSIDE the symbol not outside the symbol AND Multiplication does not have priority over division they share equal priority and can be evaluated equally from left to right as they are inverse operations by the reciprocal. When a constant, variable or TERM is placed next to parentheses without an explicit operator the OPERATOR is an implicit multiplication symbol meaning you multiply the constant, variable or TERM with the value of the parentheses. TERMS are separated by addition and subtraction not multiplication or division. 8÷2 is multiplied by the parenthetical value of the parentheses not just the 2....

@@RS-fg5mf What are you talking about ?- The expression is ambiguous.

@@amarkendale2230 only ambiguous for those who fail to understand and apply the Order of Operations and the various properties and axioms of math correctly...

Same

Maths are tools, and i guess they change just like the tools we have today.

bad thing I learned old math man being old in modern days is hard

The old way is the current way. I'm in Math 1 currently and the answer is 1 according to what I have been taught

True

Math teachers HATE him. This video will CHANGE YOUR LIFE. Watch it quickly before it gets BANNED.

Frans Mampa it’s because the internet allows people with wrong opinions too run wild but once you run into math smart people check them with facts

IKR

Yes, the Distributive Property stands.

Bro you re literally getting every this kind of problem wrong i saw your comments in other videos lmfao

An implied multiplication has implied parenthesis. ab=(ab) So is solved with other parenthesis. Divisions or no.

1 makes more sense to me TBH

It’s 1 Parentheses Exponents Multiply Divide Add Subtract Hope this helps! Remember to do it in order tho

@@maddymiller5085 in Germany we learn it as "Punkt vor Strich" which means "dot before line" division and multiplication are both written with dots so they have the same value. Addition and subtraction are written with lines which means they also have the same value. That means if a division comes before a multiplication you solve it from left to right and if a multiplication comes before a division you also solve it from left to right. Same thing with addition and subtraction. Brackets are always the first thing to solve but you solve the most inner bracket first and go to the outside. Hope this helps with confusion because in my country everyone knows that the answer is 16

@@Mark-ww1vf right?? Here in the netherlands i have also never heard people doing the multiplication with the brackets first

yea same

L to R is an arbitrary convention anyway. For equal priority operations the order doesn't matter. The issue here is that there is no agreed upon convention on whether multiplication by juxtaposition implies grouping or not, which creates ambiguity.

At least you got the right answer!

@@christophermccann1218 yesn't

@@pivottech8881, it's okay that you didn't get there. One day, you'll be able to math, too!

Same here. LOL They have time to use social media but fails to answer simple arithmetic questions. Did they went to school?

Heroic Ninja did you went to english class?

QuantumBullet learn ur English first before judging someone else

@@euler2149 Facts

@@euler2149 whoosh

I would argue it does. It’s part of a single term 🤷🏼‍♂️

I always learned that implicit multiplication takes precedence over regular multiplication and division and therefore goes first, otherwise they would use the x or •.

@@AP-yx9de are you from the USA?

@@TheJocelynrae yeah

@@AP-yx9de that's almost surprising. I'm from Canada, and we also learned that implicit multiplication takes precedence. In these debates about this problem all over social media, it seems to be only a US thing to not really understand that implied multiplication by juxtaposition takes precedence over notated multiplication. Even the first manuals that taught with PEDMAS did implied multiplication first. I saw a video a while ago that talked about how it was American educators who started treating implied and notated multiplication the same, and are even the reason that calculator companies started doing so as well - which is why you can also get calculators that function under the correct PEJMDAS instead of the modern US use of PEMDAS.

Lol you came from that tik tok🤣

Allie Marie same people were calling me wrong and i was right

Bro my sister got 1 on her calculator, I'm telling her to get a new one

Allie Marie same lol it’s 16

Sid Raghunayakula same lmfao. i had to put it as 8/2 • (2+2) instead of 8/2(2+2) for it to get 16

2(4) is not an indice... 2^4 is an indice... Indices or Exponents 2(4) is a multiplication... 2×4 M not B or I

That's how I see it too

Exactly, when there’s no multiplication symbol, there’s implied brackets (a bond). You’re one of the only people that actually understand this problem

Arjun Dureja this is exactly how it’s supposed to be. Can’t even believe people think it’s 16. 8/2(2+2) =8/[2(2+2)] =8/[2(4)] or 8/[(4+4)] =8/[8] =8/8 =1 All work is shown. I take advanced math and this is the answer.

PikaHMW Roblox Developer He just explained why it isn’t and you still use the old way. *laughs in European education system*

PikaHMW Roblox Developer Yup, this question is so obvious. Maybe it’s because i’m an engineering student but i swear I could figure this out in highschool

I’ve always wanted to go to Finland

1 is right. don't be fooled. 4a÷2a=2, not 2a^2.

1 is not correct, any calculator on the internet will say 16, Google 16, all algebraic online calculators 16, web2.0 16 etc

@@prich0382 Well, many scientific calculators say 1 as well. Though, keep on mind that calculators are coded by people too and many of them often do t consider things which are implicit. I recommend reading this if you're interested. people.math.harvard.edu/~knill/pedagogy/ambiguity/index.html

Keep in mind that just because a method was being done in 1917 doesn't mean it doesn't still hold today. Even order of operations started before 1917 and yet people use that today.

100% Also, there are examples: A recent example from another commenter: Intermediate Algebra, 4th edition (Roland Larson and Robert Hostetler) c. 2005 that while giving the order of operations, includes a sidebar study tip saying the order of operations applies when multiplication is indicated by × or • When the multiplication is implied by parenthesis it has a higher priority than the Left-to-Right rule. It then gives the example 8 ÷ 4(2) = 8 ÷ 8 = 1 but 8 ÷ 4 • 2 = 2 • 2 = 4 His argument completely ignores multiplication by juxtaposition which is tye reason 1 is just as valid as 9 today and why a large proportion of scientific calculators give 1 today too. It's very common.

​@@GanonTEKThe operations that are outside and inside a parenthesis behave as isolated and independent terms. _8÷2(2+) = (8÷2)(2+2)_ Since there is no specific sign between the parentheses then the final operation is a multiplication. _(8÷2)×(2+2)_ You perform the operation for each term. _8÷2=4_ _2+2=4_ _(4)(4)_ Now the final operation is carried out, which, as I said, since there is no specific sign, is to multiply. _(4)(4) = 4×4_ _4×4=16_ _(8÷2)×(2+2)=16_