6÷2(1+2) = ? | Correct Answer With Detailed Explanation

[@Syed_Institute]

Hi guys, please see the new revised video on this problem. A few more very interesting points to note about this problem and the answer. kzbin.info/www/bejne/oH3EgIFsgLJgprM

[@RS-fg5mf]

You are confusing and conflating an Algebraic Convention given to coefficients and variables that are directly prefixed and form a composite quantity to parenthetical implicit multiplication. They are NOT the same thing... 6/2y = 6/(2y) = 3/y by Algebraic Convention BUT 6/2(y)= 3y by the Distributive Property... ABC/ABD = C/D by Algebraic Convention ABC/AB(D) = CD by the Distributive Property 6/2(a+b)= 3a+3b not 6/(2a+2b) The Distributive Property is a PROPERTY of Multiplication, NOT Parenthetical Implicit Multiplication, and as such has the same priority as Multiplication... The Distributive Property does NOT change or cease to exist because of parenthetical implicit multiplication.... Multiplication does not have priority over Division they share equal priority and can be evaluated equally from left to right.... The Distributive Property is an act of eliminating the need for parentheses by drawing the TERMS inside the parentheses out not by drawing factors in. The Distributive Property REQUIRES you to multiply all the TERMS inside the parentheses with the TERM not just the factor outside the parentheses... TERMS are separated by addition and subtraction not multiplication or division... 6÷2 is part of a single TERM... FURTHERMORE people misunderstand Parenthetical Priority... The rule is to evaluate OPERATIONS INSIDE the symbol as a priority before joining the rest of the expression outside the symbol. It does NOT literally mean that the parentheses have to be evaluated BEFORE anything else in the expression can be done... A(B+C)= AB+AC where A is equal to the TERM VALUE i.e. monomial factor outside the parentheses not just the factor next to it... A=6÷2 B= 1 C= 2 6÷2(1+2)= 6÷2×1+6÷2×2= 3×1+3×2= 3+6= 9

[@joshuadavid7675]

This shouldn't be a 9 min video 🤣

[@BenedictRucker]

It’s a 9 min vid because the answer is 9 OK

[@joshuadavid7675]

Or milking it for the money not that there's much of it from KZbin these days, however that's probably why

[@Deepak_Joe_Daniel]

But it's a 17min vid

[@NavyGuero83]

You are using PEMDAS wrong. it is not PEMDAS it is P-E-MD-AS meaning multiplication and division is used left to right. no matter what order.

[@owendamon734]

THANK YOU! That was pissing me off lmao

[@averageasianpod9471]

Was about to say the same thing thank you

[@johnsciara9418]

If you paid attention, he did indicate that Multiplication and Division are equal and would be done from left to right.

[@NavyGuero83]

@@johnsciara9418 if you were paying attention he uses PEMDAS wrong.

[@johnsciara9418]

@@NavyGuero83 If you believe that he was using multiplication first because it came first in PEMDAS at 6:48 he indicates that division and multiplication are equal and that they are done left to right. So please indicate what you believe he is using PEMDAS wrong.

[@manlikejoel5027]

I got told that if a bracket came after a number you multiplied the number by the number from the bracket 🤔

[@RS-fg5mf]

You multiply the TERM with the bracket.

[@alexandremarichez8030]

Same

[@loribasciano4290]

See

[@davonburnett2489]

Yeah same, but now everybody is telling me that’s wrong?

[@austina6853]

@@RS-fg5mf bro i have seen you on every one of these videos with hundreds of comments how do you have this much time, please also this causes alot of stress hopefully you arent as pissed off 8 months later

[@kendavis426]

There is only one answer to this and that is 1. Math is Math, there is no change over time no modern way, no conventional way, no historical way, etc. Math is hard science like physics, it doesn’t change for the convenience of the user. That being said it is a matter of order of operations. When I learned this, there were no acronyms ( PEMDAS, BEDMAS, BODMAS, GEMA etc.). These are all for the sake of the teachers thinking they’re teaching something. We learn Mathematical properties and order of operations these acronyms are not all wrong, but they need to be applied in the order and not be carried out straight through, one time. This is also why half the calculators and a lot of these programs online give the answer wrong. The P and the E part of the acronyms they can contain there own expression, which needs to be evaluated in its own right ( Start over again ). Once that is satisfied the M and the D ( or D and M ) after that the A and the S ( or S and A ). The P, the E, the M D, the A S, are all satisfied left to right. Now for the problem, 6 / 2 ( 1 + 2 ). You have a dividend of 6, and a divisor of 2 ( 1 + 2 ). The goal is to find the correct quotient. Your divisor is an expression on it own that needs to be solved. This is the case where the distributive property gives you 2 + 4 which = 6. Your problem is now 6 / 6 which is 1. When you have parentheses and exponents ( or brackets and orders ) they need to be evaluated on they own. In conclusion, there are no short cuts or acronyms that make it easier. There is no modern way, its always been don the same way. THE ANSWER IS 1 !

[@spaceranger145]

I work as an audio programmer doing math every day I understand from a convention standpoint 6÷2(1+2) = 6÷2*(1+2), but it's just terrible notation and so far removed from any practical application! When the sum is written the way it is on the question it implies a fraction 6/2(1+2)

[@blalink6458]

(6\2)(1+2) would be 9, but since there is no parantheses on the 6\2 that means you gotta leave the six alone until everything else after the division Mark has been solved. So for me correct answer is 1.

[@Araqius]

I advise you go and study again.

[@zhiliang1086]

why is everybody ignoring DISTRIBUTIVE PROPERTY? By applying the distributive property rule, 6÷2(1+2)=1 because using the distributive property rule, you must solve 2(1+2) first then division.

[@ifeanyiogbennaya7773]

@@zhiliang1086 nope ur wrong Using distributive property U must first make sure the number outside is by itself. 6 + 2(2+1) can work because multiplication takes place before addition So u distribute the 2 inside But if it's 6÷ 2 (2+1) To distribute u must divide because multiplication and division is from left to right

[@isaacogunmuko3947]

6÷2(1+2)=9 PEMDAS: Parentheses Exponents Multiplication Division Addition Subtraction BODMAS: Brackets Order Division Multiplication Addition Subtractions Note: Brackets/Parentheses first means to find the value of what's inside the parentheses. (1+2)=3 is solving parentheses first. 2(3) means to multiply 2 *3 = 6, note this is multiplication not Parentheses. In both Multiplication & Division are done left to right, Addition & Subtractions are done left to right P: (1+2)=3 B: (2+1)=3 E: None 0: None M&D: 6÷2(3)=>6÷2*3=3*3=9 D&M: 6÷2(3)=>6÷2*3=3*3=9 A&S: None A&S: None

[@blockshaker2464]

You should go back to school 👍

[@OBmaster]

Your example @2:50 proves why a calculator came up with 1 vs. 9. The Casio on the right put in an extra set of parentheses which are not part of the original problem.

[@allenhelmer8418]

Yeah, it put it in because people keep saying it's supposed to be there. And guess what: The calculator's right.

[@Zeelian]

The calculator is wrong, if you are going to add any parenthesis they need to go around the fraction, ie (6/2)(1+2)

[@allenhelmer8418]

Thomas Andersson I'm going to have to check on that. Do you know why? Because very little that you say is true.

[@CorruptEarth]

Yeah 6÷(2(1+2) would give you 1 because the inner parenthesis go first then the outer the last would be the result of those in 6÷6=1 I don't get why he thought those extra parenthesis should be in there. If you do that in all calculators it should always be 1 in the end. I'm with everyone saying the answer is 9.

[@rohanlambert450]

@@SteinerSE well Casio programmed in 2020 gives the answer of 1 so I don't know where you are getting your statements from but they arent correct

[@supralynn]

In PEMDAS multiplication and division matters what comes first in the problem (meaning from left to right) same with the addition and subtraction so the answer is 9 and DISTRIBUTION IS MULTIPLICATION PEOPLE !!

[@ifeanyiogbennaya7773]

Facts

[@supercomet87168]

YES! Thank you!

[@snowdog993]

Tom Lehrer said this: New Math is understanding what you're doing, rather than getting the correct answer. Do it in base 9 or 8. Get it correct and use simple algebra. Build a bridge and use the wrong result and see what happens. The answer is 1.

[@massacmongo995]

No wonder Math is so unpopular with students.

[@geoffreyjones3832]

Whether conventions change or not. the answer is either correct or incorrect. You and those who come up with nine are forgetting something (1+2)= (3) not 3. Since it equals (3) the 2 that is attached to it must be used to remove the () before we proceed with any other operation. If you type the following in Excel it returns "6", =2*(1+2). If enter this formula into Excel it returns 6, =PRODUCT(2*(1+2)). However when entering 6/2(1+2)= it too fails to resolve the parentheses completely, thus it falters and returns 9, =6/2*(1+2). I am not as learned as you and other math scholars are but I see no ambiguity in this when clearly you can attack it properly, Please Excuse My Dear Aunt Sally which clearly orders the resolution of parentheses first or Brackets in Europe. Neither Brackets or parentheses disappear simply because you resolve what's contained within =6/(1+1)^2 and =6/2^2 result in 1.5 also =6+2^2 and =6+(1+1)^2 both equal 10 because you completely resolved what was in the parentheses.

[@whimseywoman]

a (b) is EXACTLY the same as a*b

[@zvonko57]

No a(b)=(a*b) !

[@SteinerSE]

Sorry, absolutely not true.

[@whimseywoman]

Zvonko Dimitrioski Absolutely NOT the same. You cannot add groups where there were none.

[@mysticwolf2768]

I got 1. My understanding is that 2 multiplies into the parentheses. 6÷2(1+2) = 6÷(2+4) = 6÷6= 1

[@alpriore4909]

You do multiplication and division as one step from left to right in both PEMDAS and BODMAS and the same is true for addition and subtraction. Think of them like PE(MD)(AS) and BO(DM)(AS). Each method has 4 steps, not 6.

[@isaacogunmuko3947]

6÷2(1+2)=9 PEMDAS: Parentheses Exponents Multiplication Division Addition Subtraction BODMAS: Brackets Order Division Multiplication Addition Subtractions Note: Brackets/Parentheses first means to find the value of what's inside the parentheses. (1+2)=3 is solving parentheses first. 2(3) means to multiply 2 *3 = 6, note this is multiplication not Parentheses. In both Multiplication & Division are done left to right, Addition & Subtractions are done left to right P: (1+2)=3 B: (2+1)=3 E: None 0: None M&D: 6÷2(3)=>6÷2*3=3*3=9 D&M: 6÷2(3)=>6÷2*3=3*3=9 A&S: None A&S: None

[@fitrisuhaimi2124]

The answer should be "syntax error"

[@timrankhan8265]

The only comment I can agree with

[@TUPPERWAVE]

(P) (E) (MD) (AS) multiplication and division always go from left to right according to the equation, regardless of which is first in the acronym. This equation does NOT need distribution Once you have solved INSIDE the parenthesis you do not need to "get rid of it" it simply turns into a 3 in this case The real answer is 9

[@allenhelmer8418]

The Vapor Room No, multiplication and division do not always go from left to right. If you convert division into inverse multiplication and subtraction into negative addition then left to right is not necessary. "This equation does NOT need distribution" So, are you trying to win the argument by just making shit up? "simply turns to 3 in this case". "in this case"?!? Do you belong to some magic universe where the rules of math sometimes apply and sometimes don't? No, the rules of math apply to all math problems everywhere in the same way every time! That is why I am arguing against the impossible outcome of 9, since it isn't logically consistent all of the time and it doesn't match up with the way that math actually works. And, on top of that, it doesn't "simply turn to 3". It stays in parentheses to show that the 2 is its coefficient. Even though you didn't mention it, I'm going to point out that 2(3) means "2 groups of 3" while 2×3 means "2 times 3". The difference is that 2(3) is 6, no matter what, while 2×3 is only 6 as long as PEMDAS doesn't interfere. The real answer cannot be 9. If you distribute division you will always get the wrong answer. For example, 12/(1+2), is 12/(3), which is 4. When you distribute division you get (12/1+12/2), which is (12+6), which is 18. It's always like that. There is never a situation where you will get the correct answer from the distribution of division. So when you do this problem with the distribution of division, you get ((6/2)*1+(6/2)*2), which is ((3)+(6)), which is 9. 9 MUST be wrong.

[@Zeelian]

Only what is INSIDE the parenthesis is handled in the parenthesis step, and that is simplifying 1+2 into 3, once the contents of the parenthesis has been simplified there is nothing more to do with it. Distribution is only needed if the parenthesis contains a variable, and when doing so you distribute the entire leading tern, ie 6/2.

[@SteinerSE]

You're really quite dense. Yes, if you convert them as said they become commutative and the order isn't relevant any longer, that is completely irrelevant to how the unconverted problem would have to be solved. Your idiotic ramblings are so stupid it's painful to just read them.

[@allenhelmer8418]

Regina Säveholm Olsson​​ The phrase, "Only what is INSIDE" turns what you say into a lie. You should try learning the philosophy of PEMDAS. When you do, you'll see that this rule that you are making up is not really part of PEMDAS. I see that, once again, I have to explain to you about how distributing division is an illegal operation, so only the 2, not 6/2, has to be distributed. Are you deliberately not learning? As to distribution only being necessary when there is a variable, do you really do your math differently when there are variables around? That is why you are getting the wrong answer.

[@Zeelian]

The "only what is inside" is very much part of Order of Operations (ie PEMDAS) the first step is "Simplify what is inside the parenthesis, working from the innermost parenthesis and out". Lets do it without distributing first since it's just arithmetic 6/2(1+2) 6/2(3) 3(3) 9 Lets write it out with a fraction bar as well 6 -(1+2) 2 6 -(3) 2 6*3 ----- 2*1 18 -- 2 9 And lets turn it into algebra as well by replacing the 1 with x Solve for 9 as the answer 6/2(x+2)=9 6/2*x+6/2*2=9 3*x+3*2=9 3x+6=9 3x=3 x=1 1=1 Now lets try it with your 1 6/2(x+2)=1 6/2*x+6/2*2=1 3*x+3*2=1 3x+6=1 3x= -5 x= -5/3 -5/3 =/= 1

[@kasper6285]

6÷2(1+2)= 6÷2(3)= Still have to rid the parentheses I thought by the multiplication. 6÷6=1 I mean yes multiplication and division at the same same time left to right but you still have the parentheses so the multiplication comes 1st.

[@عبداللهالجداوي-ك6ز]

to get rid of the parentheses, all you have to do is solving what's INSIDE the parentheses, what's outside is irrelevant!

[@MrBreakfluid]

Its actually a question of whether implicit calculation has priority over explicit calculation...If you think about it,the BO in BODMAS deals with implicit calculation as do PE in PEMDAS.The 2(1+2) is implicit multiplication and implies that 2,which is a common factor, be multiplied by (1+2)inside Brackets/Parenthesis. The 2(1+2) implies (2×1+2×2),which equals (6).Thats the Distributive law.6÷(6)=1 We can add the 1 and 2 first and get 2(3) which is still implicit but before we continue with that,lets first look at other examples of implicit calculation. •Exponents: Exponents are implicit multiplication. The equation 8÷2^2.The 2^2 implies that 2 be multiplied by itself so you have to place it inside Brackets/Parenthesis. 8÷(2×2)=2 because if you dont and express it as 8÷2×2 you will get 4x2=8,which is the wrong answer. •Fractions: Fractions are implicit Division The FRACTION 9/3 divide by the FRACTION 6/2 is implied as: (9÷3)÷(6÷2) (3)÷(3) =1 But if you dont do implied first and write it as: 9÷3÷6÷2 3÷6÷2 0.5÷2 =0.25 which is incorrect Lets prove it: 9 6 -- ÷ -- 3. 2 18 --- 18 =1 So,conclusion is that implicit calculation has priority over explicit calcution. Which brings us back to the implicit multiplication of 2(3),which implies (2×3).All implicit calculation must be treated in the same way,so: 6÷2(3) 6÷(2×3) 6÷(6) 6÷6=1

[@colinrobertson7093]

Jaymo James

[@Zeelian]

The implied multiplication is treated like any other multiplication, meaning it is done after the division.

[@MrBreakfluid]

Regina Säveholm Olsson so let put what you say to the test. I made an example of Exponents,which is implicit multiplication. 2^2 implies that 2 be multiplied by 2.So in an equation,the quantity that is implied,has to be placed inside brackets to show that it takes priority. 8÷2^2=8÷(2×2) 8÷(2×2) 8÷(4)=2 But if you say implied multiplication is treated like any other multiplication then you are saying 8÷2^2 8÷2×2 4×2=8 8÷2^2 does not equal 8 If you ignore what is implied you will get the incorrect answer

[@thesmallguard4072]

Jaymo James the DMAS bit in Bodmas or MDAS in Pemdas is left to right.

[@thesmallguard4072]

Regina Säveholm Olsson hello. I saw you from that other video..

[@stephanmashiter8421]

Thank you. I couldn't see any way that '1' wasn't the answer but.many think that '9' must be correct. But I have to agree that the issue is that the question isn't defined correctly and when you have that situation, you can't have a definitive answer. From my point of view, you have taught me something and I am grateful. Maybe I didn't understand the implications of something I was taught or perhaps my teachers didn't but you have cleared it up beautifully. Thank you again. BTW, I am impressed that your investigations showed 2 calculators from the same manufacturer giving different answers. Maybe you could suggest to them that they make the answer given as "Indeterminate'.

[@fisher2536]

The answer is 9 dumbass

[@IsaacHND]

@@fisher2536 You know, even if you are right, they are not going to believe you if you just insult them and give no explanation

[@Driftimator]

Multiplication and division are on the same level ( whichever comes first) Same for addition and subtraction

[@Of_UnCommon_Sense]

Depends on which universe you live in. The American Mathematical Society teaches PEJMDAS [i.e. implied multiplications 1st] The American Physical Society teaches EPMDAS [with multiplication always 1st] At University level PEMDAS is defenestrated. You follow either the AMS or the APS.

[@galaxyrunners]

6÷2(1+2) 6÷2(3) () First 6÷6=1 Aisa nahi ho sakta🤔

[@janetmullins8217]

At 11:18 in the video, you multiplied those two fractions and "a" should be in your denominator. You wrote it out to the side as "a' or "a/1"

[@GreenTornado]

Thank God that I'm not the only one who noticed that.

[@kennethwilliams2738]

you have to clear the parentheses. I say that 1 is correct. watch the division become a grouping symbol 6²/2(3)+4=36/6+4=36/10=3.6

[@Araqius]

Assume A = 1+2 then 6/2(1+2) is the same as 6/2A. 6/2A has no parenthesis so you cannot "clear the parentheses". Also, division is not a grouping symbol.

[@isaacogunmuko3947]

6÷2(1+2)=9 PEMDAS: Parentheses Exponents Multiplication Division Addition Subtraction BODMAS: Brackets Order Division Multiplication Addition Subtractions Note: Brackets/Parentheses first means to find the value of what's inside the parentheses. (1+2)=3 is solving parentheses first. 2(3) means to multiply 2 *3 = 6, note this is multiplication not Parentheses. In both Multiplication & Division are done left to right, Addition & Subtractions are done left to right P: (1+2)=3 B: (2+1)=3 E: None 0: None M&D: 6÷2(3)=>6÷2*3=3*3=9 D&M: 6÷2(3)=>6÷2*3=3*3=9 A&S: None A&S: None

[@Kay14911]

To me the question is, when have you 'dealt' with 'parenthesis? Just the 2+1? Or 1+2, then ×2? When is the parenthesis function complete? My final opinion is: Parenthesis is ONLY that which is INSIDE the bracket. The 2 is outside, so it reverts back to normal multiplication. In which case, it then is worked from left to right. So I'll stick with my original 9.

[@petermcmurray2807]

Wrong

[@isaacogunmuko3947]

6÷2(1+2)=9 PEMDAS: Parentheses Exponents Multiplication Division Addition Subtraction BODMAS: Brackets Order Division Multiplication Addition Subtractions Note: Brackets/Parentheses first means to find the value of what's inside the parentheses. (1+2)=3 is solving parentheses first. 2(3) means to multiply 2 *3 = 6, note this is multiplication not Parentheses. In both Multiplication & Division are done left to right, Addition & Subtractions are done left to right P: (1+2)=3 B: (2+1)=3 E: None 0: None M&D: 6÷2(3)=>6÷2*3=3*3=9 D&M: 6÷2(3)=>6÷2*3=3*3=9 A&S: None A&S: None

[@kitxxxxxxx]

"Note that different software will process this differently; even different models of Texas Instruments graphing calculators will process this differently. In cases of ambiguity, be very careful of your parentheses, and make your meaning clear. The general consensus among math people is that "multiplication by juxtaposition" (that is, multiplying by just putting things next to each other, rather than using the "×" sign) indicates that the juxtaposed values must be multiplied together before processing other operations." www.purplemath.com/modules/orderops2.htm As someone who took advanced algebra and didn't just use bedmas (and more) in elementary (i.e you guys didn't go through the advanced steps) I agree with purplemath. Another way of looking at it is the number outside the bracket is attached to the bracket and is therefore a part of that first step. Its a way of adding in an extra calculation easily which is necessary when doing large equations. I believe that not all agree with this because not all have had that training so they don't know the other rules other than what bedmas says. And perhaps teachers will lazily make equations that they don't know are wrong. Or you guys never actually saw an equation like this, which makes more sense as it's a trick meme. so 6/2(1+2) = 6/2(3) = 6/6 =1 and the other way 6/2(1+2) 6/(2+4) =6/6 =1 If you guys didn't take higher math, stop argueing.

[@Araqius]

You are so fucking stupid. Fucking idiot. 2^2(1+2) = 12 = 2^2*1 + 2^2*2 2^(2+4) = 64 2(1+2)^2 = 18 (2+4)^2 = 36 2(1+2) is not (2+4). Distributive property of *multiplication* is the property of multiplication so it has the same order as multiplication. www.mathgoodies.com/glossary/term.asp?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 2(3) is just another way of writing 2*3. It's called multiplication where the sign is omitted. It's the same for 2x, 2sin(x), 2log10, etc. support.casio.com/storage/en/manual/pdf/EN/004/fx-115_991ES_PLUS_C_EN.pdf Page: E-7. These multiplication symbols (x) can be omitted. A multiplication symbol can be omitted when it occurs immediately before an opening parenthesis, immediately before sin or other function that includes parenthesis, immediately before the Ran# (random number) function, or immediately before a variable (A, B, C, D, E, F, M, X, Y), scientific constants, [Pi] or [e].

[@nats50]

At 11:13, you wrote:1/2 divided by a/3 = 1/2 times 3/a = 3/2 times a, which is wrong! It should have been 3/2a and they're not the same! Now, everyone will be even more confused.

[@jeremyjameslv]

Where’s will hunting ?

[@junebug3807]

Schools in USA teach parentheses first. (1+2)=3 then 6 divided by 2=3 then 3X3=9

[@isaacogunmuko3947]

6÷2(1+2)=9 PEMDAS: Parentheses Exponents Multiplication Division Addition Subtraction BODMAS: Brackets Order Division Multiplication Addition Subtractions Note: Brackets/Parentheses first means to find the value of what's inside the parentheses. (1+2)=3 is solving parentheses first. 2(3) means to multiply 2 *3 = 6, note this is multiplication not Parentheses. In both Multiplication & Division are done left to right, Addition & Subtractions are done left to right P: (1+2)=3 B: (2+1)=3 E: None 0: None M&D: 6÷2(3)=>6÷2*3=3*3=9 D&M: 6÷2(3)=>6÷2*3=3*3=9 A&S: None A&S: None

[@RayGrace_]

you do implied multiplication first before. division or multiplication

[@harrymatabal8448]

Mr Isaac where did you get 2×3. Look again it is ÷2×3 = ×3/2

[@isaacogunmuko3947]

@@harrymatabal8448 (2+1)=3 2(x+1)=2(3)=2x3

[@whimseywoman]

"Ever since I have known this sum"... WTF????

[@sravankota6039]

Its actually ever since I saw this video

[@johnsciara9418]

I see that there is an updated video, but I didn't want to lose this one before I had a chance to put in my view on this one. First I appreciate that you said that there would be no solution because it is ambiguous. But I see that to look at this in a vacuum seems to be part of the problem. When I see 6 ÷ 2(1+2) I see this as the first step in finding a solution for 6 ÷ (2+4) because 2(1+2) = (2+4). If the person writing the problem wanted this to be 6 ÷ 2 x (1+2) they should have written it as 6 ÷ 2 x 3 as you did some of the time. If it was written as 6 ÷ 2 x 3 then PEMDAS from left to right would be no problem. Why would someone write 3 as (1+2) Did they simplify 3 into 1+2? If 2(1+2) was the term for (2+4) then you would need to keep the 2 that is outside of the parentheses with the rest of the term to keep the value equal to what was first written.

[@jojobaltan4142]

The answer is 1. 6 ÷ 2(1+2) 6 ÷ 2(3) 6 ÷ 6 1 The same way that 6 ÷ 2a is not read as (6 ÷ 2)a but 6 ÷ (2a). 2a in itself is grouped, same with 2(3), 2(x+1), these denote juxtaposition, which always takes higher precedence over ordinary multiplication and division. The concept of coefficient and variable bond also states that 2a is grouped and we are not allowed to separate 2 from its variable "a".

[@Araqius]

Wrong. The correct answer is 9. Juxtaposition uses division as its inverse so it has the same order as division. 2(3) is just another way of writing 2*3. It's called multiplication where the sign is omitted. It's the same for 2x, 2sin(x), 2log10, etc. support.casio.com/storage/en/manual/pdf/EN/004/fx-115_991ES_PLUS_C_EN.pdf Page: E-7. These multiplication symbols (x) can be omitted. A multiplication symbol can be omitted when it occurs immediately before an opening parenthesis, immediately before sin or other function that includes parenthesis, immediately before the Ran# (random number) function, or immediately before a variable (A, B, C, D, E, F, M, X, Y), scientific constants, [Pi] or [e]. www.wallace.ccfaculty.org/book/0.3%20Order%20of%20Operations.pdf Page: 2: Parenthesis (Grouping) Exponents Multiply and Divide (Left to Right) Add and Subtract (Left to Right) 2 +3(9 ? 4)^2 Parenthesis first 2+3(5)^2 Exponents 2+ 3(25) Multiply 2 + 75 Add You can clearly see that 3(25) is just multiplying which has the same order as division. math.berkeley.edu/~wu/order5.pdf Page 1: (1) Evaluate all expressions with exponents. (2) Multiply and divide in order from left to right. (3) Add and subtract in order from left to right. Page 2: (A) exponents first, then multiplications, then additions 17x^8 + 2x^7 ---> (17(x^8)) + (2(x^7)) You can clearly see that it is just another way of writing multiplication. 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. Page: 42 P = 2l + 2w Here, it is just another way of writing multiplication (If it does not, it doesn't have any place in the order of operations.). 6/2*(1+2) = 6/2(1+2) = 9

[@Kyrelel]

@@Araqius Wrong 2(3) is just another way of writing (2*3)

[@Araqius]

@@Kyrelel Lmao. 2(3)^2 = 18 (2*3)^2 = 36

[@abhisheksilverrrrr]

Correct answer is 1

[@kamalabrahman6925]

My answer is 1. There is no ambiguity.

[@NoGoodDirtyRicer]

Research how to do the math before posting a YT vid about it, in PEMDAS M and D (as well as A and S) are calculated as they come left to right, you do not do multiplication first and division second.

[@jurgen1843]

I think you left out a crucial part, where the multiplication by juxtaposition / implied multiplication is seen as something together, this could for Brackets aswell as variables this is used in high lvl engineering physics, its stated by The American Social style guide that multiplication by juxtaposition comes 1st. Now The American Physics style guide notes that muliplication comes before division but that division always to be written as a fraction, and i can't agree more, that only can be solved with a fraction and just 6/2(2(1+2) is unsolvable

[@ClassoduaClassodua]

there is a rule: changes of the multicatiors places in equesion should not change the answer! So 6 * 1/2 * 3 = 3 * 1/2 * 6 = 1/2 * 6 * 3

[@geonalugala]

There is another rule of division: the initial value, divided by the answer (quotient), should yield the divisor. 6 ÷ 6 = 1 means 6 ÷ 1 = 6. 6 ÷ 2(3) = 1 means 6 ÷ 1 = 2(3). Are you saying that 6 ÷ 9 = 2(2+1) ?

[@ClassoduaClassodua]

@@geonalugala how many multiplicators do you see in this equesion?

[@geonalugala]

@@ClassoduaClassodua All that is irrelevant. Remember, we can't agree on how to INTERPRET what we can see! You don't solve that by asking what "can we see?" since this is the hub of the dispute. The solution is to PUT OUR ANSWERS to the test of common sense! Here is what is important: that people cannot agree on the interpretation of {÷ 2 (2 + 1)} This means, they agree on 6. And, (let's suppose) they agree on the answer, as 9. Then, 6 ÷ 9 should CLEARLY explain what 2 (2 + 1) means. 6 ÷ 9 = 2/3. But, 2/3 ≠ 2(3). That ELIMINATES the stupid assertion that the real answer is 9. Because 6 ÷ 1 = 2 (2 + 1) even to a zombie.

[@ClassoduaClassodua]

@@geonalugala I'm sorry, but I'm a developer. Each time I have to program the computer I have to find a clear vision of how the compiler will execute my code. This is why I do not interpret any calculation, I research how the compiler interpret it and only then I write a code for it. Compilers are very stupid, they have no imagination, they only do what you say to it. And they stop with error each time I mumbling something unclear with :1: SyntaxWarning: 'int' object is not callable; This is what compiler say for 6/2(1+2) it only can read 6/2*(1+2). And there is no other way to interpret it. And it is equal to 6*1/2*(1+2) or (1+2)*1/2*6 So if the dispute do not meet the reality why to have this dispute?

[@geonalugala]

@@ClassoduaClassodua The whole world, therefore, depends on you to code your programs with enough specification, that coefficients before brackets are implied multiplication by juxtaposition. Once programmers overcome this challenge, there will be no further dispute.

[@abhisheksilverrrrr]

9 though is the correct answer... But still i find this absurd.. X ÷ ya= x/ya But not x ÷ ya = (x/y)a Hence 1 is the answer

[@johng.1703]

why is it that people think that division and multiplication go in the order of the acronym? it doesn't. and the issue with the question isn't an order of operations one, it's the question that is badly written.

[@OBmaster]

I love how you completely screwed up BODMAS and PEMDAS. Brackets / Parentheses Orders / Exponents Multiplication And Division (Both treated equally in order from left to right) www.mathsisfun.com/operation-order-bodmas.html Addition and Subtraction (Again, left to right) To get the answer 1, you have failed the BODMAS and PEMDAS rules and/or added additional artifacts into the problem like the right Casio calculator @2:50 The formula @8:08 at ax/4 is correct, not the first one. To think it x/4a is completely ignore the fact that there is an understood multiplication symbol between the 4 and a. It is easier understood if it was originally written: x/4*a. Your Wiki reference even proves you're incorrect but you conveniently ignored where in the article is says: "These mnemonics may be misleading when written this way, especially if the user is not aware that multiplication and division are of equal precedence, as are addition and subtraction. Using any of the above rules in the order "addition first, subtraction afterward" would incorrectly evaluate the expression". But seriously? Who in the hell uses Wikipedia to make an academic argument? The moment ANYONE uses Wikipedia as a valid source of information, that should end all discussions.

[@BenedictRucker]

It’s 9

[@FragezeichenFragezeichen]

This mathematical rule has been changed since 1917. According to PEMDAS you solve the brackets (so what is inside of it) first. 6 / 2 ( 1 + 2 ) -> 3 ... --> 9 You also can solve it with the distributive rule. 6 / 2 ( 1 + 2 ) ^ ^ 1 2 But the division mark has a higher precedence as the (hidden) multiplication mark from the parenthese. Multiplication and division have an equal precedence so you go from left to right. So we do that first... 6 / 2 ( 1 + 2 ) 3 ( 1 + 2 ) 3 * 1 + 3 * 2 --> 9 So yes the correct answer is 9 you can ask google or any technology after 1917 for this.

[@mr_bluesrocker4230]

Or maybe you're wrong because you forget that 2(a+b)=2a+2b?

[@Kyrelel]

This rule has NOT been changed The "(hidden) multiplication mark" means that is it NOT a multiplication, it is part of the parentheses and, therefore, a higher order than multiplication and is done during the P-stage of PEMDAS Think about this: 2(5) _____ = 1 2(5) Now, calculate 2(5) / 2(5) using your method and what happens? You get 2(5) / 2(5) = 2 * 5 / 2 * 5 = 10 / 2 * 5 = 5 * 5 = 25 Do it again using the correct method: You get 2(5) / 2(5) = 10 / 2(5) = 10 / 10 = 1 So, once we have managed to get you to understand this simple mathematical concept we can move on to other, more demanding topics, such as tying your shoelaces or how to eat without someone making aeroplane noises for you.

[@Araqius]

@@Kyrelel You sure love showing your stupidity.

[@Araqius]

............................... Think about this: 2(5) ___ = 1 2(5) Now, calculate 2(5) / 2(5) using your method and what happens? You get 2(5) / 2(5) = 2 * 5 / 2 * 5 = 10 / 2 * 5 = 5 * 5 = 25 ............................. Do you know 2(5) 5 + 5 ___ = ---------? 2(5) 5 + 5 Now, calculate using your retarded logic. 5+5/5+5 = 5+1+5 = 11

[@Araqius]

​@@mr_bluesrocker4230 Do you know (a+b)/2 = a/2 + b/2?

[@d72c]

No one disagrees that you finish the operation within the parentheses first. then it all boils down to how you interpret the division sign: is it 6/(2*3) or (6/2)*3. Is the entire expression (2*3) under division (then the answer is 1) or is it just 2 that is under division (then it is 9). The answer is ambiguous and there is no clear solution. The problem arises since the division is being shown in one line; won''t have occurred if it was clearly shown as a fraction

[@Araqius]

dictionary.cambridge.org/dictionary/english/division-sign division sign: the symbol ÷ or the symbol / used between two numbers to show that the first number should be divided by the second

[@carl7018]

Araqius you do not understand what he meant.

[@RealMesaMike]

@@Araqius The "second number" is argued to be the whole subexpression "2(1+2)"

[@kenbeidham8318]

Interesting point about conventions changing. Surely Though, if you change from a convention that does work to one that doesn't, then the logical thing to do is to go back to the original. The answer is 1, and always has been.

[@Araqius]

Totally wrong. The answers is 9.

[@whimseywoman]

Ken Beidham "The convention that multiplication precedes addition and subtraction was in use in the earliest books employing symbolic algebra in the *16th century*. The convention that exponentiation precedes multiplication was used in the earliest books in which exponents appeared." "In 1913, Second Course in Algebra by Webster Wells and Walter W. Hart has: "Order of operations. In a sequence of the fundamental operations on numbers, it is agreed that operations under radical signs or within symbols of grouping shall be performed before all others; that, otherwise, all multiplications and divisions shall be performed first, proceeding from left to right, and afterwards all additions and subtractions, proceeding again from left to right."" NOBODY here could possibly have been in school before 1913. STOP the bullshit, please.

[@alext8828]

The 2 is part of the bracket/parentheses system. You're not done with the parentheses until the 2 is included in that operation. If they wanted you to do it in PEMDAS order, they'd have used an x instead of the parentheses. REMEMBER: whether a number is inside or outside the parenthesis, it is part of that system and needs to be addressed as the P part of PEMDAS.

[@petersearls4443]

That is not accurate. Once you resolve what is inside the parens 6/2(1+2)=3 and remove the parens. 6/2*3=3*3=9.

[@brickmn808]

That is not correct. Without parenthesis 6/2x1+2 becomes 3x1+2 = 3+2=5

[@petersearls4443]

@@brickmn808 no. After you resolve the 1+2 inside parens. 6/2(1+2)=6/2(3)=6/2*3=3*3=9. Find a math solver online and enter the expression into it. You will get 9.

[@brickmn808]

Yes I realize it is 9, I have never said or suggested otherwise. My answer of 5 was pertaining to someone who said parenthesis wasn't needed. Perhaps I replied to the wrong person@@petersearls4443

[@Of_UnCommon_Sense]

@@petersearls4443 Parenthesis do not transform into a multiplication symbol. You can only drop them when complete. If you did that 2(3) would be 23. Instead distribute... 2(3)=(2*3)=(6)=6

[@arq.abrahamgrajeda9143]

The correct answer actually depends on the problem that's generating the eccuation...

[@whimseywoman]

Abraham Grajeda No. The correct solution to any applied mathematical problem depends ONLY on FACTS. There is only one correct answer. 6÷2 (1+2)=9 6÷(2 (1+2))=1 Learn the difference. flic.kr/p/QhMVDg

[@SmogginMog]

"[...] if you had to write all the necessary parentheses every time you write out a polynomial, it would obscure things rather than clarify them. Instead of 2x2+7x+1, you would have to write(2(x2))+(7x)+1."

[@geonalugala]

@C. Caner Telimenli All these folks want to assume the person who put (2+1) into parentheses, somehow, did not know how to put (6÷2) in parentheses ... It is a problem of obstinacy, not common sense. 2(2+1) = (4+2) = 6. It has no other interpretation. Look. If I gave you: x ÷ y = ? Let y = (r - 3)² = (r - 3)(r - 3). x ÷ (r - 3)² ... = x ÷ (r - 3)(r - 3) But, your teacher said "divide left to right"! So according to you (and him?) (x /(r - 3)) * (r - 3) = x * (r - 3) / (r - 3) = x. *** You notice, that just by taking ONE FALSE STEP - dividing before multiplication - they end up with a serious error. The question was x ÷ y where y = √y√y = x ÷ √y√y ..... (i). = x/y. They solved (x ÷ √y)(√y) = x√y ÷ √y ..... (ii) and got = x. If this does not open their eyes to the mistake, they will never be helped!

[@williammarkwick6932]

You have spent a long time explaining the correct answer, this could have been done in seconds. The answer to this question lies in mathematics and mathematics notation. What do the expressions 2(1+2) and 2 × (1+2) mean in mathematics? Although they give the same answer numerically they mean totally different things. 2 × (1+2) means we have a bracket which we are multiply by 2. 2(1+2) means we have a bracket which has had a common factor 2 taken out of it. The 2 is part of the bracket. Many teachers around the World have now stopped using the obelus and The International Standards for Mathematics Notation has finally sent out a recommendation we refrain from using the obelus and use the slash / or old numerator/denominator methods. So we would get 6 ÷ 2(1+2) as 6 so how can you possibly get the answer 9 from this? 2(1+2) Now instead of arguing which answer is correct what we should be doing is asking this question. Why are certain International companies still promoting and selling their products when THEY KNOW their products are giving the wrong answer? I suggest it has nothing to do with mathematics?

[@Of_UnCommon_Sense]

You are exactly right, it is because of the teachers association in the USA's demands. PEMDAS vs PEJMDAS

[@dalewilliams8077]

Stopped watching this after your very first calculation completely fails to understand what BODMAS and PEMDAS mean.

[@SteinerSE]

Just look at some of the truly absurd claims made by the residential genius Allen Helmer, he's a few cards short of a full deck.

[@allenhelmer8418]

Yes, please. He deserves to be exposed to the truth.

[@SteinerSE]

That's you who needs that, but you wouldn't recognize the truth if it bit you on the arse.

[@TheRealNintendoKid]

If it's meant as 6 halves multiplied by 3, then it should be written (6/2)(1+2). The way it's written, I was always taught that you treat it like this: 6/[2(1+2)] which gives you 6 divided by 6, also known as 1. 2/3 = 2 divided by 3, = .66666666. Therefore, the 6 is on top, and the rest is on the bottom. That's what I was always taught. Fuck this ambiguous shit.

[@Araqius]

6/(2*3) is 6/2/3, not 6/2(3).

[@idk-qx8hh]

Where tf did you get 3

[@evelynlamoy8483]

1+2

[@geographyinaction7814]

I thought that removing the paranthesis was wrong because while brackets mean multiplication, you were replacing brackets with a x sign which has a lesser precedent. I thought that after getting 3, one would have to multiply the 3x2 first...I also know that this is ambiguous and not seen at uni level maths.

[@Of_UnCommon_Sense]

Brackets do not mean multiplication - they only group. 2(1+2) is by definition, a distribution, not a multiplication. The difference is the multiplications occur inside the parenthesis. The exact meaning of this expression is that the factor of 2 has been removed from EACH element of the parenthesis. It is written only once immediately outside the parenthesis to represent the multiplications, within the parenthesis, no matter how many times it occurs. Finally the expression is represented by only 4 characters. More important, this is less complex. Now only one multiplication need be completed not two. In order to get the correct value [6] for the parenthesis, the 2 must be returned at time of evaluation. (2*1+2*2) = (2+4) = (6) = 6 2(1+2) = (2+4) = (6) = 6 2(3) = (2*3) = (6) = 6 Even tho it is now reduced to one element ! It is still a distribution. 2(3) = 2(3+0) = (6+0) = (6) = 6

[@laurablakeney4973]

M and A in PEDMAS just means multiplication OR division. But if there’s both you go LEFT TO RIGHT. this is ez math ppl.

[@davidbennett2948]

For those viewers who have been taught Arithmetic/Algebra without being taught the fundamentals, let me at least explain the signs to you. An arithmetical sign is placed before a number, a quantity or group, as an instruction showing the purpose and action. It applies to that number, quantity or group only. + This is the primary sign of Arithmetic. All other signs are derived from this. The Signs + addition (counting to the right on a number line) - additive inverse (counting to the left on a number line - subtraction) × multiplication (repetitive addition of the same quantity) ÷ multiplicative inverse (division). Which is the subtraction of repeated additions. Note: Because of repeated additions of the same quantity such as: 2 + 2 + 2 + 2 a form of short hand was introduced. This is illustrated as the quantity, the new sign, followed by the number of repeated additions. So here, we have the quantity 2, added 4 TIMES Notice the word ‘times’. Hence the ‘times’ tables. The sign for ‘times’ is × which means multiply So we have (Quantity) × (number of repetitive additions) Written as: 2 × 4 It must not be forgotten that this statement means 2 + 2 + 2 + 2 Let us look at the ÷ sign as shown in the problem in the video. As it is a multiplicative inverse, the expression ÷ a means × a -1 (power of -1). The 3rd Axiom (Distributive) states x (y + z) = xy + xz This is only true if and only if (iff) the first factor, the x, does not have a ÷ sign before it. Taking the relevant part of the statement i.e. ÷ 2 (1 + 2) In this form, you cannot apply Axiom 3 as was done in one of the examples in this video attempting to show some ambiguity in the question. Moving on: Taking the statement in full: 6 ÷ 2 (1 + 2) The very first action to take is to show what the ÷ sign actually means. 6 × 2-1 (power of -1) × (1 + 2) or 6 × ½ × 3......... i) or 6 × ½ × (1 + 2) = 6 × (½ + 1) = 6 × 1½ ……. ii) You can perform the operations in i) and ii) in any direction (commutative) to give an answer of 9. This is the only answer. Now, using Mathematical Analysis, I will break the statement down and take it back to the very essence of Arithmetic which is counting (addition). Before any calculations are done, the only sign in the statement will be a + . Basically counting, as it was at the very beginning of Arithmetic in ancient Eastern parts of the world. There was no conception of a negative number, a zero nor were there any Arithmetical signs. For instance, a herder say, would keep a record of his flock by placing a stone in his purse (one stone represented one animal). If he sold an animal, he would take one stone out of his purse. If he grouped the animals into three (say), he would allow 3 (quantity) through a pen and place 3 stones in a purse, and so on. The Mathematical Analysis will illustrate how lengthy and tedious matters can get and why shorthand/short cuts were developed to help make calculations easier. If anyone wants a full expansion and explanation of the steps involved, email me at: [e-mail] I will then give you the link to my proposed KZbin page. Note: │signs for illustrative purposes only. 6 ÷ 2 × (1 + 2) = │2 × 3│ ÷ 2 × (1 + 2) = │3 + 3│ ÷ 2 × (1 + 2) = │3 + 3 │+ˉ3│ × (1 + 2) = │3 + 3 +ˉ3│ × (1 + 2) = │this quantity │× │this number of repetitive additions │ i.e. quantity added (1 + 2) times = quantity + quantity + quantity = 3 + 3 +ˉ3 + 3 + 3 +ˉ3 + 3 + 3 +ˉ3 = 9 NOTE: the only sign is the sign of summation +. The - indicates a direction of addition. This is how the process is performed directly from first principles whether it be the man with his stones and purse, a number line, an abacus and even in the ‘chips’ of your modern electronic calculator*. *Not shown in binary Dr. David M. Bennett

[@vaishali.kri.]

I came across this question thru a meme on instagram and googled the question. I clicked on this particular video, and since it was too long, I thought to first look at the comments (IDK why), and then found your gem comment. Now I don't need to watch this biiiggg video, I appreciate your way of explaining. 😃

[@Plarndude]

No, in the Order of Operations Multiplication and Division are on the Same Level of Priority and are done Left to Right. Just like addition and subtraction are done Left to Right. Please stop teaching people math on Syed Institute until you take down this video and do it Right!

[@whimseywoman]

Aaron Ingebrigtsen Hi Aaron! I was wondering if I might find you here. Laura, here - person who used to be on Facebook and the Defenders of the O of O group. Hope you are well. There are a LOT of videos about this expression. Maybe I will see you there too. :-)

[@Plarndude]

whimseywoman Hi Laura! I'm doing well. Trying to stay off Facebook.

[@allenhelmer8418]

Aaron Ingebrigtsen Have you been made aware that the left to right guideline is incorrect? If you convert division into inverse multiplication and subtraction into negative addition then left to right is simply not necessary. 1-2+3 = 1+(-2)+3 = 1+3+(-2) = -2+1+3 = -2+3+1 = 3+1+(-2) = 3+(-2)+1.

[@paulolofsson2158]

So, why do you do that mistake? If you want to follow your own advice you have to make the division an inverse multiplication 6/2(1+2) = 6 * (1/2) * (1+2) = 9 With distibution you distribute (6/2) to the terms in parenthesis. And don't say that (1+2) belongs with the 2. Multiplication is just an operation, it's NOT a grouping symbol. If you want grouping you write 6/(2(1+2)). So even 6/2x should be interpreted as (6/2)x where (6/2) is the coefficient of x if you like to express it like coefficient. Real mathematicians don't have this problem since they don't use a slash in cases like this. And if the write (6/2)x on a paper without parenthesis they would normally write the 2 a little lower than x, and that's simply not possible in a single line of text on a computer.

[@allenhelmer8418]

Paul Olofsson If you invert a term, you have to invert the whole term, so 6/2(1+2) = 6*1/(2(1+2)) = 6*(1/2)*(1/(1+2)). So it's not a grouping symbol. That doesn't change that the 2 is the coefficient of the parenthetical expression and is therefore part of said expression. Therefore the extra parentheses are superfluous and shouldn't be necessary. Argh. How many times do I have to say that distribution of division is an illegal operation? The coefficient is 2 and cannot be 6/2. Real mathematicians won't mistake 6/2x as anything other than "6 over 2x". Well, except for the mathematician who crashed a probe into Mars.

[@esahadad]

If , 6 ÷ 2 ( 2 + 1 ) = 9 6 ÷ x ( 2 + 1) = 9 6 ÷ 3x = 9 2 ÷ x = 3 x = 0.666666 So, 6 ÷ 2 ( 2 + 1) is not equals to 9. If , 6 ÷ 2 ( 2 + 1 ) = 1 6 ÷ x ( 2 + 1) = 1 6 ÷ 3x = 1 6 = 3x x = 2 Therefore, 6 ÷ 2 ( 2 + 1) = 1 am I right??

[@Araqius]

Totally wrong and nonsense. First, 6÷x(2 + 1) is not the same as 6 ÷ 3x. You are using the commutative property of multiplication. It's a property of multiplication so it has the same order as multiplication. Second, ............. 6 ÷ x(3) = 9 2 ÷ x = 3 ............ This is clearly wrong. 6 ÷ x(3) = 6 ÷ x * 3 = 9 6 ÷ x = 3 x = 2 2(3) is just another way of writing 2*3. It's called multiplication where the sign is omitted. It's the same for 2x, 2sin(x), 2log10, etc. support.casio.com/storage/en/manual/pdf/EN/004/fx-115_991ES_PLUS_C_EN.pdf Page: E-7. These multiplication symbols (x) can be omitted. A multiplication symbol can be omitted when it occurs immediately before an opening parenthesis, immediately before sin or other function that includes parenthesis, immediately before the Ran# (random number) function, or immediately before a variable (A, B, C, D, E, F, M, X, Y), scientific constants, [Pi] or [e].

[@esahadad]

Araqius okaaayy. if that is what u say. how do you solve this equation then?? If I substitute 2 for x and 1 for y. what is ur solution to this equation then.. 6 ÷ 2 ( x + y ) ??

[@Araqius]

So easy. 6 ÷ 2 ( x + y ) = 6 ÷ 2 * ( x + y ) = 3 * (x + y)

[@wolftamesteiner540]

You can't write out bad math to prove your point, go actually test it in a math tool or math engine, it will tell you 9. You multiplied before dividing which is wrong so of course you'll get an incorrect answer.

[@isaacogunmuko3947]

6÷2(1+2)=9 PEMDAS: Parentheses Exponents Multiplication Division Addition Subtraction BODMAS: Brackets Order Division Multiplication Addition Subtractions Note: Brackets/Parentheses first means to find the value of what's inside the parentheses. (1+2)=3 is solving parentheses first. 2(3) means to multiply 2 *3 = 6, note this is multiplication not Parentheses. In both Multiplication & Division are done left to right, Addition & Subtractions are done left to right P: (1+2)=3 B: (2+1)=3 E: None 0: None M&D: 6÷2(3)=>6÷2*3=3*3=9 D&M: 6÷2(3)=>6÷2*3=3*3=9 A&S: None A&S: None

[@LungsOutJem]

There is no ambiguity in the distribution property. Distribution comes before multiplication or division.

[@ijose3070]

It’s just a freaking fraction times a parenthesis, only 9 is the possible result

[@jamesmakume2630]

I see an integer divided by a monomial expression.

[@geonalugala]

Division proves itself. If 6÷2 = 3, then 6÷3 = 2. Since your answer is 9, try getting 6÷9 Is it 2(2+1) ?

[@ijose3070]

Geo Nalugala what the hell is even that?!?! Bro read my comment again it’s a fraction times something that happens to be a parenthesis 🤷‍♂️

[@geonalugala]

@@ijose3070 Is it possible that so many people on earth learn math so mechanically, without even applying child-level thinking skills? There is something in arithmetic called internal consistency. 21÷7 = 3, also means 21÷3 = 7. Using your answer, multiplied by the divisor, should give you the initial value. So, 7*3 = 21. Also, 9 * 2(2+1) = 6. Is this true? No. Try 1 * 2(2+1) = 6. True. __________ The answer, is part of the proof. You and I seem to disagree on what 6÷2(+1) =? The issue is NOT about 6. You say your answer is 9. I say 1. ______ By internal consistency, therefore, Let 6÷2(3) = 9; or alternatively, Let 6÷2(3) = 1 You mean that 6÷9 = 2(3) That 0.66666667 = 6. You are clearly wrong. This lacks internal consistency. I mean that 6÷1 = 2(3). That 6 = 6. I am right. This is internally consistent. This solves the debate, without referring to your teacher, or PEMDAS, or your favorite uncle ... since math does not depend on them. 6÷2(2+1) = 1. Quite Easily Done!

[@ijose3070]

Geo Nalugala Fansy talking! Keep working on that and you may discover the origin of the universe, but now in simple terms, IF AND ONLY IF 6/2(2+1)=1 then prove, to me that X/2(2+1)=1 you will NEVER get X=6 because that’s only posible for X=2/3, then for X/2(2+1)=9, of course our X=6, it satisfies the equation, I like your enthusiasm thou! 👍

[@Driftimator]

My teacher said “ both PEMDAS and PEDMSA are legal whichever one comes first”

[@PyarUnlimited]

Is 9 a symbol of luck...

[@awsomeangus2480]

How did this math equation stump the internet?!

[@RealMesaMike]

PEMDAS, PEDMAS, BIDMAS, BOMDAS BODMAS, etc are all the same thing. Namely a mnemonic device to remind us of the relative precedence of a few basic arithmetic operations. Do not think it is an algorithm for evaluating expressions. It is not. Do not think that it specifies an "order of operations." It does not. There is no need to follow a left-to-right rule, because... Division is multiplication by a reciprocal (as explained in the video) Subtraction is addition of a negative. Multiplication and addition are each associative and commutative. Do them in whatever order you like. Pay attention to notation (such as implied multiplication) and how it's actually used in the real world of science and engineering, and other disciplines that use math. And.. Don't fall for thinking there is a definitive and "correct" answer to expressions that were devised to troll the Internet.

[@ifeanyiogbennaya7773]

U didn't do pemdas correctly 😪 I gave u a dislike Multiplication and division from left to right

[@theonewhoknocks4528]

Ikr

[@simp1eone]

THE ANSWER IS 9 - end of story #BODMASRocks

[@allenhelmer8418]

Missy Kay I guess the truth doesn't matter at all to you. If you do BODMAS properly, paying attention to the fact that 2 is the coefficient of the 2(1+2) expression and is therefore part of said expression (meaning that the 2 is dealt with during the B step), then you'll get the correct answer.

[@Zeelian]

But the 2 is NOT part of the grouping, it is part of the 6/2 fraction which is separate from the (1+2). Parenthesis group what is INSIDE them, not what is outside them.

[@allenhelmer8418]

In what way is it separate? Is it separated by a multiplication sign? No. Hmm.... 6÷2 is NOT a fraction, btw. It's 6 divided by 2, not 6 halfs. "Parenthesis group what is INSIDE them, not what is outside them." is just a lie.

[@Zeelian]

6 divided by 2 IS 6 halves. The /2 is the short way of writing *(1/2) 6/2 = 6*½ And yes there is an implied multiplication sign there, when there is no sign between a parenthesis and the number in front of it there is an implied multiplication. ie 6/2(1+2) is the same as (1+2)*6/2 Then do tell me, if parenthesis are not limited to what is inside them why does math books and sources explicitly specify that parenthesis only deal with what is inside them?

[@allenhelmer8418]

Regina Säveholm Olsson Again you are making the mistake of thinking 6÷2 is the same as 6/2. One is not a fraction. The other is a fraction. Therefore, 6÷2(1+2) is not the same as (1+2)*6÷2. 6÷2(1+2) equals 6÷(1+2)2.

[@user-zu1ix3yq2w]

a / b(c+d) now do it.

[@happyjack8952]

waited 17 minutes (no....thankfully i had the foresight to fast forward to end) for your final answer such an ignorant answer. there is no ambiguity. the correct answer takes about 2 seconds to come up with. it is 1.

[@ikismanon88]

It is 9

[@priyeeshofonie9615]

Manon Oudenampsen I agree

[@Jaychive_7]

It's nine lmao

[@Araqius]

happy jack You are so fucking stupid.

[@bryanargueta64]

You guys are acting like the parenthesis disappear from existence when the number inside the box has been found, you are reading this as 6/2X(1+2) you’re wrong because you’re setting up the problem in your head wrong every time there’s no number outside the parenthesis a 1 is placed there to get the reflect image and delete the parenthesis from the equation the answer is not 9 it’s 1 and this is scary for whoever this guy teaches and whoever taught y’all it’s not a difficult problem it’s a problem meant to expose incorrect passing on of information, math doesn’t change because you don’t understand it

[@Araqius]

It's high time you study real math.

[@Araqius]

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.

[@RS-fg5mf]

You are clueless. Parentheses (grouping symbols) only give priority to operations inside the symbol not outside... When there are no operations left inside the parentheses to evaluate you CAN remove the parentheses and replace with an explicit multiplication or leave them to represent implicit multiplication which is simply multiplication without the need for a physical multiplication sign... 6÷2(3) is exactly the same as 6÷2×3

[@Adonipubcom]

The correct answer is it's an undefined expression or ambiguous expression. That is the solution. However, 9 would not agree with a basic Euclidean Theorem. N(1+N)=N^2+N So the most correct solution to this ambiguous expression is to not fracture Euclidian Theorems and accept as an Axiom 2(1+2)=6 If this is not true, algebra is broken

[@Araqius]

Your brain is broken. 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/appendix4.htm 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 .... 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 + 2/2 = (4 + 2)/2 (4/2 + 2/2)(3) = (4 + 2)/2(3) (3)(3) = 6/2(3) 6/2(3) = 9

[@matttremblay4679]

PEMDAS does not intend for you to do multiplication before division. The 2 functions are grouped. You always go left to right with those functions. Same with addition/subtraction. Left to right. And you entered the problem differently in each calculator. Stop misleading people.

[@satanicmonkey666]

Pemdas as we know today states that parenthesis first, then exponents, multiplication and division carry same presedence and are done left to right if both present which is the case after the parenthesis is solved. The answer is 9

[@allenhelmer8418]

Erick Estrada Except that PEMDAS is wrong. Take, for example, (2+3)^2. PEMDAS way: Start: (2+3)^2 P step: =(5)^2 E step: =25 Non-PEMDAS way: Start: (2+3)^2 =(2+3)(2+3) Using FOIL: =(2^2+3*2+2*3*3^2) =(4+6+6+9) =25 So, as you can see, PEMDAS is a guideline, not a rule, since obviously it can be used to get the wrong answer.

[@SteinerSE]

The order of operations (PEMDAS to you) is NOT wrong, you're just a clueless math illiterate.

[@allenhelmer8418]

Thomas Andersson Ok, so the fact that real, verifiable math disagrees with you is irrelevant. You know, I'm starting to think that you are projecting. You're clueless and unwilling to admit it.

[@Zeelian]

That you are unable to properly understand it does not make it wrong.

[@SteinerSE]

"the fact that real, verifiable math disagrees with you is irrelevant." REAL verifiable math AGREES with me. before you open that stupid as fuck mouth of your again bring proof that supports you. All the proof that has been presented so far 100% verifies what I am saying and COMPLETELY disproves everything you've ever said.

[@nova2._.]

The answer is 9 6÷2(1+2) (P)(E)(MD)(AS) (left to right for (MD)(AS) Brackets first(Parenthesis) 6÷2(1+2) 6÷2(3) (MD) from left to right 6÷2(3) 3(3) 9 Written in fraction 6/2(3) is wrong 6/2 × 3/1 is 18/2 simplify 18/2 =9

[@taylorr7480]

period

[@Rockdocs]

Its 9

[@jaysmith4152]

as soon as you get 3 the equation removes the parenthesis and becomes 6/2 *3 and at that point the rules change and go left to right

[@allenhelmer8418]

Actually, the parentheses don't go away. 2 continues to be the coefficient of the parenthetical expression. Coefficients are part of the expressions that they modify. As a part of the parenthetical expression, the multiplication is handled during the parenthetical step, before the addition.

[@LeonaDarkwind]

Allen Helmer no, 0.5 it's the coefficient because it's preceded by a division symbol, thus 6/2(1+2)=6•0.5(1+2)=6•(1•0.5+2•0.5)=6•(0.5+1)=6•1.5=9 But wait it gets weirder. You can also distribute the 6 6(1•0.5+2•0.5)=6•1•0.5+6•2•0.5=3+6=9 or if you prefer, distribute both at the same time (6/2)(1+2)=1(6/2)+2(6/2)=3+6=9

[@allenhelmer8418]

Duncan Panthera No, when you invert the denominator, you have to invert the whole denominator. So when you multiply by 1/2, you also have to multiply by 1/(1+2).

[@LeonaDarkwind]

Allen Helmer 2 is the denominator. It's outside the parenthesis.

[@allenhelmer8418]

Duncan Panthera​ incorrect. The inverse of 2x is 1/2x. The inverse of 2(1+2) is 1/2(1+2). The 2 is very much connected.

[@paulhandley1467]

Oh I see. All the software used by Mathematicians, Matlab, Mathematica, Julia, are all wrong. You must be the next Stephen Hawking? Hmmmmmm.

[@dgkcpa1]

Answer is 1, Proof in three lines: 2(1+2) = 6 Divide both sides by 2(1+2) 1= 6 ÷ 2(1+2) Done!

[@nsmiley1277]

6/2(2+1) (2+1)=(3) 6/2=3 3*3=9 6/2(2+1)=9

[@dgkcpa1]

6÷2(1+2) = ? is a simple division problem, where 6 is the dividend, and 2(2+1), ( a product), is the divisor. Division by a product (6) is the same as dividing by the multiplicand (2) and the multiplier (3). 6 6 2(3) 3 6÷2(2+1) = --------------------- = -------------- = ------------ = -------- = 1 2(2+1) 2(3) 2(3) 3 Write the expression as 6(2+1)÷2 , instead of 6÷2(1+2) , if the desired output is 9.

[@dgkcpa1]

Sorry pal, no sale. 6÷2(1+2) simplify 6÷2(3) eliminate common factor 2 3÷(3) 1

[@Ally-1290]

dgkcpa1 I thought it’s multiplication in the middle not division but ok

[@RealMesaMike]

It;s not a matter of proof, but of agreement (or not) on what the specific notation used means.

[@harrymatabal8448]

6÷2(1+2). There's so much argument about pemdas and bodmas. Some of must have seen my other comments. Why all the fuss. 6÷2(3) = 6÷2×3. Let's divide first giving 3× 3 = 9. Those of you who say let's multiply first. You get 6÷6 = 1. This is your mistake. Ok let's multiply first, you must get 6 × 3. NOT 2×3. The 2 has a ÷ sign. If this is not convincing then let's try 6÷2×3 as 6 × 1/2 × 3 = 9. Remember that the rule for division is invert and multiply. That's my final say. Have a good day

[@harrymatabal8448]

Let me educate you when you used PEMDAS. 2×3=6. But ÷2×3=3/2. Sometimes i wonder which planet some people landed here

[@jahanghazazadeh8779]

X/YZ = (X/Y)Z, NO! , thus the answer is 1 because X/YZ = (X/Y)(1/Z)

[@chilewong1324]

Totally Wrong! PEMDAS doesn't mean Multiplication before Division or Division before Multiplication They are same Precedence Solve Inside the Parenthesis the first,Multiplication and Division are the same Precedence,and then,left to right to solve that! So 6 ÷ 2(1+2) = 6 ÷ 2(3) = 6 ÷ 2 × 3 = 3 × 3 = 9 Using the factorizations concept of ABC to solve this equation: A(B+C) = A × (B+C) = AB + AC Let A = 6/2 B = 1 C = 2 , it will be 6/2(1+2) = 6/2(3) = 6/2 × 3 = 3 × 3 = 9 Or Written as 6/2(1) + 6/2(2) = 3 + 6 = 9 Let A = 48/2 B = 9 C = 3 , it will be 48/2(9+3) = 48/2(12) = 48/2 × 12 = 24 × 12 = 288 Or Written as 48/2(9) + 48/2(3) = 216 + 72 = 288 Solutions: 6 -------- (1+2) = 3(3) = 9 2 48 -------- (9+3) = 24(12) = 288 2 9 is only one Correct Answer!!!!

[@quartzium837]

Chile Wong Actually, I think the rules are that when there is only division and multiplication, it is done from left to right. But when there are the other operations, it is done from PEMDAS.

[@SmogginMog]

"Order of operations. In a sequence of the fundamental operations on numbers, it is agreed that operations under radical signs or within symbols of grouping shall be performed before all others; that, otherwise, all multiplications and divisions shall be performed first, proceeding from left to right, and afterwards all additions and subtractions, proceeding again from left to right."

[@Plarndude]

Uh, no Wobbuffet, PEMDAS Always applies, you just misunderstand what it means. Parentheses, do what's inside first Exponents, do these next Multiplication and Division left to right Addition and Subtraction left to right

[@quartzium837]

Aaron Ingebrigtsen I know now. . . No need to call me an idiot . . .

[@allenhelmer8418]

Chile Wong Here's where your "proof" went wrong. You are not allowed to distribute division. When you set A as equal to 6/2 and then distribute it, you are performing an illegal mathematical operation. Proof: 12/(1+2)=12/(3)=4, right? but when you distribute division you get (12/1+12/2)=(12+6)=18. When you distribute division you will *always* get the wrong answer. When you distribute division in this problem, you get ((6/2)×1+(6/2)×2)=((3)+(6))=9. Since distributing division will *always* give the wrong answer, 9 MUST be wrong. Another way in which your proof went wrong is: 6 --(1+2) 2 equals 6(1+2)/2, not 6/2(1+2). The correct way to write this expression using fractions is: 6 ---------- 2(1+2)

[@yairidan5007]

לפני יום 1 (ערוך) If there is no multiplication sign between arguments the connection is stronger, like 2πr or πr² 6÷2π = 6/(2π) 6÷πr² = 6/(πr²) 6÷π(r * 2.54)² = 6/(π(r * 2.54)²) So 6÷2(1+2) = 6/(2(1+2))

[@DarelArtetxe]

Por eso es importante conocer las reglas de asociación y distribución, el orden es belleza y se impone para dar el mejor de los resultados. Una simple pregunta para los grandes genios de internet: un edificio se construye de arriba hacia abajo, los cimientos están en la antena de comunicación en lo más alto del edificio?, Es primero la antena, o la piedra angular? El Esquizofrenico Revisionismo Cultural, no solo es histórico, sino ahora también matemático. Increíble¡¡¡¡¡¡

[@dayrenist]

another failed video lmao. multiplication and division have the same priority. this is true because you can rewrite any multiplication or division as its respective inverse fraction

[@endercake4127]

In the USA PEMDAS is weird you have you multiplication and division left to right and same with addition and subtract as see in the problem since the are equal

[@Kyrelel]

So, the same as everywhere else, then.

[@kennethwilliams2738]

what about the distributive property? should it not be ½•1+½•2? lol no solution it is.... ambiguous

[@Araqius]

2^2(1+2) = 12 = 2^2*1 + 2^2*2 Distributive property of *multiplication* is the property of multiplication so it has the same order as multiplication.

[@geographyinaction7814]

I hope that was sarcasm? London accent and a Utd supporter...local?

[@MattBrownSr]

Your first calculator added a set of parenthesis so it came out with the wrong answer.

[@nyambi251]

So many people are familiar with math,but very small number is familiar with grammar.Instead of analyzing this,take a grammar book or something,do something usefull instead of doing pointless fcking math problem.I'm tilted as fuck...

[@Harshal4598]

But the answer is still inside the parenthesis after solving it, you can't remove it, to remove the bracket you need to first multiple it then you can use DMAS rule. 6 ÷ 2(3) 6 ÷ 6 = 1 The quantity 2x3 & 2(3) is equal but by following the correct orders 1. [ ] 2. { } 3. ( ) 4. ÷ 5. × 6. + 7. - You have to consider the parenthesis first.

[@Araqius]

It's high time you study real mathematics. Take a look at 2(3)^2. 2(3)^2 = 18 Parenthesis has higher order than exponent. 2(3) does not. Also, if we assume that A = 1+2 then 6/2(1+2) = 6/2A. 6/2A has no parenthesis. How the hell will you "remove parenthesis" when there is no parenthesis?

[@Kyrelel]

@@Araqius 2(3)^2 = 18 Correct, but nothing whatsoever to do with this problem. if we assume that A = 1+2 then 6/2(1+2) = 6/2A Again, correct, but it also means 6/(2A), which means 6/(2(1+2)) = 6 / (2(3)) = 6/6 = 1 Glad I could help.

[@Araqius]

@@Kyrelel Basic math is far above your level.

[@isaacogunmuko3947]

6÷2(1+2)=9 PEMDAS: Parentheses Exponents Multiplication Division Addition Subtraction BODMAS: Brackets Order Division Multiplication Addition Subtractions Note: Brackets/Parentheses first means to find the value of what's inside the parentheses. (1+2)=3 is solving parentheses first. 2(3) means to multiply 2 *3 = 6, note this is multiplication not Parentheses. In both Multiplication & Division are done left to right, Addition & Subtractions are done left to right P: (1+2)=3 B: (2+1)=3 E: None 0: None M&D: 6÷2(3)=>6÷2*3=3*3=9 D&M: 6÷2(3)=>6÷2*3=3*3=9 A&S: None A&S: None

[@lilithslittlemoon]

16:50 me @ any math problem ever

[@dgkcpa1]

Bad input=bad output. The whether the answer is 1 or 9 depends on the order of calculation, which is in turn dependent on how the operator keys the data into the calculator. If he feeds it in as (6÷2)x(1+2) he'll get one answer, if he inputs 6÷{2(1+2)} he will get another. Good idea to know how the calculator works, so you know how to set up the problem to get the correct answer, which could be either 1 or 9 depending on how the problem is set up and the data fed to it. Garbage in=Garbage out.

[@joshuadavid7675]

But anyway for those of you who want a quick answer rather than watching a 9min video BODMAS 6÷2(1+2) Brackets 1+2=3 Division 6÷2=3 Multiplication 3×3=9

[@geonalugala]

Remember the logic of division is that, you have something you are breaking down into pieces. You are sharing out. Take this example: You have $6. And you have 2 children. You care for them equally. And each kid wants books and pens. Each book costs $2 and each pen costs $1. Exactly 6÷2(2+1). Would you say you can buy 9 shares of books and pens? Or somehow give each 9 dollars? *** Here is the logic. 1. Find the cost of one set (book and pen). Sum = $3. 2. Find the combined cost on both kids 2 of ($3) = $6. 3. How many sets of book AND pen can you buy? Simple: $6 ÷ $6 = 1 set per kid. How many sets could you buy if you had $30? Of course, 5 of (book+pen) per kid. You cannot say this has no solution.

[@hoshiisaurus]

both methods have the same answer to the equation

[@clarissamendoza5606]

he did PEMDAS wrong

[@chilewong1324]

PEMDAS rules:Solve Inside the Parenthesis the first, Division and Multiplication are same Precedence, And then left to right to solve that! 6/2(1+2) = 6/2(3) = 6/2 × 3 = 3 × 3 = 9 48/2(9+3) = 48/2(12) = 48/2 × 12 = 24 × 12 = 288 It can be written as: 6 ----- (1+2) = 3(3) = 9 2 48 ------- (9+3) = 24(12) = 288 2 The Coefficients are 6/2 and 48/2 They are fractions bar!!!! Include the concept of Algebra: x/2(9+3) = 288 x/2 = 288/(9+3) = 288/12 = 24 x = 24(2) = 48 48/x(9+3) = 288 48/x = 288/(9+3) = 288/12 = 24 x = 48/24 = 2 48/2(x+3) = 288 24(x+3) = 288 x+3 = 288/24 = 12 x = 12-3 = 9 48/2(9+x) = 288 24(9+x) = 288 9+x = 288/24 = 12 x = 12-9 = 3 48/2x = 288 24x = 288 x = 288/24 = 12 So should be nine!!!!

[@Kyrelel]

6/2(1+2) = 1 48/2(9+3) = 2 You're welcome

[@isaacogunmuko3947]

@@Kyrelel 6÷2(1+2)=9 PEMDAS: Parentheses Exponents Multiplication Division Addition Subtraction BODMAS: Brackets Order Division Multiplication Addition Subtractions Note: Brackets/Parentheses first means to find the value of what's inside the parentheses. (1+2)=3 is solving parentheses first. 2(3) means to multiply 2 *3 = 6, note this is multiplication not Parentheses. In both Multiplication & Division are done left to right, Addition & Subtractions are done left to right P: (1+2)=3 B: (2+1)=3 E: None 0: None M&D: 6÷2(3)=>6÷2*3=3*3=9 D&M: 6÷2(3)=>6÷2*3=3*3=9 A&S: None A&S: None

[@notahotshot]

In both PEMDAS and BODMAS the multiplication, and division have equal priority, and are solved left to right. The same is true of the addition, CX and subtraction. The mnemonic helper is deficient in that it does not make this clear.

[@allenhelmer8418]

There is no ambiguity. 2 is the coefficient of the 2(1+2) expression. Since coefficients are part of the expression they modify, then the 2 is part of the parenthetical expression. That means that the multiplication is done during the P step if PEMDAS is properly applied.

[@Araqius]

Totally wrong and nonsense. The word coefficient is used only in polynomial. "Since coefficients are part of the expression they modify, then the 2 is part of the parenthetical expression." 2^2(1+2) = 12, not 64 " That means that the multiplication is done during the P step if PEMDAS is properly applied." LOL. 2(3)^2 = 18, not 36.

[@allenhelmer8418]

Araqius "The word coefficient is only used in polynomial." In addition to being wrong, it suggests that you don't even know what polynomial means. When you add exponents to an expression, it changes the nature of the expression. Haven't you yet figured out that your exponential arguments are incorrectly applied and therefore irrelevant? If your arguments keep relying on irrelevant exponential mathematical trickery, then don't even bother trying. And, on top of that, your argument isn't even correct. 2^2(1+2) is 2^(2(1+2)), which is indeed 64. (2^2)(1+2) is 12.

[@Araqius]

"Araqius "The word coefficient is only used in polynomial." In addition to being wrong, it suggests that you don't even know what polynomial means." LOL. Type in google "definition of coefficient purplemath" and here is the result. Polynomials: Definitions / Evaluation - Purplemath www.purplemath.com/modules/polydefs.htm If the question is 2(3)^(-1) then there is no coefficient because it is not a polynomial term. Also, here is what the site say. "Any term that doesn't have a variable in it is called a "constant" term" "the constant term doesn't have a coefficient." Please show me the definition of polynomial and show me how "The word coefficient is only used in polynomial." is wrong. "When you add exponents to an expression, it changes the nature of the expression. Haven't you yet figured out that your exponential arguments are incorrectly applied and therefore irrelevant? If your arguments keep relying on irrelevant exponential mathematical trickery, then don't even bother trying. " LOL again. Here you cannot even explain why "it changes the nature of the expression." or why "my exponential arguments are incorrectly applied and therefore irrelevant". Why does adding exponents changes the nature of the expression while adding multiplication, division, addition, and subtraction doesn't change the nature of the expression? You are using your stupid trick, "If you cannot explain it just keep saying "It's wrong.".". Also, take a look at 2^2x where x equals 1+2. This means 2^2x is 2^2(1+2). Now, 2^2x has no parenthesis so how the hell can it be called "parenthetical expression"? Why don't you just shows me all the definitions of the parenthetical expression? If you cannot even explain anything, then don't even bother trying. Oh, please provide a proof from a reliable website or a textbook. Don't make it up on your own. And, on top of that, your argument isn't even correct. 2^2(1+2) is 2^(2(1+2)), which is indeed 64. (2^2)(1+2) is 12. LOL again and again. Multiplication by by juxtaposition, implicit (implied) multiplication, or multiplication where the multiplication sign is omitted has lower order than exponent. Type in any scientific calculator and you will find that 2(3)^2 = 18. (2(3))^2 = 36 18 =/= 36

[@allenhelmer8418]

Araqius Instead of homing in on websites with incorrect definitions, why don't you broaden your horizons and try to learn what those words *actually* mean. "Now, 2^2x has no parentheses, so how the hell can it be called a 'parenthetical expression'?" It's not, you fucking moron. 2^2(1+2) isn't a parenthetical expression, either. It's an exponential expression. Do you remember what I said about adding exponents changing the nature of the expression? Ah, I think I have figured out what you might be getting at and it shows how little you know. If you had enough experience with math, you might have noticed that variables are given preferential treatment as if they were parenthetical expressions. That's because variables are parenthetical expressions in disguise. You know what a parenthetical expression is. Don't be stupid. And again you are ignorantly doing the same stupid argument without any apparent awareness of its irrelevance. When you add exponents to an expression, it changes the nature of the expression because exponents are part of the expression that they modify. Since coefficients are also part of the expressions that they modify and exponents have priority, then the exponent is taken care of during the parenthetical step, just like the coeffient, but before the multiplication of said coefficient. So, your example, using correctly applied PEMDAS: Start: 2(3)^2 P step (E substep): =2(9) P step (MD substep): =18 Do you understand enough to stop using that stupid example, yet?

[@SteinerSE]

Where do you get this idiotic notion that there are coefficients in arithmetic? Only variables have coefficients (other than the natural coefficient of 1 all natural numbers have)

[@Somewhat-Vexing]

Did anyone else notice the sneaky extra pair of brackets? Minute 1:57 Minute 3:00

[@priyeeshofonie9615]

JV G i did

[@harrymatabal8448]

6÷2×3. How many of you agree that it is the same as 6×1/2. ×3. That what you have been taught in primary school. You don't need a bachelor's degree or a spinsters degree.😂

[@1993JoshG]

Allow x=1+2 or 3, 2x=2 (3), =6 Answer is 1

[@Araqius]

The answers is 9. 2(3) is just another way of writing 2*3. 6/2*(1+2) = 3*3 = 9

[@mathstar9064]

@@Araqius 2(3) is just another way of writing 2*3.WRONG !! 2(3)= (2*3)

[@Araqius]

@@mathstar9064 Lmao. 2(3)^2 = 18 (2*3)^2 = 36 2^2(3) = 12 2^(2*3) = 64

[@Kyrelel]

@@Araqius Not sure why you are laughing, math star is correct.

[@Araqius]

@@Kyrelel You knows nothing about math.

[@realtoastymilk8416]

Usually for PEMDAS taught from my school it was P Parenthesis E Exponents MD Multiplication + Division Left to Right AS Addition + Subtraction Left to Right And so I would get 9 and I would think this would be the right answer

[@kennethjmccaslin5567]

It would be nice if those putting out videos as an authoritative voice on a subject actually understood what they are talking about instead of blathering on such nonsense.Pemdas and bodmas are the exact same thing simple using different terminology. The rules and the steps are precisely the same when correctly applied. Whether you call them brackets or parentheses in the system terminology, the rule is the same. The maker of this video made a mistake at step one by failing to properly resolve the parentheses-brackets BEFORE moving to the next steps in the process. There is a solution and no ambiguity! The problem this presenter has is he does not know the actual full process of how to correctly eliminate parentheses from an equation. He obviously does not know the place, purpose, and correct application of the parenthetical multiplier in mathematical equations. This is evidenced by the fact he simply drops the parentheses or brackets out of the equation where that shortcut does not apply. Whenever you have parentheses or brackets, the parenthetical multiplier is either given or understood to be 1. The parenthetical multiplier is part of the parenthetical equation that must be resolved in order to eliminate the parentheses or brackets before moving on to the next steps to solve the entire equation. The first step in bodmas and pemdas is to eliminate parentheses and brackets by fully solving any such parenthetical equations contained in the overall equation. This is a 2 part operation or process: First, solve the problems inside the parentheses or brackets. The answer is still within the parentheses or brackets; this part does not eliminate the parentheses or bracket. I.E . (1+2) = (3) and 2(1+2) = 2(3) Second, finish the parenthetical equation to eliminate the parentheses or brackets by multiplying the result inside the parentheses or brackets by the parenthetical multiplier outside the parentheses or brackets. NOTE: Here is where the shortcut comes into play and causes the controversy. When no parenthetical multiplier is shown, it is understood to be 1, so multiplying the sum inside the parentheses or brackets by one equals the sum inside the parentheses or brackets, so the parentheses or brackets are simply dropped out without having to think about exactly how the are eliminated. So: (1+2) = (3) are parenthetical equations with an understood parenthetical multiplier of 1; and are the short form of 1(1+2) = 1(3); and 3 x 1 = 3 Because the parenthetical multiplier is 1 and anything multiplied by 1 is itself, this is written with the shortcut as (1+2) = 3 However the shortcut cannot be used when the parenthetical multiplier is not1.

[@kennethjmccaslin5567]

Continuing with my post: When the parenthetical multiplier is a value other than 1, the shortcut does not apply. IE : 2(1+2) is a parenthetical equation with 2 being the parenthetical multiplier which must be resolved in order to complete remove the parentheses from the equation. So the parentheses or brackets are eliminated by the two part process first solve inside the parentheses, then multiply that result by the parenthetical multiplier BEFORE moving on to further steps in the pemdas or bodmas process. When you multiply the result in parentheses or brackets by the parenthetical multiplier, you are competing the parenthetical equation necessary to finish the parentheses or brackets step, you have not gotten to the multiplication and division from left to right step of the pemdas or bodmas process. So : 2(1+2) is resolved as: 2(1+2) = 2(3) and 3 x 2 = 6 In equations 2(3) and 2x3 are not the same expressions. 2(3) is a parenthetical equation and 2x3 is the multiplication process by which the parenthetical equation is being solved to eliminate the parentheses or brackets. Thus trying to shortcut and write 2 x3 instead of 2(3) in an equation is error as you remove the parentheses or brackets without completing the math required to do so in the parentheses or brackets step, and are adding values to change the multiplication and division to be done in later steps of the pemdas of bodmas process. So: the equation 6/2(1+2) is properly solved by : 6/2(1+2) = 6/2(3) = 6/6 = 1 The error of failing to complete the math required to eliminate parentheses or brackets in the parentheses or brackets step results in 6/2(1+2) = 6/2x3= ERROR = 3x3= WRONG ANSWER This equation has no ambiguity and has only 1 answer. The correct answer is 1 to this equation as written is 1.. The equation that correctly results in an answer of 9 is very similar... just add a multiplication sign between the 2 and the parentheses. 6/2x(1+2) Here the parenthetical multiplier is 1. 6/2x(1+2) = 6/2x1(1+2) = 6/2x1(3)= 6/2x 3

[@kennethjmccaslin5567]

I challenge syed institute to admit error up to this point and put out a video explaining the proper way to eliminate parentheses and brackets and educate the public on the proper role and function of the parenthetical multiplier in these forms of equations. Take what I have given, study it. You will come to understand that this entire controversy stems from improper and overuse of shortcuts and a lack of understanding of the intricate details of the mathematical process involved when such shortcuts are overused.

[@LiracyonLeague]

Distribution happens before division. Simification takes places before you multiply or divide. 1 is the only answer.

[@RS-fg5mf]

You FAIL to understand and apply the Distributive Property correctly... 6/2(1+2) Distributed equals 6/2×1+6/2×2= 3×1+3×2= 3+6=9 6/(2(1+2))= 6/(2×1+2×2)= 6/(2+4)= 6/6= 1 Two different expressions with two different answers...

[@Araqius]

The correct answer is 9. 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 + 2/2 = (4 + 2)/2 (4/2 + 2/2)(3) = (4 + 2)/2(3) (3)(3) = 6/2(3) 6/2(3) = 9

[@TegridyMadeGames]

Its 9... you do order of operations left to right, if the problem is written left to write (especially with DIVISION SYMBOL as you are using) you assume (6÷2)*(1+2)

[@GanonTEK]

It just depends on which interpretation of multiplication by juxtaposition you use. Academically, juxtaposition implies grouping and multiplication (1). Literally, juxtaposition implies multiplication only (9). Both use the same order of operations after the implicit notation is interpreted. It's just an arbitrary convention since notation is a form of language. You can't prove notation using maths rules in the same way you can't prove English using laws of physics. This is because they are language independent. Both answers are correct since both conventions are in use. Depends on the scientific calculator too and 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 9: 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. 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 which implies grouping (1). 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 (1). TI later changed to the programming/literal interpretation (9) but when I asked them were unable to find the reason why. Some commenters have said it was pressure form American teachers but I've no confirmation of that. You can see more information on the Harvard and Berkeley maths ambiguity pages and the PEMDAS Paradox, a paper by a PhD student on this.

[@smallk6453]

1

[@DarelArtetxe]

el orden es importante.

[@Wehn.]

How has anyone not noticed that if you input it as 6÷2(1+2) the answer is 9 But if you input it as 6÷(2(1+2)) the answer is 1.

[@Wehn.]

Pause the video at 1:56 and you will see what I mean

[@OtakuTalkOD]

@@Wehn. because it literally becomes a different problem the first is (6/2)*(1+3) and the second would be (6/(2*(1+3)). Its not about noticing so much as its obvious.