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

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Skip to 15 minutes if you just want to know the correct answer but if you do come back and check the reasoning behind the answer.

In this video we look 6÷2(1+2) - also written as 6/2(1+2).

This is a viral maths problem which has got people discussing, arguing and debating.

The debate finishes with this video as I give the correct answer. And the answer I have given in this video is the one agreed upon with most academics.

I look at BODMAS, BIDMAS and PEMDAS.

This video also applies to 48÷2(9+3) or 48/2(9+3).

I also used examples and definitions from higher level maths to give clarity to this problem.

I also showed how many common solutions to this problem are actually not correct.

Thank you for watching.

[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.

[manlikejoel]

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

[joshuadavid]

This shouldn't be a 9 min video 🤣

[NavyGuero]

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.

[geoffreyjones]

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.

[jojobaltan]

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".

[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

[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

[blalink]

(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.

[spaceranger]

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)

[isaacogunmuko]

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

[alpriore]

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.

[kendavis]

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 !

[snowdog]

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.

[stephanmashiter]

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'.

[kasper]

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.

[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 !!

[massacmongo]

No wonder Math is so unpopular with students.

[Kay]

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.

[Driftimator]

Multiplication and division are on the same level ( whichever comes first)

Same for addition and subtraction