6 ÷ 2 (2 + 1) = CORRECT WAY TO SOLVE

This is how to do the equation: 6 / 2 (2 + 1) = x to get the right answer of 9. This is the correct way. I also show how people are getting the wrong answer of 1. Post this on facebook to end this dumb argument forever. I am tired of having to explain this to every person I meet.

If anyone has any questions or arguments, post them and I will respond to them. This is the correct way to solve the equation.

[Blackout]

"the people getting it wrong are doing it incorrectly."

STATEMENT OF THE FUCKING MILLENNIUM!!!

[kurapikakurta]

Here's the problem in this situation. The obelus(➗) in this situation is interpreted differently in different parts of the world. Using its original meaning, everything to the left divided by everything to the right 6➗ 2(2+1) would've meant 6➗(2(2+1)). Plus the parenthesis just makes 2(2+1) is the ame way as writing 2a, where a=(2+1). If I were to write it 6➗2a, it's the same way as writing 6/2a(6 all over 2a). If I were to solve it as 6/2a i can cancel out 6 and 2 making it 3/a. Since a=2+1, then 3/(2+1) is 1. Don't need to stress out yours is the only correct way to solve this problem because depending on the programming language we are using, and the calculator you're using you'll get different results(try inputting this problem to a graph calculator you'll also get 1. I'm not bullshitting here math is my subject and even my grandmother who graduated valedictorian in highschool and cum laude in college and who is an accountant does it the same way as a lot math nerds I know here where I'm from. But I do understand that Math standardized exams may have a different rules on this one.

[slashingpunch]

Both answers 1 and 9 make sense. This is actually an example of ambiguous notation. Although some people will read this as 6÷2*(1+2)=9, it is also valid to read it as 6÷(2(1+2))=1. This is why we avoid using equations like these.

[noobie]

I like how the whole internet went crazy 9 years ago because of a simple math equation.

[broski]

in algebra, we learn that 6 ÷ 2y is the same as 6 ÷ (2y). Literally any math equations after learning algebra takes this approach

[johnli]

My take on evaluating 6 / 2 (2 + 1) is this:

1) Argument 1 using the so called order of operation - answer is 9

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

2) Argument 2 using simple mathematical convention - answer is 1

This is based on the fact that when expanding

A / B(C +D) = A / (BC + BD) since B is the common factor

In other words, B is closely associated with what's in the brackets,
almost like a function such as 2a or cos(a) which are taken as one entity, so

6 / 2 (2 + 1)
= 6 / (2x2 + 2x1)
= 6 / (4 + 2)
= 6 / 6
= 1

3) Argument 3 - solution is undefined as question is ambiguous (This is the correct answer)

The problem with writing inline equation is that if we're not careful we'll be causing all sorts of problems as the above arguments demonstrated where you can have two answers to a simple arithmetic question which in fact should have only one answer.

So the moral of the story is that:

A) If you expect the answer to be 9 and you try to represent

6
---- (1 + 2)
2

then you should write it as (6 / 2) x (1 + 2) = 3 x 3 = 9

or better still write it as 6( 2 + 1) / 2 = (6 x 3 ) / 2 = 9

B) If you expect the answer to be 1 and you try to represent

6

2 (1 + 2)

then you should write it as 6 / (2 (2 + 1)) = 6 / (2 x 3) = 6 / 6 = 1

The fact that people, even mathematicians have to debate whether the answer should be 1 or 9 on this simple arithmetic primary school question is already a prove in itself that the problem lies with the question where you can interpret it in different ways and come up with different answers. The beauty of mathematics is that you can use different ways or methods to arrive at the same answer. Maths also teaches us to have an open mind and to accept that different people have a a different approach to solving problems and yours is NOT the only method or the only right method that works or that Bodmas is the ONLY rule on earth and to be ignorant of general sound mathematical principles and tchniques. For example:

Evaluate 875 x 99 + 875 x 1

Now Bodmas will say you have to do the two multiplications before the addition but not so because if you factorise

875 x 99 + 875 x 1 = 875 (99 + 1) = 875 x 100 = 87500

And you don't need me to tell you which is quicker especially if you don't have access to a calculator.

Now, using brackets is cheap and free, so may as well use it if they can overcome any ambiguity to explicitly represent what you're trying to convey, whether we're trying to write inline equations on paper or to code an equation or formula in a programming language such as C++, Ada or Python.


Imagine a software engineer writing a piece of flight critical software in Ada to compute the coordinates of latitude and longitude of a moving target you're trying to intercept with a missile and he meant to represent:

A
Target Lat =
B(C + D)

Instead of writing
Target_Lat := A / (B*(C + D));

he mistakenly writes
Target_Lat := (A / B)*(C + D);
or
Target_Lat := A / B*(C + D);

And the result would be catastrophic because the first one is coded wrong and the second one he's relying on the compiler to decide what should be calculated first rather than telling the compiler explicitly what to do with his calculations! Of course in real life, to calculate lat and long would involve much more complex functions such as sine, cosine, velocity, direction, time, distance, etc.

[GeoffreyHowells]

From a historic advantage... According to mathematical order of operations prior to 1917, the correct answer would have been 1

[oldstudent]

I have a degree (as in Ph.D.) in mathematics. The order of operations allows terms to be calculated because the 2 in something like 2x is always part of this term, this avoids needing parenthesis in all sorts of algebraic terms.

You are doing it incorrectly, the answer to this non-problem is 1.

[TheRealBigSol]

Here is the correct solution that I shared on Facebook. Maybe I should do a video.

Solution time. 6÷2(1+2) = 1. Here's why:

Everyone remembers PEMDAS. That's awesome, but the distributive property applies here as well. To solve, say the equation as a number sentence.

Six divided by twice the sum of one and two.
6÷2(1+2)

The 2 to the left of the parentheses is connected to that value as described by the distributive property which says a(b+c) =ab + ac. The 2 in this case means double the value inside the parentheses. It is not a 2 to do with what you will.

So...6÷2(1+2)
=6÷2(3)
=6÷6
=1.

The only way the answer could be 9 with these numbers is to group them like this:
(6÷2) * (1+2). The distributive property would not apply here and the multiplication symbol clearly separates the two values.

[northerngryphon]

2(2+1), without a multiplication sign, is a polynome, like 2a. It means two of whatever is between the brackets. The equation is 6/2a. It is not 6/2*a.

[gabrielesimionato]

Call (2+1) as x
You have:
6/2(x), or 6 / 2x if you prefer. Since x is 3, the output is still 6 / 6 = 1

[TheSpeedracer]

try this
f(x)
f(1+2): 6÷2x = 1
NOT 9.

[marcostecca]

Why doesn't anyone get it? 2(... is not a normal multiplication, it is more. In fact, if you wrote it like this:
6/2y

where y is (2+1) you would never say it's 6 divided by 2 and then multiplyed by y. Since 2 is a coefficient of (2+1) it has priority on whatever.

If you say it's 9 you say 6/2y = (6/2)*y, that's not true at all.

[dogwithwigwamz.]

The narrator doesn`t seem to see that 2(2+1) is one term. Ref : examsolutions.
Also, enter into any reasonably sophisticated Scientific Calculator 6/2(2+1) and then enter =. The answer is 1.

[caperUnderscore]

This information is worthy of its own comment.  It was explained in a sub-comment somewhere else and is buried:

A renowned mathematician explained why this solves for 1.
I explained why it solves for 1.  I am a computer engineer.
I asked other engineers from various fields. All solved for 1. One of them did solve for 9 initially and when they asked what I solved it for and I told him, he changed his answer voluntarily. 
A research scientist solved it for 1. 

The question is: HOW do we get 1 as a solution ??

The answer is simply and is best explained by Texas Instruments:

_"Implied multiplication has a higher priority than explicit multiplication to allow users to enter expressions, in the same manner as they would be written. For example, the TI-80, TI-81, TI-82, and TI-85 evaluate 1/2X as 1/(2*X), while other products may evaluate the same expression as 1/2*X from left to right. Without this feature, it would be necessary to group 2X in parentheses, _*_something that is typically not done when writing the expression on paper._*_"_

There you have the explanation. It is a convention used by people reading and writing papers to avoid over-cluttering their work with parentheses so that a machine or software program will solve it the way they intended to. 
Example: 

On paper we will write: abc / xyz
This is equal to (((a)(b))(c)/((x)((y)(z)))

The first expression is easily read and we continue on. The second example, one would have to consider each and every parenthesis to ensure the order.  What if there was a parenthesis missing? Then the reader would have no idea of the intended meaning.  So instead of wasting time deciphering a myriad of parentheses, we omit them on paper, and through education, we learn where there are implied parentheses. In 6/2a we take it to mean 6/(2a). If a=3, then we have 6/2(3) = 6/(2(3)).  Again, on paper we keep parentheses to a minimum.  If we already know that 6/2a = 6/(2a), then we choose the one with LESS parentheses.  Keep in mind that THIS IS A CONVENTION.  
Let us look up the word _convention_:
*Convention*: A mathematical convention is a fact, name, notation, or usage which is *generally* agreed upon...

_"A convention is a choice made because it is convenient"_

_"some notation and terminology, while standard at the high school level in many countries, may be different from those used in other countries _*_or from those used at higher or lower levels of mathematics._*_ Because it is impossible to ascertain which notation and terminology should be clarified for an individual test taker, more material than necessary may be included."_

Therefore, by our(my) convention, we(I) solve this equation as ONE.  

I am *not* saying that if you solve it for 9 that you are wrong either. You are using a different convention from me, obviously. 
It is necessary to state your convention when there is a possibility of more than one convention that can be used. 

Now let's analyze how it solves for 9:
If we have for example, 6/2a, and we let a=3, then we would need to solve it as follows:
6/2a   = 6 / 2 * a.     let a=3:  
6/2(3) = 6 / 2 * (3) = 9

In the above case, all multiplication is explicit and there are no implied parentheses.  This is a perfectly acceptable convention as well. 

Now, after reading all that, I hope you all understand the differences in convention. Remember, we are talking about human beings doing math usually on paper. It is a different can of worms when you want to use software programs because those were designed by a person or persons who controlled which convention was programmed into the software.
You must figure out how the program works and handles your problems and use parentheses around things we normally wouldn't.  

I hope this helps clear up some of the misunderstandings.  

[fausimo]

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

[jmosier]

you forgot to distribute before gotta distribute the 2 to the (1+2) which gives you (2+4). Then you'll have 6/(2+4) now you do pemdas which gives you 6/6 = 1

[ajborne]

The answer is still 1. You don’t use pemdas to solve 2(2+1). That is a distribution of (4+2) =6. If you take a 2 out of the brackets with distribution, it applies to the brackets and is part of the same expression. You must finish calculating the distribution of 2(2+1) before moving along the pemdas order of processing. Essentially 6 / 2(2+1) is NOT the same as 6 / 2 * (2+1). Because the first expression has a distribution in it.

[atheoangl_old]

I think the problem here is the *equation itself*. It's poorly written. And seriously, who still uses the obelus (÷)?

[dmattis]

We are taught that 2(1+2) means the 2 is bound to the parenthesis so we would read the equation as 6 / 2(1+2). There’s a reason it’s written as 2(1+2) and not 2*(1+2)