6 divided by 2 x 3
6 didvided by 6
= 1

No, the way you wrote that equation, it's 6 divided by the product of 2 times the sum of 1+2.

2(1+2) is one unit--you have to do that portion of the problem BEFORE you divide 6 by the answer. Otherwise, the 'sentence' makes no sense at all.

For your answer to be correct, the problem would have to be written this way: (6 divided by 2)(1+2)--that would mean 6 divided by two times the sum of 1 plus 3.

Sorry, but the answer is 1

I forgot to say that you always complete whatever is in the ()'s first, then go on to do the rest. And any number that is in front of the () is multiplied by the the sum inside (3.)

Just enter the equation in google, hit enter and you will get your answer.

Order of operations... Parentheses, Exponents, Multiplication & Division, Addition & Subtraction

I say "1", too .

o j

Hey, I said "1", also -- and even simple math has never been my "strong suit"! :>

Yup, it's 1.

Add what's in the parenthesis first. 2+1 = 3.

Then multiply the results (3) by the number immediately preceeding it (2). 2x3 = 6.

6 divided by 6 = 1.

I knew this in eighth grade...I was a math whiz back then, but I lost interest in math when I got to Calculus.

9 is the correct answer

Here is a link that might be useful: 6�2(1+2)=?

Sorry, Debby. The first answer says 9, as do a couple of others. But if you read the subsequent answers, the explanation and answer is 1.

the answer is 9...i originally thought 1 also then stopped and thought about the order of operation.. parenthesis first (1+2)= 3 then 6/2=3 x 3= 9 my DH's $400 engineering calculator also confirms it's 9. ~ liz

I don't like the way it's written (vague and in many cases would constitute "void for uncertainty"). Although Google says it's 9, and at first I went with 1 by the way it's written even though it's poorly written.

However, after pondering it and doing some research (it's been a while since my math school days so I needed to refresh my memory), I now am convinced that Google was correct. Had it been written 6 divided by (2(1+2)), or more properly 6/(2(1+2)) then it clearly would be 1 and Google agrees. In that case, the product of 2x(1+2) would have a priority but following the rules, given the way it's written, it cannot have the priority.

Here's why:

First the order of operations:
"PEMDAS": "Parentheses, Exponents, Multiplication and Division, Addition and Subtraction" PEMDAS can generate its own confusion; some students sometimes tend to apply the hierarchy as though all the operations in a problem are on the same "level", but often those operations are not "equal".
The order goes:
1) Parentheses
2) Exponents
3) Multiplication and Division (each with same rank = equal weight or importance)
4) Addition and Subtraction (each with same rank = equal weight or importance and are outranked by multiplication and division)

Order of operations also specifies that when operations have equal rank (weight or importance) you go from left to right. Generally it's best to simplify the statement as best possible and sometimes you work from the inside out which is what's required with this question.

So, by following the order and simplifying for clarity and illustrative purposes:
6 divided by 2(1+2)=6/2x(3) since 1+2 takes priority and 1+2=3
Then the equation is 6/2x3
Note that 2x3 does not take priority over 6/2 by order of operations as they have same rank and same rank always goes left to right.
Therefore, since 6/2=3 and 3x3=9, you simplify and it become 3x3 which equals 9
Therefore as demonstrated above, the correct answer is 6 divided by 2(1+2)=9

All would have been solved had it been better written for clarity. This is why there's laws both in life and even in math and arguments can rage on!

Ambiguity. Source of many problems. Much like what does this phrase mean:
You can never have too much water in the system.
A) It is dangerous to have too much water in the system
B) It makes no difference how much water you put in the system, it can't cause damage.

Well, it's kind of like a misplaced comma question (The panda eats shoots and leaves. The panda eats, shoots, and leaves.)

Is it 6/(2(2+1)) or is it (6/2)(3+1)?

I'm not really sure there is a correct answer, because the "puntuation" isn't clear.

Tally, it's

6/2(1+2)=? the slash is the division symbol, as I can't make that symbol even using the clipboard. It appears here as an empty box, which gets my message rejected.

we say 1

I say the answer is ONE.

Because when reading, the fact that they wrote out the words "divided by" the meaning is that the 6 is "divided by" answer of the rest of the statement.

Problems like this can by written as fractions with:
The numerator (number above the line) being 6
The denominator (number below the line) being 2(2+1)

That makes a fraction (after each is worked out) with 6 above and 6 below. Six divided by 6 equals ONE.
Like this:

6
________ =
2(2+1)

6
________ =
2(3)

6
_________ =
6

1

I think if it was all written out like an equation (in numbers) rather than a sentence, the answer would be nine.

Debby, I understand. But it can be read two ways:

6/2 times (1+2)

OR:

6 divided by (2 times (1+2)

In Mathmatical punctuation it could read as either

(6/2)(1+2)= 3X3 = 9

OR

6/(2(2+1)) = 6 divided by (2X3) = 6/6 = 1

Because the mathmatical "punctuation" is unclear, it could be construed either way. That makes it ambiguous as to which answer was intended.

Should also add that mathematicians and scientists are generally very prescise in their language.

My guess is that this question was intentionally written for ambiguity. Like the misunderstanding that can occur with misplaced punctuation.

That is why it is controversial.

Because when reading, the fact that they wrote out the words "divided by" the meaning is that the 6 is "divided by" answer of the rest of the statement

I wrote out "divided by" because as in my last post above, there is no symbol for division on my clipboard or keyboard.

The question as posed makes sense; It is not vague, but straight forward. The divisor is 2(1+2) or 2x3 or 6. Therefore, 6 divided by 6 is 1. Why would one need a calculator for this one?

The standard symbol for division on the keyboard is /

It's the tool in Excel for performing the calculation.

Debby,
Sorry, I missed that above.
What symbol was used?
The / also means "divided by"
I think in using the / the 6 before it would be on the top of the fraction, and the 2(2+1) would be the bottom of the fraction.
No no no, I'm beginning to see the other way!
In that case the 2 plus 1 would be handled first, and then working from left to right, the division would come before the multiplication. Then it would be NINE!

Oh, it is midnight, I need to go rest my brain!

You've asked what is 6 divided by another quantity (6) and the answer can only be 1.

On the other hand, if you had asked what is 6 divided by 2, times another quantity (3), then it would be 9.

Only a non-mathematician or someone trying intentionally to cause confusion would consider 9 a valid answer to the problem as posed.

Further, mathematicians don't write equations with words. They use symbols, and there is a universally recognized order of operations, and use of clarifying brackets, so that there is none of the ambiguity that was artificially injected by trying to state and interpret the problem in a non-standard manner.

So that nobody would be confused, a mathematician would write either:

6/[2(2+1)] = 6/(2*3) = 6/6 = 1, or
(6/2)(2+1) = 3*3 = 9

P.S.: This isn't a criticism of the original poster; it's just a reaction to the sad state of decline in math skills in this country. The tenuous grasp that many people have of the most basic mathematical concepts -- sometimes called "innumeracy" -- explains why this kind of question could even be making the rounds on Facebook, or cause people to think this was some fascinating paradox.

It *is* vague for people who want to interpret. However, if you follow the order of operations, the answer is clear and must be derived in a proper fashion following the rules that were established as far back as the 1500s. Math can't be subject to interpretation. You follow the rules. You can't say "I'd rather do it MY way!" or "I've always done it like this."

To get a correct answer you must take the priorities first, then work the remainder from left to right pursuant to the mathematical order of operations as I explained above.

jemdandy, the divisor is not 6, by order of operations, the divisor is 2. And no you don't need a calculator if you understand the rules and follow the rules but if you ignore them, then a calculator will show where you made your mistake since you used the wrong divisor. The calculator will follow the rules.

It's very easy to understand if you understand the established rules and not interject opinion as I almost did at first. The applicable rules here are basic:
⢠Do operations in parentheses and other grouping symbols first. If there are grouping symbols within other grouping symbols do the innermost first.
⢠Do multiplication and division operations from left to right.
⢠Do addition and subtraction operations from left to right

Course I s'pose we could build a time machine, go back in time and set up new rules! :)

The answer is 1. Brackets, Multiplication, Division. Doesn't matter what order the equation is in.

The answer is 1.

zeetera, are you saying that multiplication takes priority over division? If so, on what do you base that? The rules specify they're equal in rank and therefore you go left to right in processing the equation, as already explained above.

Long story put SHORT:

the 6 is divided by the total of what follows the / sign.

6 / 6 = 1

Yes, I'm just trying to get the last word in! lol AND let you know my poor little brain was rested!

The answer is 9. I thought it was 1, but DH says it's 9. He would know better than me, since he uses equations for a living.

If the answer is to be 9 then the phrasing would have to look like (6/2)(2+1).
No brackets, thus you do not divide 6 by 2 first.
Bracketed is always done first.

Susan. You're right...it's 1. If your husband thinks that the answer to the equation posted originally by debby_ab is 9, he should look at exactly how it's stated and see if he still thinks that.

And it makes my head spin around like the girl in the Exorcist that people are still looking at this as a complicated math question. I give up...I have to go now so I can prepare my application to emigrate to some other country!

He explained it to me, but I don't remember...lol.

Yeah, you're right. BOMDAS, from left to right if equal. But I remember being taught to do the brackets and then what was directly outside of the brackets.

So I read it as:

6
_______
2(1+2)

I still say 1. And, mathmatics aside, a bracket is this: [ ]. These (as in this problem) are parenthesis: ( ).

"Brackets" convey the idea. I was too lazy to look up and make sure that the plural of parenthesis is parentheses...which I just did and it is.

Quote"

The standard symbol for division on the keyboard is /.

Unquote.

It is true the the forward-slash ( / ) is the standard symbol division for computer math languages such as BASIC and FORTRAN. It is also used in mathematical expressions within Excel.

However, math and engineering books all use the shorthand notation for multiplication, e.g., 2(1+2) is interperted as 2 times the quantity (1+2). The times sign is "understood".

The problem is that computer programs and programing languages are not that smart; These have to be told what is meant to remove ambiguity. The example above written in BASIC would be: 2*(1+2). The "star" is used to denote multiplication. If I wanted to express 2 to the (1+2) power, it would be written: 2^(1+2).

If I wanted to write the function 6 divided by 2(1+2) in EXCEL, BASIC, or FORTRAN, it would be:

6/(2*(1+2))

Parenthesis (brackets) must be carefully used in computer math functions. There are strict rules that determine the operation. If the outer brackets were removed giving, 6/2*(1+2), the expression would be evaluated as 6/2 times (1+2) which would be 3 times 3 or 9. But notice this is not the original statement. Omitting the outer brackets has changed the computation and problem statement.

And you wonder why kids today cannot even make change in high school.
Math basics taught the old fashioned way had a bigger success rate than the new methods of confusing math.
1+1 will always equal 2. I don't care what anybody else says...LOL!!

maybe they've changed the rules of math since the 70's, but you "always" solve the equations in parenthesis first. Then if the equation calls for multiplication directly to the left of the parenthesis, then you multiply that number by the equation in parentesis. Once that is concluded, then you move to the farthest left of the problem and begin
to solve each equation until the entire problem is solved. In this problem, you begin with the equation (1+2). Then you find that it wants to be multiplied, so you multiply the equation by 2. Then you go to the furthest left (the beginning) and see that the solved equation (6) must be divided into 6. Therefore, the concluded answer can only be 1. I understand why some solve the equation in parenthesis first, then move to the beginning and divide 2 into six, and then multiplication last; to come up with nine. Although division and multiplication are equal in their operation, multiplication "ALWAYS" preceeds division in the operation of any mathematical conclusion to a problem. All mathematical equations within this problem must be solved by doing the multiplication before doing the division: if the division preceeds the multiplication. Here's why. What if the problem were:
2 divided by 2(1+1)= X What would your answer be? Those who said that the answer to this site's problem was 9, would say the answer to this problem is 2. However, the answer should be one half or .5 Remember, both problems began by asking you to take a (whole) number and dividing it by the results of solving the proceeding equations. Instance: 6 divided by .... = X Some said 9; while others said 1. How do you get an increase of 3 after adding 2 + 1 together, but then never ordering it to be added to 6? Notice that the problem ordered that 2 be multiplied to the equation (1 + 2); not 3. You would have to re-write the problem: 6 divided by 2 + 2(1 + 2) in order to get 9. The problem asked: What is 6 divided by 2 x (1 + 2)? The answer then correctly would be 1.

I say the answer is 1.

I don't care about the answer. The order of operations here is based on language.

My question is....

WHERE IS DEBBY_AB????