6/2*(1+2)=?
 

I've seen some debate about what the answer is to this, and its a chance for all of you to flex your mathematics muscles. Is the answer 9 or is it 1?

Getting 9 is a case of doing 6/2=3 * 1+2=3 therefore 3*3=9.

Getting 1 is a case of doing 2*(1+2)=6 and it becoming 6/6=1.

I say the answer is 9. Which would you say is right, and why? GO!!!

You're always taught to do whats in paranthesis first.
After that you multiply or divide from left to right.

So...

6/2*(1+2)=?

Parenthesis -
6/2*(3)

Divide -
6/2 = 3

Multiply -
3*3 = 9

The answer is 9 you are correct.

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

Parentheses
Exponents (and Roots)
Multiplication
Division
Addition
Subtraction

This is like sixth grade math guys, seriously.

Mathematical Order Of Operations

Multiplication and division are grouped together, so if that's all you have you just go from left to right. Same with addition and subtraction.

I was always taught BODMAS, which puts division ahead of multiplication. Thats why I have the 6/2 and (1+2) as separate equations.

Edit: And as storymilo says, multiplication and division are grouped. So the only way oojay's way works is if he adds another set of parenthesis around the 2*(1+2), which would make the 6.

I learned the order of operations as:

Brackets (parentheses)
Exponents
Division
Multiplication
Addition
Subtraction

So therefore, the answer is 9

You needed a thread for this?

I learned PEMDAS, that is

Parentheses
Exponents
Multiplication
Division
Addition
Subtraction

But the only reason division is after multiplication (and subtraction is after addition) is that you can't have two letter in the same spot. They get the same priority.

The answer is you need more parentheses.

Short answer: You're always taught BOMDAS (Brackets Order Mult Div Add Sub) over here, but...

Mathematically correct answer:

Multiplication does not precedence over Division. Division is defined as the inverse of multiplication rather than being a separate operator: if a is a number 1/a is it's inverse. That is, a*(1/a) = 1. Similarly, (x*a)/a = x, since a/a = a*(1/a) = 1.

The result of this is, you cannot define an operator or it's inverse taking "precedence". In fact, you cannot define any operator taking precedence over another, as that is the realm of ambiguous convention. You might as well just say 1+1 = 3 while you're at it. The only true mathematical description of precedence is through the use of parentheses, as that is their explicit function. The fact is that the order in which operators are evaluated is a dangerous form of shortcut which honestly shouldn't be taught.

To give an example. You are taught BOMDAS in schools here, that is to say, multiplication before division. So in this circumstance, 6/2*(1+2) = 6/6 = 1.

However, if you use any calculator, it will evaluate the operators in the order they come up. If there is an addition, or subraction, it will simplify everything before the sign and then simplify everything after it, but if the only operators outside parentheses are * and /... well, I'll show you.

This is directly from Google Calculator:

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

As you can see, it simply took the first operator, simplified it, and then did the second, regardless of what order they were in.

Conclusion: The statement is ambiguous. In order to have a "true" answer, another pair of parentheses needs to be added.

This is what i was taught also.

But then wouldn't the answer be different than what it should be?

Lol @ "this is like sixth grade math guys, seriously" and then you got it wrong.

Multiplication and Division are interchangeable.
Just like addition and subtraction.

What do you mean? The answer should be nine... it is nine. I think Kirby had it right before but basically:

6/2*(1+2)

Everyone agrees that parentheses go first. So

6/2*3

Multiplication and division both have the same priority, and since that's all this problem contains, we just move from left to right.

6/2 = 3

3*3 = 9

The standard order of operations, or precedence, is expressed here:

Terms inside Parenthesis
Exponents and Roots
Multiplication and Division
Addition and Subtraction

This means that if a mathematical expression is preceded by one operator and followed by another, the operator higher on the list should be applied first. The commutative and associative laws of addition and multiplication allow terms to be added in any order and factors to be multiplied in any order, but mixed operations must obey the standard order of operations.

Multiplication takes precedence over Division, as Division is the inverse of it, deeming Multiplication the "positive" operation.



THE ANSWER IS STILL 1

You can LOL all you want, but the answer is 1, not 9. Read a math book.

I see it now, it's just not the way I learned it. Doesn't mean that it's wrong to use that system. I just asked because oojay answered using the exact same formula, but then got the answer wrong.

You were correct until the bolded part. Just as division is the inverse of multiplication, multiplication is the inverse of division. It works both ways. Neither should be dealt with before the other, unless they come first in the equation.

I'm just gonna quote this seeing as everyone apparently missed it last time :P You're all right, and wrong.

Yeah... oojay's fatal flaw is his conviction that multiplication is always done before division.

The answer is definitely nine. You can't just move parentheses about... they're in the equation for a reason.

Neither takes precedence over the other. It goes from left to right.

http://www.onlinemathlearning.com/im...es/pemdas1.gif
Order of Operations - PEMDAS (with worked solutions & videos)

Every math textbook you read will tell you this.

Regardless of left-to-right, Multiplication always takes precedence over Division, as Addition always does over Subtraction. You must simplify it into the most basic terms before performing the "left-to-right" mathematics. The correct order is as follows:

Parenthesis
Exponents
Multiplication
Division
Addition
Subtraction

Applying that to the equation: 6/2*(1+2) will yield:

Parenthesis: 6/2*(1+2) = 6/2*(3)
Exponents: 6/2*(3)
Multiplication: 6/2*(3) = 6/6
Division: 6/6 = 1
Addition: 1 = 1
Subtraction: 1 = 1


THE ANSWER IS 1

To me, it looks like an expression simplifiable (is that a word?) to 3*3, so I'd say 9.

There aren't any exponents in the equation, though.

Well I guess I'm not eloquent enough to simply convince you, so perhaps this will help?

Order of Operations

edit: check example three

This was pointed out earlier, but when I put it into google, I also get 9.

omgsh, there's even exercises on that page! Time to practice math!

Ha it's just the first google result when you search "order of operations." It's not meant to be demeaning.

It is not a fatal flaw, it is a fact:

PlanetMath: order of operations

So once again:

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

THE ANSWER IS STILL 1

There seems to be disagreement with everyone's internet sources, and our own personal mathematical teachings. Whether this varies by country or textbook, I'm not sure. The order of operations is clearly different in each of our sources. Hmmm, what to do...

I guess I'll stick to my way and you to yours? I've always been taught that multiplication does not take precedence over division. In fact I'm still being taught that. That link of yours is the only source I've ever seen that says otherwise, but maybe things are just different in other places.

edit: Nine is also the answer that comes up when I put the equation into my calculator.

I see you really read my post there. At no point did I say you could just move the parentheses around. The answer is ambiguous. The only way you can "solve" it is by using a convention, of which there are multiple, which this thread is clearly proving.

And I have always been taught the exact opposite. With multiplication taking precedence over division, and addition over subtraction. From grade school through high school, and even through my Calculus I,II, III and Differential Equations math courses at my University. It's astounding that something as finite as mathematic could be interpreted differently by different people.

...because the equation is ambiguous. I've been saying this for four pages :P

Same here, and I have a graphing calculator that cost me over $150. I'm hoping it's not spitting out crap.

When I plug it into both my Texas Instruments and Casio scientific calculators (the entire equation as it is written, not part by part) they both give me the same answer: 1.

Yeah, I always assumed it was the same everywhere. This thread has been an eye-opener.

That's interesting. I was almost certain that most math was taught the same way in the US and Canada, because our educational curricula are almost the same. Maybe it varies from state to state?

I've only been out of high school for ~3 years, so everything that I've learned is still pretty fresh in my little brain.

It really has. Perhaps I will learn more about different math formulas, etc, when I get to teacher's college.

I have a Texas Instruments too (a graphing one) and it gave me nine. Even our calculators are different...

I suppose if you were to look at the equation with all different orders in mind, it would be ambiguous. When you pick just one, it has a clearly defined answer. As it's presented, without any extra parentheses, the only way to solve it is to use an order of operations. So that's what I did.

It would seem it varies from state to state, as oojay is in Missouri and I'm in Connecticut.

"pick one" is not a solution. If you have a equation x + y = 5, you can't just "pick a y" and then assume your answer for x is correct. You need more information, namely a value for y, or in the case of this thread, extra parentheses to define whether the * or the / should be done first.