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.