Originally Posted by storymilo

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.

Originally Posted by oojay

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

Originally Posted by Burning Down

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

Originally Posted by Kirby

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.

Originally Posted by storymilo

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

Originally Posted by oojay

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.

Originally Posted by MoonlitSunshine

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.

Originally Posted by Burning Down

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.

Originally Posted by MoonlitSunshine

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

Originally Posted by oojay

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