Originally Posted by MoonlitSunshine
(Post 1045317)
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.
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