- Thread starter TheJason
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18\(\displaystyle \dfrac{2(3)^{2}}{2}\)

Is the top 36 or 18?

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Do the parenthesis first: \(\displaystyle 3^2 = 9\)

So

\(\displaystyle 2(3)^2 = 2 \cdot 9 = 18\)

-Dan

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Side note: If one cancels the common factor of 2 first, then …Do the parenthesis (sic) first …

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You need to know that 2(3)

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WHY: well there is absolutely no way to force: authors of computer languages, makers of calculators, members of the MathEd hierarchy and/or publishers of mathematics textbooks to agree on any one standard. For the last fifty years I have been in that mix.

I see no way to declare one correct answer.

For what it is worth I vote for 9 as a final answer.

PEMDAS does not cover every operation, however. My favorite example is \(\displaystyle -3^2\). Is this interpreted as \(\displaystyle (-3)^2 = 9\), or \(\displaystyle -(3^2) = -9\)? It can be reasoned that it should be interpreted as \(\displaystyle 0 - 3^2 = -9\), as there is an implicit leading zero. However, in applied fields such as computer programming, it can instead be reasoned that the \(\displaystyle -\) symbol denotes

Wikipedia uses the same example and suggests that there is no universal rule in this situation--the context determines its meaning. Once again, parentheses help to circumvent the possibility of misinterpretation in the event the reader doesn't happen to know the intent of the \(\displaystyle -\) symbol.

As an aside...

In computer lingo, the order of operations is called operator precedence, which has its foundations in mathematics and is unambiguously defined for all operations (in before someone brings up compound assignments). In most (all?) programming languages, the negation operation has higher priority than multiplication, even in languages (such as C in the link above) that don't have an operator for exponentiation.

Because operator precedence is completely unambiguous, parentheses are only needed when the order of operations needs to be modified. My go-to example (pun intended) for this is the expression

`a & b >> c`

, which shares the same precedence relationship as the expression `a + b * c`

. People have `a & (b >> c)`

to avoid confusion, "in case the reader doesn't know the precedence rules", yet they take no issue with `a + b * c`

being written without parentheses, "since the reader should already know that". The way I see it, if you know that multiplication happens before addition, you should also know that right shift happens before bitwise AND. If you Ultimately, those people get the last laugh: gcc has a warning for those cases "whose precedence people often get confused about". If I want my code to compile without warnings in all cases (enabling all warnings is considered good form), I have to use those redundant, unnecessary, condescending, space-wasting parentheses. *grumble*

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Agree. When we teach order of operations and grouping symbols, we ought to include how to parse factors.… 2(3)^{2}means 2*(3)^{2}… before you multiply you need to know what you are multiplying …

\(\;\)

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When I look at that example, I see (-1)(3… PEMDAS does not cover every operation … My favorite example is \(\displaystyle -3^2\) …

\(\;\)

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That is just how I think of it.My favorite example is \(\displaystyle -3^2\). Is this interpreted as \(\displaystyle (-3)^2 = 9\), or \(\displaystyle -(3^2) = -9\)?It can be reasoned that it should be interpreted as \(\displaystyle 0 - 3^2 = -9\), as there is an implicit leading zero.

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solve parenthesis first. so, you will get 18 as the numerator.\(\displaystyle \dfrac{2(3)^{2}}{2}\)

Is the top 36 or 18?

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Actually, "parentheses first" doesn't help here; all that says is that you evaluate (not "solve") the 3 before doing anything else. What matters here is "exponents first" (before multiplication).solve parenthesis first. so, you will get 18 as the numerator.