Where does factorial fit in the order of operations?

Is ? I think not.

Is ? Now I’m not so sure.

What about 3^n!=(3^n)! ?

So is it PEMDFAS?

Or PEFMDAS?

Or PFEMDAS?

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The mathematics I encounter in classrooms

Where does factorial fit in the order of operations?

Is ? I think not.

Is ? Now I’m not so sure.

What about 3^n!=(3^n)! ?

So is it PEMDFAS?

Or PEFMDAS?

Or PFEMDAS?

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This entry was posted in Problems (math) and tagged bedmas, factorial, order of operations, pemdas, permdas. Bookmark the permalink.

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Parentheses are always first. Factorial is in the next group.

See http://en.wikipedia.org/wiki/Order_of_operations in the programming language section.

I wonder if Christopher was really asking this question.

My thinking is that the ! applies to the term to the left (as with exponents). So, 2*3! = 2*6 =12 whereas (2*3)! = 6! = 720. But if my audience finds the first expression ambiguous, maybe it’s up to me to communicate my intended meaning more clearly as 2*(3!).

Interestingly, to me at least, is that whether we’re talking factorial or exponents, it is my understanding of brackets as grouping symbols, not BEDMAS or BFEDMAS, that determined how I evaluated the expressions above. It’s similar for something like 2*(3 + 4). Grouping, not following a checklist.

What about absolute value? logs? sine? nCk? What might that mnemonic look like? Or, maybe just an F to represent any function? Just think about how the F in PFEMDAS or PEMDFAS could enhance ‘Please Excuse My Dear Aunt Sally’.

Fun fact: In the U.K., it’s called BIDMAS (Brackets, Indices). One could postulate that factorial is an index, much like an exponent or root.

This comment came in from a dear colleague via email: