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PEMDAS

As a math educator, I get many requests from former students. The variety of questions is great, rather than having to always focus on the best way to teach division of fractions.

An example is an unexpected note from T.S. (WWU). I had him in calculus for two terms, when he was a freshman and planning to become a math teacher. Now, he about to graduate, and is focusing on a computer science degree.

Nonetheless, this is his e-mail note:


Hey Jerry

First of all long time no see, hope you are doing well.

Last Friday we were covering stuff in my Csci 401 class regarding how to deal with the order of operations in programming. In modern languages, the order of operations is taken for granted but we are studying how exactly to get a computer to parse an expression to evaluate on a primal level. This brought up something I've never really thought of before. We take the order of operations for granted today, but where exactly did they come from, who proclaimed "This is the way it shall be!"? I figured you might be able to shed some light on this question of mine.

Thanks for your input, hopefully I'll see you around soon.


Caught off-guard, I realized that my focus on teaching the history of mathematics was not helping me. In fact, I had never thought about it...which makes it a great question to me.

Below is my response after some research....


T.S....

Good question....I do not know the answer, but in my search, found these resources helpful (though not definitive):

This should help....hope all is well, and thanks for the question.

What would you have said? Do you know the answer or history to PMDAS? If so, please share it so I can post it...and I will also send it on to T.S.


M.J. (Belliingham) adds these Wikipedia qualification: "There are examples, including in published literature, where implied multiplication is interpreted as having higher precedence than division, so that 1/2x equals 1/(2x), not (1/2)x. For example, the manuscript submission instructions for the Physical Review journals state that multiplication is of higher precedence than division with a slash, and this is also the convention observed in prominent physics textbooks such as the Course of Theoretical Physics by Landau and Lifshitz and the Feynman Lectures on Physics. Additionally, Wolfram Alpha considers that implied multiplication without parentheses precedes division, unlike explicit multiplication or implied multiplication with parentheses. 2*x/2*x and 2(x)/2(x) both yield x2, but 2x/2x yields 1.[7] The TI 89 calculator yields x2 in all three cases.

Textbooks, tutorials and teachers generally highly recommend taking care to avoid writing potentially ambiguous expressions, using a horizontal fraction line format in handwritten documents or if mathematical typesetting is available, or by inserting additional parentheses.

Many programming languages use precedence levels that conform to the order commonly used in mathematics, though some, such as APL and Smalltalk, have no operator precedence rules (in APL evaluation is strictly right to left, in Smalltalk it's strictly left to right)."