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## PEMDAS is Problematic; BODMAS is Bogus!Table of Contents [show/hide] PEMDAS is Problematic; BODMAS is Bogus!
I was helping my daughter with her homework the other day. Math. She had to convert an algebraic expression into a word problem (by which she was supposed to express the order of operations correctly so the reader could follow them.) Reviewing what she wrote, I pointed out that it wasn't quite correct and urged her to try again. "PEMA", I said. "What?" "PEMA", I repeated: "Parentheses, Exponentiation, Multiplication, and Addition." "PEMDAS" she corrected me. "Oh, really?" I remarked, somewhat incredulously. How unfortunate. Being a product of New MathYes, For those that don't know, PEMDAS is just PEMA with Division and Subtraction tossed in. On the surface, that might seem reasonable, but there's a dark underbelly to this.
You see, neither PEMA nor PEMDAS are **Parentheses**: Everything inside matching parentheses before anything outside them,*from the innermost out*.**Exponential**operations: Raising things to a power*in right-to-left order*.**Multiplicative**operations: Multiplication and Division,*in left-to-right order*.**Additive**operations: Addition and Subtraction,*in left-to-right order*.
That's it. Any time you have two operations to be evaluated (or This has been conventionTo be sure, there is no great law of mathematics that says you And you'll notice, that's "But..." I hear you exclaim, "...what about division and subtraction? Don't they deserve equal time?" That is the rationale for the If you've been taught math correctly, you are aware that division is just a kind of multiplicationThe term is "inverse operation", and each of the operations have their inverses. Similarly, subtraction is just a kind of addition. Subtracting 3 from Besides, if you want to be On the other hand, PEMA isn't bothered, because taking the n Yeah, yeah, yeah... so why is PEMDAS so bad? While the device is taught to represent P, E, (M This is not an isolated incident, Math Forum's Confusion over Interpretation of PEMDAS points out that "Students take PEMDAS letter by letter, tending to do all multiplication before any division, rather than working from left to right." Students are one thing. University Math departments are another. There, the author, Harvard professor Dr. Knill, asks What is x/3x? I take a moment to correct Dr. Knill and point out that both JavaScript and Perl use the same conventional operator precedence that most other languages do. Both—like most programming languages—are neither PEMDAS nor BODMASSince these are already "damaged goods" I use them to mean specifically Multiplication before or after Division, respectively... just like Dr. Knill and many others do., but PEMA, with proper left-to-right behavior. The issue here is that the problem as stated, 2x/3y-1 is wildly ambiguous. Mathematicians would generally avoid this notation, using either explicit parentheses or—more properly—a proper fraction, 2x over 3y, with the subtraction of 1 either behind or under the line to disambiguate the order. But give the equation 2*x/3*y-1 to a programming language and of course it applies the only rules it has been instructed to follow. In this case, multiplication and division from left to right. So the expression is understood to be 2 times x, divided by 3, multiplied by y, with one finally subtracted from it. Not what you intended? Then you need more bananas...parentheses....
In any event, Dr. Knill pontificates for a bit and concludes with a reference to ScienceBlogs which treats the matter rather more succinctly. "So What's the big deal?" I hear you ask. Very simple: PEMDAS (and BODMAS) were meant be mnemonic devices to help remember the order of mathematical operations, but have instead served to confuse students. I thank those visionary math teachers—Helen Joseph and Al Bertie (both gone, but not forgotten!)—who spared me and my classmates from this by just teaching us all proper math, and the mnemonic PEMA. Now, if only all students could be set straight. If a consumer product is defective—such as brakes on a car or the cord on an appliance—such that it is the source of repeated injury, such a product is recalled and replaced. In the same vein, PEMDAS—clearly demonstrated to be defective as a tool to understand math—should likewise be removed from the curriculum. In any event, I'm taking the liberty of teaching my daughters math done right. It will just take a while to undo the damage. Sections: 2
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