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I'm having trouble remembering PEMDAS (in regards to precedence in mathematical equations), ie:

  • Parentheses
  • Exponentiation
  • Multiplication & Division
  • Addition & Subtraction

I understand what all of the above mean, but I am having trouble keeping this in my head. Can you recommend any tricks or tips you use to remember this.

Thanks

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This was incorrectly tagged as being related to functional equations. –  Simon Hayward Dec 9 '12 at 12:49
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you may want to try: xkcd.com/992 –  Dave Hartman Dec 14 '12 at 13:12

5 Answers 5

up vote 7 down vote accepted

PEMDAS is an acronym to help you remember. try different forms of mnemonic devices, like acrostics: Please Excuse My Dear Aunt Sally; Pancake Explosion Many Deaths Are Suspected; Purple Egglants Make Dinner Alot Sickening; Pink Elephants March, Dance, And Sing;

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+1: Did you make up these hilarious mnemonics yourself or did you find them in a book? –  Dominik Dec 9 '12 at 13:28
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lol, i heard them over time from teachers and classmates –  lias Dec 9 '12 at 17:48

Well, I suggest you remember the word 'pemdas'. Another way:

  • brackets were designed to be evaluated first, so they go first
  • the other operations go from advanced to simple
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3  
Yup, not sure you can get much simpler than a one word acronym. Otherwise there's nothing so good as practice! –  Simon Hayward Dec 9 '12 at 12:50

Daan's suggestion of remembering that parenthesis go first, then advanced to simple is good because there is some meaning in it instead of just having a random word. But if you want to remember a word, and you remember that multiplication and division go together (they're inverses of each other), and addition and subtraction go to gether (again, they're inverses), you just have to remember PEMA or PEDS or whatever, and then fill in the gaps.

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I think it makes most sense to remember it in four steps:

  1. Parentheses trump everything else -- because that's what they are for.

  2. Addition and subtraction have the same priority, because they are each other's inverse.

  3. Similarly, multiplication and division have the same priority. But that's rarely relevant, because proper mathematics prefers writing division with a faction bar, which delimits its arguments unambiguously without referring to rules.

  4. The ordering between the various groups of operation is chosen such that polynomials work. What "polynomials work" means is that we can use the laws of arithmetic to rewrite everything into something that doesn't need parentheses:

    • Exponentiation must come before multiplication, because then we can rewrite $(2x)(3x)$ into $6x^2$. If multiplication had higher priority than exponentiation we'd need either parentheses as $6(x\text{ to the power of }2)$, or introducing square roots to make $\sqrt 6 \cdot x\text{ to the power of }2$, both of which are inconvenient.

    • Multiplication must come before addition and subtraction, because the distributive law allows us to rewrite an arbitrary product of sums into a sum of products, but not the other way around: $$ (5+x)\cdot y = 5y+xy $$ but there's no product of sums that correspond to $3x+5y$, so it would be inconvenient if we couldn't write that without parentheses but had to write it as $(3\text{ times }x)+(5\text{ times }y)$.

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I always taught students to remember this mnemonic as PE(MD)(AS) since multiplication and division are performed left-to-right in the order they appear, just like addition and subtraction.

I'm sure many have seen this viral Facebook question: $$6 \div 2 \ ( 1 + 2 ) = \ ?$$

Is is 9 or 1? Here's a video that shows you how it's done.

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division and subtraction aren't commutative operations, when using them you should always employ parentheses. –  Zackkenyon Jun 30 '13 at 18:40
    
I think that we should get rid of the dreadful $\div$. The only time I have used it is when I teach it. –  Baby Dragon Oct 25 '13 at 5:18

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