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
$\endgroup$ 613 Answers
$\begingroup$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; Pizza ended my donuts addiction Saturday
$\endgroup$ 2 $\begingroup$I think it makes most sense to remember it in four steps:
Parentheses trump everything else -- because that's what they are for.
Addition and subtraction have the same priority, because they are each other's inverse.
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.
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 $(3\text{ times }x)+(5\text{ times }y)$.
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
please eat mom's delicious apple strudel
$\endgroup$ 2 $\begingroup$I recommend thinking about precedence a different way.
- What did you learn first? Addition and subtraction.
- What did you learn after that? Multiplication and Division.
- What after that? Exponentiation.
If you perform these operations in the opposite order that you learned them, you don't have to remember about anyone's Dear Aunt Sally. When these rules are not enough to avoid ambiguity, use parentheses.
$\endgroup$ $\begingroup$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.
$\endgroup$ $\begingroup$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.
$\endgroup$ 2 $\begingroup$I think a better acronym would be
$P$arenthesis $E$xponents $F$actors $T$erms.
Students often think that multiplication has higher priority than division because $M$ is before $D$ in $PEMDAS$.
However, if you want a funny way to remember $PEMDAS$, then
$P$lease $E$xcuse $M$y $D$ope $A$ss $S$wag.
$\endgroup$ $\begingroup$Aunt Sally (PEMDAS) has been banished from mathematics.
Read this very short article to understand why:
PEMA is the new mnemonic: Purple Elephants Munching Apples ???
- Parentheses (and other grouping symbols).
- Exponents.
- Multiplication and Division from left to right.
- Addition and Subtraction from left to right.
The importance of from left to right is absent in PEMDAS.
$\endgroup$ $\begingroup$I am a step by step person. (remembering always left to right) 1. Parenthesis 2. exponents 3. multiply/divide 4. add/subtract
$\endgroup$ $\begingroup$- Please Excuse My Dreadful Art Skills
- Please Eat My Delicious Anaconda Snakes
- Please Excuse My Dear Aunt Sally
The first $2$ I came up with. The last is a commonly used phrase to remember PEMDAS.
$\endgroup$ $\begingroup$I Think a good P.E.M.D.A.S Is
Parrots eat up magic dassies and snoozed off
$\endgroup$ $\begingroup$Please Excuse My Dear Aunt Sally.
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