PEMDAS, GEMDAS, BIDMAS and BODMAS. It sounds like the start of a wacky kids TV show tune … but they’re all actually clever mnemonics – acronyms to be exact – to help you remember one thing: the order of operations for mathematical calculations.
Confused? Not for much longer:
Let’s un-muddle this mnemonic PEMDAS puddle, shall we?
First up: mnemonics. What are they?
To put it simply, mnemonic devices are clever memory aids to help you remember stuff: from shopping lists to all the bones in the body.
If you need to remember something, a mnemonic device can help you retain AND retrieve that info when you need it most (be it in the supermarket or exam hall!).
There are several kinds of mnemonics. You’re probably familiar with some of this list: acronyms and acrostics, method of loci (memory palace), the pegword method, chunking, songs and rhymes, and association.
Want to learn more about the mysteries of mnemonics and how they work? Get the low down right here with mnemonics 101.
Acronyms and acrostics for memorable maths
PEMDAS, GEMDAS, BIDMAS and BODMAS are acronyms.
Acronyms (and acrostics) probably the most common type of mnemonic devices. In fact, some acronyms have slipped into everyday language:
- “We’d better check the radar [radio detection and ranging] before we go scuba [self-contained underwater breathing apparatus] diving!”, we cry before jumping into the boat …
As you can see, acronyms take the first letter from a list of words in sequential order and condense them to make a new (often made up!) word.
The best acronyms form a pronounceable word – that’s far more memorable that string of gibberish letters. Hence using the R and A from “radio”: radar is far easier to remember than RDAR!
Acrostics are like the fun sibling of acronyms: they take that string of letters and expand them again into a witty, memorable phrase.
The idea with both acronyms and acrostics is that remembering them will help you to recall the original list when it matters most: and a short word or catchy phrase is far more likely to tickle your memory at crunch time.
So, these PEMDAS and BODMAS mnemonics: why are they different?
Let’s call up our list of mathematical mnemonics again: PEMDAS, GEMDAS, BIDMAS and BODMAS.
These mnemonics are all about one thing: helping students to remember the correct “order of operations” when solving maths equations. (Psst: “operations” are mathematical processes)
PEMDAS or BODMAS: the mnemonic showdown
So why are there so many different acronyms then?
Well … interestingly enough, the acronym is simply different depending on which side of the pond you hail from:
- Our US (and French) friends will know PEMDAS
- Our young UK friends however, are taught BIDMAS (which used to be known as BODMAS)
- And any Canadians among us learn GEMDAS – sounds sparkly!
Which maths mnemonics do you use in your country to get your calculations correct? Let us know in the comments!
As for those different letters – well, it’s all a matter of language. They simply use synonyms to describe the exact same steps:
The PEMDAS / BIDMAS rule: what does it actually mean?
So what actually is the “order of operations” for mathematical calculations?
Whether you follow PEMDAS or BIDMAS, it’s the rule that defines the order of steps to take to get the right answer to your calculations.
Here’s the secret: it might not sound like it, but our wacky acronyms all stand for exactly the same thing, in the same order:
- PEMDAS = Parentheses, Exponents, Multiplication, Division, Addition, Subtraction
- Whereas BIDMAS and BODMAS = Brackets, Indices (Orders), Division, Multiplication, Addition, Subtraction
- And GEMDAS = Groupings, Exponents, Multiplication, Division, Addition, Subtraction
In practice, it looks like this:
Brackets, groupings and parentheses? Same thing: you must simplify inside the ( ) symbols FIRST.
Exponents, indices and orders? Same thing! They mean powers like squaring, cubing (and their roots) etc – that’s the second step.
Have you noticed the different order of division and multiplication between PEMDAS and BIDMAS?
This doesn’t matter because multiplication-and-division are grouped as a pair (as are addition-and-subtraction). You simply do whichever in the pair comes first as you work left to right along your equation.
Want to get funny with your maths? It’s acrostic time
If you’re finding all these acronyms a little dry and forgettable, don’t worry. There are some pretty funny, well-known acrostics that go with our mnemonic friends PEMDAS, GEMDAS, BIDMAS and BODMAS.
So, why not choose one of these acrostics to tickle your brain when it comes to your next maths test:
- PEMDAS =
- Please Excuse My Dear Aunt Sally
- Please Email My Dad A Shark (credit: Randall Munroe)
- GEMDAS =
- Good Evening My Dear Aunt Sally (she’s popular!)
- Giants Eat Massive Donuts As Snacks (credit: students at Burleson Collegiate High School)
Personally, I love that shark-email mental image!
Unfortunately, there’s aren’t any commonly known acrostics for BIDMAS or BODMAS.
So, if you’ve got your own memorable (BIDMAS / BODMAS) mnemonic, why not leave it in the comments below – perhaps it will catch on! (Bonus points for the silliest, most memorable phrase!)
Maths mastery, here you come
So there you have it! All the mystery behind the mnemonic, from PEMDAS to BODMAS, has hopefully evaporated before your eyes.
Which means it’s time to get calculating – good luck!
If you’re looking for more mnemonic tricks to boost your memory and remember everything you need for your exams, why not try our articles on:
- Mnemonics: the lowdown (find the best method for you!)
- Acrostics and acronyms (full of popular examples for students of all disciplines)
- The pegword method (perfect for remembering short lists)
- Chunking (a memory technique we swear by at Exam Study Expert)
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