mscroggs.co.uk
mscroggs.co.uk

subscribe

Blog

 2017-01-13 
I wrote this post with, and after much discussion with Adam Townsend. It also appeared on the Chalkdust Magazine blog.
Recently, Colin "IceCol" Beveridge blogged about something that's been irking him for a while: those annoying social media posts that tell you to work out a sum, such as \(3-3\times6+2\), and state that only $n$% of people will get it right (where \(n\) is quite small). Or as he calls it "fake maths".
A classic example of "fake maths".
This got me thinking about everyone's least favourite primary school acronym: BODMAS (sometimes known as BIDMAS, or PEMDAS if you're American). As I'm sure you've been trying to forget, BODMAS stands for "Brackets, (to the power) Of, Division, Multiplication, Addition, Subtraction" and tells you in which order the operations should be performed.
Now, I agree that we all need to do operations in the same order (just imagine trying to explain your working out to someone who uses BADSOM!) but BODMAS isn't the order mathematicians use. It's simply wrong. Take the sum \(4-3+1\) as an example. Anyone can tell you that the answer is 2. But BODMAS begs to differ: addition comes first, giving 0!
The problem here is that in reality, we treat addition and subtraction as equally important, so sums involving just these two operations are calculated from left-to-right. This caveat is quite a lot more to remember on top of BODMAS, but there's actually no need: Doing all the subtractions before additions will always give you the same answer as going from left-to-right. The same applies to division and multiplication, but luckily these two are in the correct order already in BODMAS (but no luck if you're using PEMDAS).
So instead of BODMAS, we should be using BODMSA. But that's unpronounceable, so instead we suggest that from now on you use MEDUSA. That's right, MEDUSA:
This is big news. MEDUSA vs BODMAS could be this year's pi vs tau... Although it's not actually the biggest issue when considering sums like \(3-3\times6+2\).
The real problem with \(3-3\times6+2\) is that it is written in a purposefully confusing and ambiguous order. Compare the following sums:
$$3-3\times6+2$$ $$3+2-3\times6$$ $$3+2-(3\times6)$$
In the latter two, it is much harder to make a mistake in the order of operations, because the correct order is much closer to normal left-to-right reading order, helping the reader to avoid common mistakes. Good mathematics is about good communication, not tricking people. This is why questions like this are "fake maths": real mathematicians would never ask them. If we take the time to write clearly, then I bet more than \(n\)% of people will be able get the correct answer.
                        
(Click on one of these icons to react to this blog post)

You might also enjoy...

Comments

Comments in green were written by me. Comments in blue were not written by me.
We use BEDMAS in Canada (Brackets, Exponents, Division, Multiplication, Addition, Subtraction) But we are taught that you do whichever comes first from left to right if they are the addition/ subtraction or multiplication/division. So it could also be BEMDAS, or BEMDSA, or BEDMSA. It just uses the order the that rolls off the tongue more.
Brodaha
                 Reply
we use BOMAL - Brackets, Overs, Multiplication/Division, Addition/Subtraction, Left to Right. I agree they need to know negative numbers to fully understand and use BODMAS, BIDMAS, BEDMAS, PODMAS, PIDMAS, PEDMAS, BOMAL or MEDUSA
tiny
                 Reply
If we could just teach young children about positive and negative numbers, then this wouldn't be a problem. Subtraction is just the addition of negative numbers. Division is also the multiplication of fractions. This is why BOMA/PEMA is the optimal method. I think MEDUSA is very creative, though.
Blan
                 Reply
 Add a Comment 


I will only use your email address to reply to your comment (if a reply is needed).

Allowed HTML tags: <br> <a> <small> <b> <i> <s> <sup> <sub> <u> <spoiler> <ul> <ol> <li> <logo>
To prove you are not a spam bot, please type "sixa-x" backwards in the box below (case sensitive):

Archive

Show me a random blog post
 2024 

Feb 2024

Zines, pt. 2

Jan 2024

Christmas (2023) is over
 2023 
▼ show ▼
 2022 
▼ show ▼
 2021 
▼ show ▼
 2020 
▼ show ▼
 2019 
▼ show ▼
 2018 
▼ show ▼
 2017 
▼ show ▼
 2016 
▼ show ▼
 2015 
▼ show ▼
 2014 
▼ show ▼
 2013 
▼ show ▼
 2012 
▼ show ▼

Tags

christmas menace puzzles national lottery hats folding tube maps mathsteroids machine learning javascript polynomials matrix of minors binary graph theory cambridge people maths pi recursion determinants tennis craft hyperbolic surfaces noughts and crosses flexagons ternary wave scattering pythagoras guest posts logic pi approximation day newcastle football weather station youtube talking maths in public radio 4 stirling numbers royal baby hexapawn books oeis weak imposition speed hannah fry palindromes martin gardner crochet signorini conditions logs databet electromagnetic field harriss spiral light game of life matt parker exponential growth misleading statistics folding paper plastic ratio sobolev spaces bubble bobble news royal institution fractals error bars the aperiodical computational complexity interpolation preconditioning sound geometry squares datasaurus dozen stickers runge's phenomenon manchester science festival accuracy cross stitch pizza cutting gerry anderson dragon curves game show probability ucl curvature nine men's morris games zines fence posts programming finite group mathsjam chess numerical analysis map projections rugby 24 hour maths chebyshev numbers raspberry pi sorting london underground realhats mathslogicbot bempp edinburgh tmip countdown fonts errors frobel turtles coins quadrilaterals reuleaux polygons big internet math-off inverse matrices world cup captain scarlet pascal's triangle phd logo dinosaurs london matrix multiplication advent calendar convergence statistics manchester crossnumber mean python dates anscombe's quartet live stream geogebra dataset platonic solids latex data visualisation a gamut of games video games boundary element methods simultaneous equations reddit php draughts data inline code probability finite element method arithmetic correlation standard deviation bodmas european cup final fantasy approximation golden spiral sport pac-man matrices matrix of cofactors trigonometry estimation rhombicuboctahedron christmas card propositional calculus gaussian elimination gather town braiding triangles golden ratio go wool graphs asteroids chalkdust magazine

Archive

Show me a random blog post
▼ show ▼
© Matthew Scroggs 2012–2024