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.

Similar posts

Harriss and other spirals
Christmas card 2018
Christmas card 2017
MENACE at Manchester Science Festival

Comments

Comments in green were written by me. Comments in blue were not written by me.
 2017-11-27 
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.
Reply
Brodaha
 2017-11-15 
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
Reply
tiny
 2017-11-15 
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.
Reply
Blan
 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>
To prove you are not a spam bot, please type "s" then "e" then "g" then "m" then "e" then "n" then "t" in the box below (case sensitive):

Archive

Show me a random blog post
 2019 

Jul 2019

Big Internet Math-Off stickers

Jun 2019

Proving a conjecture

Apr 2019

Harriss and other spirals

Mar 2019

realhats

Jan 2019

Christmas (2018) is over
 2018 
▼ show ▼
 2017 
▼ show ▼
 2016 
▼ show ▼
 2015 
▼ show ▼
 2014 
▼ show ▼
 2013 
▼ show ▼
 2012 
▼ show ▼

Tags

game of life folding paper big internet math-off python php royal baby sound map projections final fantasy misleading statistics chalkdust magazine mathsteroids manchester puzzles london flexagons countdown approximation martin gardner plastic ratio christmas card national lottery graph theory pizza cutting logic realhats bodmas hexapawn games rugby books golden spiral propositional calculus curvature london underground probability frobel wool dataset light pythagoras go captain scarlet mathsjam radio 4 bubble bobble polynomials draughts folding tube maps game show probability craft speed trigonometry geometry dates manchester science festival harriss spiral javascript arithmetic gerry anderson nine men's morris rhombicuboctahedron latex data machine learning coins reddit people maths raspberry pi binary golden ratio sport interpolation oeis accuracy fractals electromagnetic field world cup pac-man inline code dragon curves sorting a gamut of games palindromes the aperiodical stickers ternary triangles statistics platonic solids matt parker braiding mathslogicbot menace chess football reuleaux polygons error bars twitter estimation christmas chebyshev european cup programming news noughts and crosses hats tennis asteroids weather station video games cross stitch

Archive

Show me a random blog post
▼ show ▼
© Matthew Scroggs 2019