# Blog

## Archive

Show me a random blog post**2019**

**2018**

**2017**

**2016**

**2015**

**2014**

**2013**

**2012**

## Tags

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

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 "

**B**rackets, (to the power)**O**f,**D**ivision,**M**ultiplication,**A**ddition,**S**ubtraction" 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**:**M**abano (*brackets*in Swahili)**E**xponentiation**D**ivision**U**kubuyabuyelela (*multiplication*in Zulu)**S**ubtraction**A**ddition

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.

**2017-11-15**

**Add a Comment**

2017-11-27Brodaha