I just can’t resist another ‘who came up with this nonsense post’. Here is the offending image which popped up on my facebook feed this time:
I think the idea is you’re meant to go through and use the ‘order of operations’ everyone was taught at high school – you may remember it being called ‘BODMAS’ or ‘PEMDAS’ or something else like that. Here are the problems with that:
1) BODMAS or PEMDAS is a load of nonsense. I last used BODMAS (just typing it annoys me) when I was 11 because I was forced to at school. I remember failing a test on it and almost getting put in the bottom set. I have not used it since – I bracket terms in formulae like any other rational human being.
2) Even if we insist on using the standard order of operations, they don’t really exist for a string of operations like this. The order is kind of a ‘if in doubt use this, whether or not it looks like you should ’.
3) Even using the standard order of operations is ambiguous. Does 1/2x mean (1/2)x or 1/(2x)?
4) OK, so we’ll still try and use the standard order of operations. Did the question specify we should? No! There is absolutely no rule saying we must use this order!
5) No one would ever write out a formula like that. It’d be like writing a sentence without any punctuation:
You will be required to work twenty four hour shifts.
You will be required to work twenty four-hour shifts.
You will be required to work twenty-four hour shifts.
You will be required to work twenty-four-hour shifts.
Which one is correct!?
For a string of operations, our ‘punctuation’ is brackets. We would bracket the terms as required. You do the operations in brackets first.
6) The final insult: there is no equals sign! Who’s to say there shouldn’t be a ‘<’ sign at the end? Without an equals sign (or similar) it’s not even a question anyway.
So the correct answer to this ‘question’ is “the question is undefined…….now get out”
There is a reason a standard order of operations exists. If you put the string into a computer program it needs to know what order to do the operations in or else it would probably just crash. As I said though, that doesn’t mean it’s the correct way of doing it – it’s just the way the computer defines and interprets the problem. Don’t believe me? Put the string into a few different calculators (use a scientific one and a non-scientific one) – you’ll get different answers because different calculators use different orders of operations! Are the calculators wrong? No, we just haven’t given them enough information to ensure a consistent answer.
Before anyone else points out hilarious the irony of me misusing a Venn diagram – just think of it as an informal picture. This post is probably not the place to get into the details of Set Theory.