Badly-Written Maths Questions [BODMAS]

I have ranted in the past (albeit briefly) about badly written maths questions. These are the kind of question that do the rounds on Facebook, where - due to the deliberately ambiguous way that the question is written - there are at least two different answers.

The idea of these questions isn't to test people's maths skills.  It's designed to 'go viral' by generating conflict and disagreement between the know-it-alls, the qualified mathematicians and those who can't recall or don't know how to handle maths questions when there isn't enough information to easily proceed.

You know the kind of thing:

What is 3 + 4 * 5 + 6 - 7?
Only 1 out of 10 will get this right!

Firstly:  this is NOT proper Maths.  It just isn't.  Don't worry if it's confusing - it's deliberately intended to be.

Secondly:  if you don't get it 'right', then you'll probably continue feeling that maths is irrelevant, complicated, meaningless and inaccessible.  Because that's probably what you thought before, and the long list of comments that say it's 22  or 34, all equally convinced that they're right and the other person is wrong.  There'll be a few comments about showing how they've worked it out, and then a few people will say BODMAS.

BODMAS?

BODMAS is the agreed way in which we carry out calculations like my example.  Mathematicians don't like uncertainty or ambiguity, and will go to great lengths to make their meaning perfectly clear and precise.  All scientists are the same - they show great precision in language, whether that's words or numbers.

BODMAS states that a calculation should be carried out in a particular order:

Brackets - any terms in brackets (or parentheses) should be calculated first.
Orders - any numbers which are raised to powers (squared, cubed, square root) are done next, after any calculations in brackets.  (Previously called Operators)
Division - divisions are the next priority.  Any two numbers or terms which are next to each other have to be divided, after any brackets and operators, but before anything else.
Multiplications - after you've done all the divisions, you then do all the multiplications.
Additions - any terms which are to be added together are done after the multiplications.
Subractions - finally, any remaining amounts are to be subtracted.

So, to take my example:

3 + 4 * 5 + 6 - 7  =  ?

There are no brackets or orders (powers) in my calculation, so the first calculation I will do is the Multiplication.  4 * 5 = 20.

So now, my calculation looks like this:

3 + 20 + 6 - 7 = ?

There's no dividing in my expression, so I can move on to the additions:  3 + 20 + 6 = 29

Which leaves me with:
29 - 7 = 22

And the answer is therefore 22.

While it may be possible to read the question differently, this will give a mathematically inaccurate [wrong] answer.  It may seem natural to read the question from left to right, but this will give a different and wrong answer:

3 + 4 (=7)
*5 (=35)
+6 (=41)
-7 = 34

Wrong answer = 34.

If you think that it's unfair or unrealistic to have to follow such precision, let me present some examples from written English, that show how important it is to state things clearly and in the right order:

I'm glad I'm a man, and so is Lola
Is Lola a man?  Are you reading from left to right, or did you go back to the middle?
He fed her cat food.
Was he looking after her cat?  Or was he making a culinary error?
John saw the man on the mountain with a telescope.
Who has the telescope?

Or how about this one, which has recently started going around Facebook, and is (almost certainly deliberately) full of mathematical and grammatical problems.

1 rabbit saw 6 elephants while going to the river.
Every elephant saw 2 monkeys going towards the river.
Every monkey holds 1 parrot in their hands.How many Animals are going towards the river ???

Does "to the river" count as "towards the river"?
"Every elephant saw 2 monkeys" - is that each elephant saw 2 monkeys, or they all saw the same 2 monkeys?
"How many animals?" - this depends on if you include birds in your definition of animals (some do, some don't).

This is the epitome of a trick question, and this kind of uncertainty is completely unacceptable in maths - but that's what drives the apparently viral threads on Facebook.  People will argue vehemently about one answer or the other - confusing everybody else and leading to the frustration that we see (it's much easier to explain things in a five minute conversation than it is with five paragraphs of comment text on social media).

Maths has enough of a bad reputation for being confusing, inaccessible and frustrating; it doesn't need people asking "What's 5 + 6 *7 -8? Only 1 in 5 know the real answer!" to make it any worse.

(The answer is 39)
(The answer to the Albert Einstein question (which is particularly devious)  is -13
3 - (6*3) + 2 = 3 (- 18 + 2) = 3 - 16 = -13