School Maths: 12 divided by zero = 12?!

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My DS came home yesterday quite sad and frustrated because he other classmates had lost marks in a school maths (his best subject) test for not getting the 'correct' answer that '12 divided by zero = 12'.

His reaction, upon coming home, was to look up the expected result of dividing by zero on several reputable maths sites and, as expected, none of them gave the answer that 'X divided by zero = X'. They all backed up his (and my) reckoning that the only possible correct answers could be 'undefined/impossible', 'infinity' or (possibly, at a real outside semantic push) 'zero'.

Thankfully, the teacher raised it the following day (I don't know if she had looked into it herself - it was a centrally-set test - after seeing the pattern of usually-able children unexpectedly all getting it 'wrong') and re-instated all the lost marks; but I'm still baffled as to how anybody could arrive at that answer in the first place, and it's bugging me!

Suppose the sum had been the simpler '12/2=6', the reckoning process would mean that you could have 12 apples and remove 2 apples 6 times, thus ending up with zero apples afterwards (as a valid 'checksum'); equally with '12/12=1', you could remove 12 apples once and again end up with the sum-validating 0 apples; but if 12/0=12 were true, you could thus remove 0 apples 12 times and be left with 0 apples - but of course, you wouldn't have 0 apples left after that: you would have 12 apples left; indeed, just as you would have if you removed 0 apples a thousand billion times!

Was this just a brain-fart by a tired maths test-setter - and one that wasn't immediately obviously wrong to a maths teacher yearning for half-term, who initially insisted that it was right when it was queried - or is there some kind of maths/philosophy train of reasoning that any boffins out there know of by which you could legitimately justify/argue that 'X/0=X' can indeed be correct, the same as 'X-0=X' naturally would be?! It doesn't really matter, obviously, but it's still irritating me a bit!

Genuine question as I'm crap at maths
... would 0÷0=0? Or undefined?

I am a specialist in transmathemtatics, which deals with division by zero, amongst other things.

In transreal arithmetic, infinity is defined by ∞ = 1/0. Let’s use school level arithmetic to work out what 12/0 is equal to.

12/0 = (1 x 12) / (0 x 12)

but 12/12 = 1 = 1/1 so replacing 12 with 1 cancels the common factor 12, giving

12/0 = (1 x 1) / (0 x 1)

now multiplying out gives

12/0 = (1 x 1)/(0 x 1) = 1/0 = ∞.

So twelve divided by zero is infinity.

This is school level arithmetic but very few schools have ever taught transreal arithmetic - though that might change!

Now, before you flame me, remember the “I am a specialist” bit and read this paper:

www.engineeringletters.com/issues_v29/issue_2/EL_29_2_17.pdf

I am happy to answer serious questions.

And dyslexic too!

That's interesting, they basically only just split them into two GCSEs.

Have they literally nothing better to do in education than keep messing around with the qualifications?

Is a transmathematician really an Engineer who self identifies as a Mathematician?

Sorry.

I don't have a problem with that

At my school, part of learning our times tables involved reciting them.
So, for the twelve times table we were taught to say:
One 12 is 12
Two 12s are 24
Three 12s are 36
and so on ...

Thinking back, we were never taught to multiply by zero - I dont remember it ever arising - but following the pattern above, it would have made perfect sense to me to say 0 x 12 as 'No 12s are nothing'

Why would anyone flame you?

Because if you google, lots of people have flamed him. He's not just a specialist, he's the inventor of...

Sorry but I cant see this as a proof.

I cannot see any mathematical operation that connects

12 / 0 = (1 x 1) / (0 x 1)

With

12 / 0 = (1 x 1) / (0 x 1) = 1 / 0 = infinity.

Certainly not "multipliying out".

Perhaps what you mean is that trans mathematics defines 1 / 0 as infinity, but there is no formal mathematical proof here.

Oh.

It all gets far too advanced for my understanding, but does he actually claim to be able to divide by zero?

And i have looked at the paper.....

I'm actually wondering how @JamesADWAnderson came across this thread?

Ds has started A-level maths this school year and says that he was taught hat anything divided by 0 = undefined.

I think he just says 'the answer is now defined to be infinity' then sallies forth.

The whole education system is currently being re-arranged part of the new Curriculum for Wales and new GCSE courses are supposed to get aligned with that and to be less exam based than currently.

I thick there were plans to get rid of GCSE entirely but those were scrapped in end as I think public consultation was negative.

However I am glad our youngest is missing the GCSE changes.

They also found many universities wouldn't consider the numeracy and maths GCSE as equivalent which they had wanted.

Undefined!

Wow thank you! This stuff blows my mind x

What blows my mind is why 0^0 = 1. That is zero raised to the power of zero = 1.

Any number raised to power of zero = 1.

Don't ask me....dont understand!!!

I'm a science teacher recently drawn into teaching maths due to maths teacher shortage. But I genuinely.love teaching it

This is such a useful thread. Thank you for asking this question and ope inf the door for so many great explanations.

my maths teacher told me once that mathematically 1 +1 doesnt equal 2. i can remevmber how though!

Assuming of course we're not dealing with five-dimensional objects in a basic Euclidean geometric universe, given the essential premise that all geomathematics is based on the hideously limiting notion that one plus one equals two, and not as Astemeyer correctly postulates - that one and two are in fact the same thing observed from different precepts.

What do you hope to gain by posting such a load of utter shit? This whole comment is just gibberish nonsense.

56

Any thing divided by 1 is the same number.

Anything divided by itself = 1

Anything divided by 0 is impossible or infinity

0 divided by anything is 0

As for 0/0 well that is undefined because it is something divided by itself so could be one, but it could be divided by 0 which would be infinity or it could be 0 divided by anything which equals 0.

Then there is the question of whether 0 is a number at all or just a symbol used to identify the lack of a number.

What do you hope to gain by posting such a load of utter shit? This whole comment is just gibberish nonsense.

It's a quote from Red Dwarf.

Reading back through the thread and I think I found a better way to explain dividing by half.

Obviously, you can prove it mathematically by flipping the half and then multiplying.

12/1 × 2/1 = 24/1

If you want a practical demonstration, it's easier to think of pizzas. 12 pizzas divided by 2 is 6 pizzas. But 12 pizzas divided by half is each pizza getting cut in half, so you now have 24 pieces of pizza.

If you had 12 guests coming and now you have 24, divide your pizzas by half and everyone gets a share.