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!

You can't divide by 0.

If you have 12 sweets and divide them by one child, the child gets 12 sweets. Divide them by two children, each child gets 6 sweets. Divide them by no children isn't 12, it's just impossible. You're being told to divide them but there's nobody to divide by.

To say it's 12 is to misunderstand what division is. Dividing by 0 isn't the same as not dividing. It's not 12, it's just impossible. You can't divide the sweets among nobody.

Same here. Also 50s.

i was taught that if you divide by 0 you’re effectively not dividing so the original number stays the same.

I am in my 50s and was taught that the answer was impossible/infinity

The original number stays the same only if you count the person dividing the sweets as one of the groups getting a share, but they're not. They're not there, in terms of the question. The task is not to not divide the sweets and keep them. It is to distribute the sweets equally among children who aren't there.

Impossible.

More accurately, to distribute the sweets equally among no children. Don't keep them, that's simply not dividing. Divide them, but among nothing and nobody.

You can't.

It’s primary maths … the teacher may not have great maths ability themselves, and almost certainly isn’t a maths specialist (hence the relying on a centrally set test). This kind of thing happens from time to time at our primary, teachers working outside of their knowledge area and just getting it wrong. An over reliance on Twinkl doesn’t help.

that said, I think the teacher has handled it well, she noticed an issue, went away to check and has rectified it. At the end of the day we all make mistakes but how we handle them is what really matters. I’d be happy with the way she has role modelled this.

If you look at it another way.
12/3 you can do as subtraction
12-3=9
9-3=6
6-3=3
3-3=0

So you took away 3, 4 times until you had none left so the answer is 4

So do the same with 12/0
12-0=12
12-0=12....

You can do that forever and you don't get any closer to 0.
So the answer is undefined, or infinity. Do it on a calculator and you will get E for error.

To your ds you'd look at 12/x and what happens as x gets smaller.
As x gets smaller 12/x gets bigger.
So we say as x approaches zero, 12/x approaches infinity.
Or perhaps easier to grasp is as x gets infinitely small, 12/x gets infinitely large.

Infinity isn't a definite number, it's a concept.
Infinity +1=infinity
Infinity x infinity = infinity

This is fascinating but hurting my head!

I honestly didn't understand OP's post till I read all the answers.

I understand, given that you've explained it.

Just pointing out that @TenoringBehind and I were taught that no dividing happened, so the number was intact.

I'm not arguing, just expressing surprise that the rest of you all know the truth. A bit like the 'don't flush tampons' thing. Those of us who hadn't read the instructions for 40 years missed the memo.

And now Earrings as well!

I'm guessing the teacher was a grade C GCSE teacher not an a one, and just went with the answer, before rethinking overnight.
These things happen, no great harm done.

Primary teachers know a lot but can have their weak spots, as long as they correct them it's OK.

Sadly I know of plenty of maths teachers who would be likely to get the same answer. There are not lots of good ones out there.

That's where the misunderstanding comes in.

It's an equation, so in terms of what it's doing theoretically, you can't simply not do it and not divide. It is telling you to divide the sweets. So you must divide the sweets. But you have to divide the sweets nowhere.

Keeping them is either not dividing, or dividing by one. Neither of which is what the equation says. Divide them, by nobody and nothing. Put them nowhere, do nothing to them, but divide them.

Impossible.

Or, if you take the more pure maths approach outlined by MargaretThursday, infinity. To put that into my version, it's because you'd be standing there forever trying to divide them. Because it's impossible. Infinity, or impossible.

But it's certainly not 12!

This thread shows it’s a tricky question, beyond expected in y5.
Ive never been taught specifically that /0 can’t be done. I got A at GCSE (before A*) and didn’t hear about this in my PGCE either (primary).
The teacher did the right thing using it as a teaching point the next day and that’s something your ds wont forget.

Loving this thread

more maths puzzles please!

But then the 12 apples are still in 1 group, so by this logic, is an illustration of 12 x 1.

Charitably, I'll assume that it's a computer error, because if the question set has ever been looked at by a human, they're not competent at the job they've been asked to do.

It's basic primary school maths. We need to stop valuing it so poorly and being so proud of being so bad of it as a nation.

Zero is the absence of numbers not a tradional number as such. It didn’t exist for a long time because people didn’t really have the reason to count zero apples or zero gold pieces. That is why multiplying by zero is not the same as other number division, the answer is undefined the standard rules don’t apply.

Just for you, I shall prove that 2=1

Suppose a = b
Then multiply by a gives a^2 = ab
Subtract b2 gives a2 - b2 = ab - b2
Factorising gives (a+b)(a-b) = b(a-b)
Divide by a-b gives a+b = b
So if a=1, then as a=b, b= 1, so substituting gives 1+1=1, ie 2=1.

12 x 0 is the same as 0 x 12. It doesn't matter how many times you multiply no apples, you've got no apples.

I'm in my 50s and was taught that 12 divided by 1 is 12.

Anything divided by 1 is the original number.

a 2 - b 2 = ab - b ^ 2 (MN formatting strikes again)

Give up.
a squared - b squared = ab - b squared

Obviously I meant dividing here not multiplying 😫

Could you write it on a piece of paper, take a pic and upload?

No. I'm not that clever. Using a laptop.