School Maths: 12 divided by zero = 12?!

[WeBuiltThisBuffetOnSausageRoll]

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!

I went to a grammar school in the 60's, my maths teacher was terrifying.

I've really enjoyed this thread, delighted to realise she didn't know everything.

Infinity is incorrect. It is impossible to split something into 0 groups therefore the answer is undefined, as in there is no answer. You could say it tends towards infinity but really it is an impossible complex.

Also, in defence of the teacher, I’m a maths teacher, with a maths degree and taught primary for years. I often make mistakes when marking that the kids point out the next day. We always look at why I got it wrong and learn from it. It’s good for kids to see that it’s ok to make mistakes!

*I think it’s WHY the fact that you still have 12 sweets is irrelevant is where people get confused, because it doesn’t translate to real life.

Yes, that's the issue. You have to get that you, holding the sweets, aren't in the equation and it's about what the equation is telling you to do: hand the sweets out to nobody. Practical examples of theoretical concepts are always tricky.

I understand why it's not a perfect explanation and where the confusion comes from. But it seems to have helped some people so that's good.

I think it is actually quite a good way of illustrating the concept of 0. In true 0, you're not there holding the sweets either. They're just there by themselves and the task is to distribute them nowhere and to nobody. Divide them by nothing.

As a PP said, the question is not "how many sweets are there?".

It is a difficult concept!

Yes, that works too!

Oh don't be ridiculous, everyone makes silly mistakes at times.

😂😂😂
do feel free to explain to any year6s in your care the difference between "infinity" and "an impossible complex that tends towards infinity". I think my explanation is appropriate for most 10 year olds though.
you do realise that most of the science and a lot of the other subjects as taught to children is a simplification from what the fullest specialist understanding would deem to be "correct"?

Fair play to the teacher to be honest, I think how they handle being wrong is more important than the error (of course assuming the error is picked up and its not taken on as fact by the children). It's a good lesson in itself to accept being wrong graciously and illustrate that you're happy to learn.

I guess it depends on whether people were taught that zero represents nothing, so in this question nothing would have changed re the original number, or that they can go ahead and divide by zero and the answer is infinitesimal.

To those mathematicians who say infinitesimal, to actually get an answer that is not the original (ie 12) suggests that division has taken place. Even infinitesimal suggests a number of sorts, but so tiny that they can't be counted. But still a fraction of a fraction (times infinity) of an actual number.

Or else, why isn't the 12 still the same? Protected in its entirety as 12 instead of being split into infinitesimal numbers?

@ReneBumsWombats It is a difficult concept, I understand it now as an adult with no anxiety/chance of getting told off or makings an idiot of myself and therefore able to think about it but under schooling conditions it can be very difficult for people to grasp. Especially with the way the curriculum works and moves on so quickly. If you don’t ‘get’ the work one day then two days later when it has been built on and moved forward you are basically fucked. And God help you if you have a week off sick!

Is this the new, alternative math?

@EerieSilence it is a practical real life understanding of maths.

Well I’m absolutely rubbish at maths but have just learned quite a lot by reading this thread. Thanks everyone!

I’m like pickedwalnuts too - both on the maths front and tampons! (I don’t flush them btw.)

But now you’ve explained it Rene, it makes sense, thank you. I’m just now going to check to see that my school-ages DC know this too…..

Yes, that all makes a difference and it's a shame that so many people had that experience. I hope things are better now.

Oh dear god. I hope you're not teacher.

This is bloody horrific.

I absolutely would if they were interested!! I teach year 6 that dividing by 0 is impossible. I do not teach them that it is infinity. It is important that children are taught correct mathematical concepts from an early age. If they were interested I would give them an investigation dividing by numbers less than 1 and let them see that the answer increases as the fractions decrease. They could then come up with a statement that dividing by smaller and smaller fractions means the answer gets larger and larger towards infinity. Many Year 6’s could absolutely understand this!

Probably proves why only certain people should be teaching maths though…

No, it's a bollocks understanding of maths. 12/0 is 0. Anything divided or added by 0 will be a 0. You can't have 0 groups. 12 apples will always be there but you cannot divide them into 0 groups. Those 12 apples are 1 group. I wish people would cop on. Not sure when you learned maths, for me it was a long time ago but even some 46 years ago practical people teaching maths understood how to explain the fact about 0.

I love some of the explanations & will be using them to help explain further to my kids. They are both really interested by things like this

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I am 48 and was taught that you can´t divide by zero, the unswer is error or undefined. The proof is that you cannot multiply anything by zero and get 12 as an answer. And I was a nuncie at maths.

@EerieSilence has perfectly demonstrated my point about some people who ‘get’ maths being completely unable to see why other people don’t.

I just asked year 6 DD and it confused the crap out of her. First it was 12, then she said it can't be because 12/1 is 12 , so 0. Now she's mad at me for blowing her mind so early in the morning.

To complete the sum we'd have to define 0, which is BIG and somewhat theoretical maths, and hence, for the sake of argument, anything divided by 0 is infinity and we standardise infinity as 0.

Anything divided or multiplied by 0 is 0.

Best to just encourage a child to accept/remember that & move on!