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!

I don't know about how they got it wrong. I do wonder if it was an actual maths teacher. In many schools if you are breathing and have a pulse they will hire you to teach maths.

As a simplified explanation, division is about splitting into a certain amount of equal groups.
6÷2 can be shown as 6=●●●●●●
You split it between 2 groups and you have ●●● and ●●●, so 3

If you split something between zero groups you are left with the original number.

Your answer is correct in that 12/0=impossible/error as no number can be divided by 0. How old is your DS? Whilst it would be worryingly poor subject knowledge for a primary teacher to get that wrong I could understand how the wrong assumption could be made. If this was a secondary maths specialist though, then this is very concerning.

The simple way to prove 12/0=error is take the inverse and multiply.
If 12/0=0 then 0x0=12 (which it doesn't as anything multiplied by 0 is always 0)
Therefore 12/0 can never be 0.

Not quite, if you split something into 1 group you are left with the original number. It is impossible to split something into 0 groups as in this case 0 represents an 'absence of groups'. An amount will always be in at least 1 group.

Exactly, an absence of groups means you are left with the original number. The number of items doesn't then disappear. If you split 3 apples into no groups you are left with 3 apples, they don't vanish.

You are correct, dividing by zero is undefined (mathematician)

Thanks, all - that makes me feel a bit more assured!

My DS is 10 - Year 6.

If you split something between zero groups you are left with the original number.

I sort of see the reasoning behind this, but I still can't rationalise it as correct, though. In dividing, the only answer you're interested in is how many there are in each of the resulting groups - not how many there were in the original total.

If you say 12/3=?, the only answer you care about is clearly 4. The original 12 is now history and is only part of the question and not the answer you're after!

Lol!
12 divided by 2 is 6.
12 divided by 1 is 12.
12 divided by 0.5 is 24.
12 divided by 0.1 is 120.
12 divided by 0.01 is 1200...

Can you see the way this is going? 12 divided by 0 isn't 12!

Pretty shocking that it takes the teacher noticing that all the bright children got this 'wrong' to realise that something's up.

While we're at it...I have never understood why X x 0 = 0 ...
If you have 12 apples and multiply them by nothing, the 12 apples still exist don't they?

2 lots of 12 apples is 24 apples.
1 lot of 12 apples is 12 apples.
0 lots of 12 apples is 0 apples.

probably just a typo in the question paper, or the mark scheme, ans no, not shocking that the teacher didnt notice first time through, they may not have even read the question.

if I am marking preset tests, I dont necessarily read the question, unless something odd is turning up in the pattern of marks

Sometimes in a computer science context the division operator is.modified to make it "safe" and avoid division by 0 errors. Was this a computerised test? If so maybe it used a "safe" version of division rather than the true one.

Lord save us. Well even if you hadn't bothered to look at the questions, surely you wouldn't have to wait for a pattern to emerge, with an answers sheet saying "12", as soon as your first able pupil wrote "infinity"!

probably just a brain fart or typo from the setter. glad to see it was corrected next day. don't over think it.

infinity is the best actual answer.

12/1 = 12
12/0.1=120
12/0.000001= 12000000
12/0.000000000001= 12000000000000

the closer the denominator gets to zero, the bigger the answer.

I reckon they though "if you have 12, then do 0/nothing to it, you'll still have 12".

The answer comes from how many items are in each group. Imagine you draw a circle for each group, share the items between the circles then count the number of items in each circle to give you the answer.
So 12 ÷ 3 =
12 apples (for example) shared equally between 3 circles.
There are 4 apples in each circle so the answer is 4.
12 ÷ 0 =
You have 12 apples but no circles to put them in, so you can't count the apples in the circle, therefore there is no answer.

Multiplication is commutative.

That means the order of the numbers doesn't matter so 12 x 0 = 0 x 12 = 0

1 x 2 x 3 x 4 = 24
1 x 3 x 2 x 4 = 24
2 x 4 x 3 x1 = 24

So you don't 'start' with 12 whether they are apples or not.

Another way to think of it is on a graph, if you plot x = 2 and y = 4 as a dot, then drop down a line to the x axis and then a horizontal line to the y axis you will have a rectangle with the area of 8 ie 2 x 4.

If you were to plot on a graph as x=12 and y= 0 you do not get a rectangle, the area is zero.

Your method is wrong, so you are getting the wrong conclusion.

Like or not, I won't try to show you why you're wrong - would take too long.

Just take it from someone who knows for sure dividing by zero is impossible.

The only "result" you get is "infinity" which is not a defined number.

Try any search engine and ask "division by zero" en.wikipedia.org/wiki/Division_by_zero explains it pretty well

If this is the standard of teaching maths, that's worrying, to put mildly!

This "test" is so fundamentally wrong that if that happened to mu child I would take the trouble to make enough fuss to have whoever devised it sacked without thinking twice.

If this is the standard of teaching maths, that's worrying, to put mildly!
Utterly shocking.
I am by no means a mathematician but the 'answer' was clearly wrong.
No doubt the usual suspects will be along shortly to blame 'the Tories' 😁

Almost certainly a mistake by someone working quickly. I recently made a silly mistake marking children’s times tables (really silly - something like 5
x 5 = 50). It’s just one of those things that happens when you’re working fast. I marked probably 100 questions correctly but for some reason wrote that one down wrong on the answer sheet. Mistakes are really good and healthy in teaching though, it gives me an opportunity to model resilience to the children so I’m never worried when it happens. I’m secure enough in my subject knowledge that it’s just one of those weird things that sometimes happens to human brains!

Sorry, this is not any kind of "silly mistake".
If you know your maths, that's the kind of most basic stuff you should get right even if someone wakes you up in the middle of the night with a bucket of ice over your head, let alone admonishing kids you're teaching that they got it wrong.

How old are you guys?

I'm mid fifties and think I was taught 12/0=12

I might be wrong... but I think I was!

Its simply unrealistic - far too many questions to mark in a week sometimes

Students should be marking their own anyway, for this sort of question

Fair enough if they were at high school with a specialist maths teacher this would be unacceptable. At primary where it's possible the teacher's own maths qualification doesn't have to be high I think it's forgivable. They acknowledged the mistake and rectified it.

I would be getting your child away from that maths teacher as soon as I could. Any mathematician - at GCSE level - knows that dividing by 0 gives no answer. How can this be a maths teacher. And I am also shocked by how convinced some people on this thread are that the answer is 12!!!