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!

If you have some sort of drawing programme, maybe write it and take a screenshot?

Yes I'm 46 so a similar demographic.

I guess I wasn't asked 12/0 as a rule but definitely taught that 12/0 = 12.

Though the explanations here have been really interesting to read & of course make sense!

I must ask my own DC about this!

@ReneBumsWombats

That's a great explanation re not following the equation.

12 / 0 is just a stupid question that shouldn't be there, like "how long is a piece of string". Not something written by a maths teacher, it isn't testing them on anything.

I’m in my 50s and was taught that 12/0 can’t be done.
Also, it’s pretty obvious that if 12/1=12 then 12/0 can’t also be 12. Or at least I’d hope it’s obvious that dividing by a different number gives a different result.

If you split something into 1 group you would have the original number.

You can’t split something into 0 groups, it’s impossible. If you are holding 12 objects you have 1 group of them. Therefore it’s classed in maths as “undefined” to divide by 0.

Try this

Me too, age 62. Makes me wonder how I passed my maths O-level!

I'm surprised by the number of people who think it's blindingly obvious that 12 is the wrong answer. I had no idea it was wrong - either I have no recollection of learning it at school or we weren't taught it. Although maybe it's generational as I'm the same age group as the other posters who were clueless about it.

Trying to illustrate it with examples of apples or sweets isn't helping (although an infinite number of sweets sounds appealing). If you have 12 of something and do nothing to them, the 12 things still exist. (Numeracy, not mathematics?) @ReneBumsWombats explanation that it's an equation, not 'real', is more helpful. But we didn't learn about equations until the first year of secondary school, so wouldn't have understood it in primary school.

Ditto!

I suspect people 'remembering' the divide by zero, are similar to people 'remembering' (or not) order of operations rules (correctly BODMAS or similar).

12/2 = 6

So 6*2 = 12

One implies the other

So

12/0 can't be 12 as 12*0 - twelve lots of nothing is 0

Or as the bottom number gets smaller the answer gets bigger - 12/6 is 2 12/12 is 1 so you would expect 12/0 to be bigger than 12 and sone people would say infinity

Division by 0 is undefined mathematically
Stick it into a calculator and see what it says

Bloody aweful if they are being taught incorrect things
I'd go mad

🙂

It's the downside of thinking of maths problems as practical thought experiments rather than as pure maths. I can see why someone would think the answer was 12 because you're standing there with 12 sweets. But in the equation, you're not really there holding the sweets as a group to be included in the division. You're just a vessel for the equation, and the equation is to divide them by nobody.

If you have 12 things and divide them into 0 piles each pile will have nothing and you have a remainder of 12

It's like diving 13 by 2 / 6 sweets each and one left over

That 1 isn't in any of the 6 piles

I'm loving this thread!
I'm in my 60s and I'm sure that I was taught 12÷0 is 12 although I admit that I've never really thought about it until today. However if
12 ÷ 12 = 1
12 ÷ 6 = 2
12 ÷ 1 = 12 how can
12 ÷ 0 also equal 12? It can't. One number divided by 2 different numbers can't give the same answer, can it?
Therefore I now see that 12 ÷ 0 cannot equal 12

Yes, the explanations are great.

I think it belongs in the realm of 'things that don't happen, so don't actually matter'. Theoretical.

I mean, infinity makes no sense either.

Maybe we were taught 12/1=12, but were simply never asked about or taught 12/0, so we've misremembered?

It's counter intuitive according to the way we were taught to understand division. The 'no hoops, so no apples' explanation makes sense.

Bags of twelve apples, and no bags of twelve apples, makes it even clearer.

Zero is a freaky number that didn't exist in many ancient cultures

You may well not have been taught because it could be considered advanced maths

If you put this equation into my calculator on my phone it pops up with a message saying 'cannot divide by zero'

This is why it's useful for actually understanding what division and multiplication actually means.

Rather than just focusing on methods.

What does 12 /2 actually mean?

What does 12 / 0 actually mean?

Or...asking "why" when someone gives an answer? Critical thinking and all that

The teacher got confused. x to the power of zero = 1
So 12 to the power of zero is 1

Don't focus on the sweets. Focus on the other number. The question is about the other number.

There are 12 sweets on a table. 4 children come along and divide the sweets between themselves. How many sweets does each child have? 12/4=3

So, there are 12 sweets on a table. No children come along. How many sweets does each child have? None. Because there are no children.

The question is never "how many sweets are there?"

What does "zero" mean anyway?
A place holder?

I don't think the Romans had a symbol for Zero - must have been fun doing MMXVI - MXXVIII in Roman school

I think people were probably taught 'you can't do it' and have misremembered.

12/12 = 1
12/6 = 2
12/2 = 6
12/1 = 12
12 / 0.5 = 24
12 / 0.25 = 48
12 / 0.1 = 120
12 / 0.01 = 1200
12 / 0.001 = 12000
12 / 0.0001 = 120000
so as the dividing number tends to zero the result gets larger and larger

There will be no piles. You can't divide 12 things into 0 piles, that's the point. It's impossible.

The equation isn't telling you to keep the 12, which would be either no equation or dividing by 1, depending on how you want to think of it. That is still a pile of 12. The equation is telling you to divide the 12 into no piles.

And that's impossible.