My sister and I have a debate.
I say that if you divide 5 apples between 0 people, you keep the 5 apples so 5 ÷ 0 = 5
She says that if you have 5 apples and have no one to divide them to, your answer is ‘none’ which equates to 0 so 5 ÷ 0 = 0
But we’re both wrong. Why?
Comments
Because dividing by 0 is like asking a bald guy what his hair color is
If you divide 5 apples by 0 people, who owns the apples? Where do they go? If you’re including yourself, you’re diving 5 apples between 1 person.
In your analogy, you would actually be dividing by 1, with yourself being the 1. You wouldn’t be diving by zero because if you “keep” the apples, you are essentially dividing by one.
Because in scenario 1, “you” become the “1” and get all the apples, thus it’s five / one. Scenario two still maintains a “you” this 5/1.
Imagine if you have 0 cookies, and you divide them among 0 friends. How many people does each person get? You see, it doesn’t make sense. And Cookie Monster is sad he has no cookies. And you are sad you have no friends.
That’s what Siri used to say. Anyhow, both you and your sister are wrong. 0 divided by 0 is undefined. Anything divided by 0 is undefined.
Just a thought, but in your example you are subtracting 0 from 5, not dividing by 0. Which is 5 of course.
Dividing the apples is putting them into groups. Dividing by 1 is putting all the apples into 1 group. All the apples go into 1 group.
Dividing 5 apples by 5 would be putting them into 5 groups, each group gets 1 apple.
Dividing by 0 is trying to put the apples into 0 groups. This is undefined, because you cannot put the apples into 0 groups.
Think about it like this: If you have 5 apples and I ask you to put them into piles where each pile has zero apples. How many piles can you make before you run out of apples?
Look at what dividing by numbers close to zero does:
5 ÷ 1 = 5
5 ÷ 0.1 = 50
5 ÷ 0.0000000001 = 50000000000
So clearly 5 ÷ 0 should be somewhere in the neighbourhood of infinity except that we completely failed to consider fully half the numbers close to zero!
5 ÷ (-1) = -5
5 ÷ (-0.1) = -50
5 ÷ (-0.0000000001) = -50000000000
So 5 ÷ 0 must be negative infinity. Right? But also positive infinity. At the same time. Which doesn’t math.
Which is why we leave it as undefined.
In addition to good analogies here, division is defined as the inverse of multiplication.
So if a ÷ b = c, then b x c = a. But if b = 0, there’s no number c that makes 0 x c = a
If you divide 5 by zero that means there’s some number times 0 that equals 5, 0 X ? = 5. There no such number.
because 1 is the limit . if you multiply by 0, you get 0. let’s say you have 5 apple . if you divide by 5, you make 5 equal pile. by 2, two equal pile. by 1, you leave as is. by 0? how can you leave it more as is than just leaving it as is? thus, 1 is the limit
I saw a really good explanation for this recently let me see if i can find it.
Let’s start with a simple division example:
So, division is really the question:
“What number multiplied by the divisor gives the dividend?”
Let’s try the same logic with division by zero:
12 ÷ 0 = ?
So we ask: What number times 0 equals 12?
But any number times 0 is 0 — there’s no number that you can multiply by 0 to get 12.
So:
Think of it this way: the smaller the number you divide something by, the larger the result, right?
12 divided by 6 equals 2
12/4 = 3
12/3 = 4
12/2 = 6
12/1 = 12
But what happens when your divisors go beneath 1? Then you get more than your original number.
12 divided by 0.5 is 24.
12 divided by 0.25 is 48
12 divided by 0.1 is 120
12 divided by 0.01 is 1200
12 divided by 0.001 is 12000
Do you see where this is going? As the divisor approaches zero, the answer approaches infinity. Which is clearly bonkers. How can you have an infinite amount of anything?
And it gets even weirder, because, like multiplication, if one term is negative, the answer is, too. So if you divide negative numbers by smaller snd smaller divisors, you wind up going to negative infinity. Divide one number by zero, negative infinity. Divide another number by zero, positive infinity. It just doesn’t make any sense.
I think OPs head must’ve exploded by this point lol, im about there myself ;w;
This is exactly why you can’t divide by zero, you can get any number you want by changing the scenario.
No matter how I describe it, if I have 2 apples and I add two more apples, I’ll have 4 apples.
But when deciding by 0, you can wind up with a correct answer for any number. So “5/0 = indeterminate.”
There is no single answer when dividing by zero. That is why you can’t divide by zero in math.
Its just government propaganda to distract us from how good apples taste.
/s
Because there is nothing (0) to divide or divide by.
I think that by asking “Why don’t we divide it by 0”, you’re essentially saying “Why don’t we not divide it?”. Well, ok, but then what’s your question, “what happens if we don’t divide it?”? Then we’re back to wherever we were at the start.
Let’s explain it like this:
Multiplication and division are connected, as in 5 x 2 = 10 and 10 ÷ 2 = 5 (or 10 ÷ 5 = 2).
So, if 5 ÷ 0 = 5 was correct, 5 x 0 = 5 would also be correct, which isn’t the case, it’s 5 x 0 = 0.
BUT 0 ÷ 0 isn’t 5, or more accurately isn’t ONLY 5 because any number multiplied by zero gives us zero (5×0, 6×0, 7×0 etc.)
5 x 0 = 0 -> 0 ÷ 0 = 5
6 x 0 = 0 -> 0 ÷ 0 = 6
7 x 0 = 0 -> 0 ÷ 0 = 7
etc.
By this logic, 0 ÷ 0 has an infinite number of solutions! But also 5 ÷ 0 has no solution because there is no number that you can multiply by 0 and get 5 as a result.
It’s nonsensical to divide something into “0” piles. There are 0 places to put the things, so there’s no way to answer “how big would each pile be.” It’s not that the piles are size 5, or size 0, it’s that there are no piles, you can’t specify the size of something that doesn’t exist.
OTOH I guess dividing something into -1 piles is also a bit nonsensical, so perhaps that’s no litmus.
It also depends in what context said math is being used.
How many people can you share 0 apples with? 0.
If you have 10 apples How many can you give to zero people? Infinite.
It’s just broken and left undefined because either way it doesn’t solve the problem.
Which is the ultimate goal of math.
100 / 10 How many times does 10 fit into 100? Ten times.
4 / 2 How many times does 2 fit into 4? Twice
1 / 1 How many times does 1 fit into 1? Once
1 / 0 How many times does 0 fit into 1? Uhhh… infinite times?
Division isn’t asking how many you have left. Division is asking “if you split 5 apples between zero people how many apples will each person have”
It’s an unanswerable question. You could say each person has 1 apple, or a million apples. So you just get an error code out of your maths.
The closest you can say is infinity, as that is what the answer “tended to” as the number of people got smaller, but you want to be careful doing maths with that (since negative infinity is also “tended to” when you approached from the other direction)
Try looking at the equation the other way around. You know that if x / y = z, then it must be that z * y = x.
For example: 6 / 3 = 2, because 2 * 3 = 6.
So, say you want to do 5 / 0 = ?
Then “?” must be a number that, multiplied by 0, gives 5. So it must be that ? * 0 = 5. There is no such number, so “?” does not exist.
I’m explaining this way just as an alternative, as others have already used the “apples example”.
Think of it this way.
If you divide 120 apples equally between 5 people, each gets 120÷5 = 24 apples
If you divide 120 apples equally between 4 people, each gets 120÷4 = 30 apples
If you divide 120 apples equally between 3 people, each gets 120÷3 = 40 apples
If you divide 120 apples equally between 2 people, each gets 120÷2 = 60 apples
If you divide 120 apples equally between 1 people, each gets 120÷1 = 120 apples
If you divide 120 apples equally between 0 people, each one of the zero gets …. there is nobody…. The applies are nowhere, you cant count them
Division is counting how many times you can fit x into x, Not how much you didn’t fit. So even though your physically left with 5 apples, you count how many times you can fit 0 into 5, which is 0. (undefined technically)
Assume you have 4 bubble gums. You need to give those 4 to 2 people, equally. So, you divide by two because thats the amount of people you need to give it to equally.
So, 4/2=2.
However, if you needed to give it to 0 people equally, how many would you give?
You are counting yourself in that scenario, so you are dividing by one.
If you divide 5 apples by 0 people there are no people to have apples. And if no on has apples there are no apples. So where did the 5 apples go? It’s a fundamentally broken equation.
> you keep the 5 apples
That’s one person, not zero.
If there are five apples and zero people, and you divide the apples equally between the people, how many apples does each person get?
The question doesn’t make sense. There are no people.
You’re both “right.” In conventional mathematics, you can make “x/0” equal anything you want. It’s trivial to prove it approaches both infinity in the positive and negative direction.
Dividing by 0 therefore doesn’t work in conventional mathematics similar to how square rooting a negative number doesn’t work in the mathematics you’re taught in grade school. In that example, imaginary numbers were created because use cases were found for them.
So far, dividing by 0 has not resulted in new axioms being created to define it because no widespread use case has been found to attribute a brand new axioms to it, so it remains undefined.
Just as an FYI, in mathematics “axioms” are basically ground rules that define simple things like addition and multiplication. You can’t prove addition. It just carries a set definition. Dividing by zero would require something like that to be invented
Keeping the five apples would be dividing by 1 (5 apples split between 1 person).
If you divide by zero, you need to find some number that, multiplied by zero, will give you five. There is, of course, no such number.
Here’s my take on it. There are mathematical reasons for why this isn’t possible, but I doubt these are going to settle the argument if your sister is convicted of a mathematically obvious falsity (edit: at least among the real numbers, but we’re talking about sharing apples here).
So, without involving any math, let’s consider what division means. If there are 5 things which have to be divided them equally among N people, 5/N is the number of objects each person will have. Right? So after the division, there are going to be N people, each with 5/N things.
If you have 5 apples and you divide them between 5 people, there are going to be 5 people with 1 apple each.
If you divide them between 2 people, there are going to be 2 people with 2 and a half apples each.
If you keep them all for yourself (dividing between 1 person) there’s going to be only 1 person with 5 apples “each”. This is the case your sister is thinking of, which is not division by 0 (because you still have 1 person: you).
If you divide by 0… these apples are going to be distributed between 0 people. So, how many apples does each of these 0 people have? 0? 5? 100? Well, there are 0 people with 0 apples, so 0 could be an answer. But there are also 0 people with 5 apples. Or 0 people with 100 apples. There are 0 people with -3 apples as well. The truth is, there is no answer to this question because at the end of the “division”, those 0 people could have any number of apples each (because there are always going to be no people with that amount of apples).
Your sister is not considering that when she says that you have 5 apples, she is not dividing by 0: she is dividing by 1 (giving all the apples to a single person: you). You are not an external entity to the division, you still count as 1 person.
All of these problems are why mathematicians declared that you can’t do it.
If you have 5 apples, then you are 1 person, not zero. You would be dividing by 1 and you would keep all of the apples.
If you mean to say the 5 apples are owned by nobody, then divide them by 0 people, then nobody would end up owning the apples, not even you.
This isn’t the greatest example, just working off your example.
If you keep all the apples, then as you are 1 person, you have divided by 1, not zero
If you have 5 apples to split between 0 people, you are trying to find the value that evenly distributes those 5 apples.
You don’t keep the apples, because then that’s including yourself, which is 5/1.
It’s not 0, because how do you give out 0 apples from 5? You could cut up the 5 apples to small enough pieces where you give each pile 0 at a time, you could do that infinitely and still have 5 apples that still need distributing.
It’s undefined because there is no number that can evenly distribute 5 apples over 0 people where you no longer have apples to give out and everyone has an even amount
If 5÷0=x, then 0×x=5
But it doesn’t.
This is the distributive property that does NOT allow you to divide by zero.
Divide is a math term asking you to take action.
It’s asking you to take the action of division 0 times.
So it’s basically asking you to not do math.
You can redefine things a bit and come up with some trivial ways to handle /0 when it comes up to better suit real life.
Example – take a whole pizza and place it on the counter.
You can divide the whole pizza by 1, by having one person take the whole thing.
You can divide by 2 by making one cut and giving each half to two different people.
But to divide it by 0, you are saying don’t do math. So the pizza just sits there on the counter. The world doesn’t explode.
You can get really really close to 0 by using increasingly small numbers of division so much so that they say you can approach near infinity by using smaller and smaller numbers.
But the truth is 0 is a point of no math. Above it division and multiplication work, below it in the negatives math works as well.
But dividing something 0 times is isn’t math.
I’ve been toying around with /0 = keep intact and whole (do not do math here) to replicate the pizza still sitting on the counter.
It works with every instance i can find so far.
/0 then shifts from “undefined” to “unacted.” That’s powerful, especially in symbolic systems or metaphysical math where the absence of transformation has meaning.
In storytelling, programming, or system logic, this could even be formalized:
Division by zero returns the original operand untouched.
It could also be used as a way to keep some bit of math intact as it travels through other operations, but I’m working on how to phrase it.
If you keep the 5 apples, them you divide by 1, not 0.
I think you fundamentally misunderstand the concept of division.
You’re not 0. That’s the error you’re both making. You’re 1. You are splitting the apples with yourself so it would be 5 (apples) ÷ 1 (person). Or 5 for 1.
You can’t split anything with nothing. You can’t give 5 apples to “no one”. Otherwise it wouldn’t even be an equation, it would just be “5”.
Both of your answers are wrong because you’re answering the wrong question. 5 / 0 isn’t asking how many apples you’d have left. That would be the remainder or modulus. It’s also not asking how many you gave out.
5 / 0 when dividing 5 apples by 0 people is asking how many apples did each person get. But there were no people. So you could just as easily say “each person got no apples” as “each person got one apple” or “each person got 10 apples” or “each person got infinity apples”. All those statements are equally meaningless because there were no people. All the answers are meaningless, which means the question is meaningless.
The best way I could explain it is to just show you.
5/.1=50, 5/.01=500, 5/.001=5000, etc. as you keep dividing by smaller and smaller numbers the answer keeps getting larger, so if you actually try to divide by zero the answer is infinity.
I love how presenting this as a word problem turns them into Schroedinger’s apples. You have 5 apples divided by 0 people? Who is the you? There needs to be at least one person to have / count the apples and that means you are dividing the 5 apples by 1. If there are 0 people then the apples both exist and do not exist in infinite number until someone is there to count them. At that point there are no longer zero people.
Division isn’t an operation in its own right. It’s a derived one; derived from multiplication. a/b means ‘the number which, when multiplied by b, gives you a.’ So 5/0 would mean ‘the number which, when multiplied by 0, gives you 5.’ There is no such number, so 5/0 doesn’t mean anything. It’s based on a faulty assumption, like saying ‘I insist that every letter in the alphabet has a letter that comes after it, and I demand to know what letter comes after z.’
There are other correct, intuitve approaches. I’m going to give one a little fancier: Depending how you ask the question you get different answers.
If you want to know what 100 ÷ 5 is, you can say it’s between 100 ÷ (5.1) and 100 ÷ 4.9, then 100 ÷ 5.01 and 100 ÷ 4.99 . The numbers get closer to the same number: 19.6 and 20.4, then 19.96 and 20.04 and if you keep going you’re pretty obviously going to get 20 . Technically “the series converges.”
So 100÷ 0.1 and 100 ÷ 0.01 and 100 ÷ 0.0001 give you 1000 , 10000 and 100 000. Looks like it’s heading to positive infinity. A weird answer but math can deal with that.
But 100 ÷ -0.1 , 100 ÷ -0.01 and 100 ÷ -0.001 give you -1000 , -10 000 and -100 000. Heading to NEGATIVE infinity.
So the closer you get to dividing by zero, the farther apart the answers get. “The series diverges” (technical terms! I’m so smart.) and you get different answers to the same question. So that’s what they mean by “undefined”.
To use your analogy of 5 apples and zero people, if you have 5 apples and share with zero people, before you can say you get the 5 apples you have to acknowledge that sharing with zero people is NOT SHARING. So if you ask the question, “I have 5 apples and share with zero people, how many apples do I have left?” And the answer is, “you don’t share so it’s a trick question”.
If you divide 5 apples between 5 people, each person gets one apple.
If you divide 5 apples between no people, no person gets as many apples as they want.
Nobody gets as many apples they want.
We have 0=0*0. Dividing both sides by 0 gives 1=0.
So division by 0 is only possible if 1, and by extension, every number is equal to 0.
OP is dividing 5 by 1.
Same reason you can’t multiply by infinity.
Dividing 10 by 2 is like asking “how many 2s do I need to add up in order to get 10?”. The answer is 5, because you need five twos to make ten. So dividing 10 by 0 is like asking “how many zeroes do I need to get ten?”.
You can keep adding zeroes together forever and you will never ever get 10, there is no number of zeroes that can solve this problem. Even an infinity number of zeroes won’t get you anywhere because adding another zero won’t get you closer to 10.
Usually folks think about division like this: 5 divided by 2 means that I slice 5 into two equal parts. That mental model works well when the thing you divide by is larger than one and breaks down when it’s smaller than one (how do you slice an apple into 0.5 pieces??)
However, a better way of thinking about division is: how many times does 2 go into 5? (2.5). That works with 0.5 as well. How many times does 0.5 go into 5? 10 times.
So – using that second mental model: how may times does 0 go into 5? Turns out that number is INFINITY! So division by zero does not give you an actual number.
> I say that if you divide 5 apples between 0 people, you keep the 5 apples so 5 ÷ 0 = 5
If I tell you to divide four bananas among two people, you give each person two bananas, right?
And then you don’t have any left. That’s what it means to successfully divide the bananas among the people, that you distributed them all and everybody got the same amount.
If you divide five apples between zero people, you didn’t distribute anything, you still have all five apples. Your division operation has failed.
An operation that fails has no answer.
You both need to get off the weed
If you think of bottom number as a limit. As the divisor approaches zero … you can see the quotient approaches infinity.
12 ÷ 4 = 3
12 ÷ 3 = 4
12 ÷ 2 = 6
12 ÷ 1 = 12
12 ÷ .5 = 24
.
.
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12 ÷ 0 = infinity = undefined.
If you keep the 5 apples, it’s not 0. It’s dividing by 1. You.
>I say that if you divide 5 apples between 0 people, you keep the 5 apples
If you keep the five apples then that’s dividing them by one, you, the person keeping them. 5/1=5.
Have you ever tried to give equal ammounts of pie to no one? It’s pretty hard
We are so fucking doomed.
Why would you keep the 5 apples?
I know you’ve had a lot of answers here but it can be a remarkably interesting problem to think about.
Numberphile cover this on their YouTube channel: https://youtu.be/BRRolKTlF6Q?si=g6SyI8x55a2Kecu9
Dividing is putting things into groups. If you have 0 groups to put the apples into, then it doesn’t work.
I actually always use apples when I review this.
0 apples divides by 5 people is 0 because it just means that each person gets 0 apples.
But, if I have 5 apples and 0 people to give them to, then what? I can’t do it. That’s why it’s undefined.
You are a person, so if you are there to keep the 5 apples, you are not dividing by 0 people, but by one person: you. (5÷1=5)
Your sister is a lot closer, there are indeed no people to divide the apples over. But that doesn’t mean that everyone gets zero apples, that means you can’t divide the apples at all.
So the correct answer is: you can’t divide by 0. The action of dividing itself is impossible.
Another example: imagine that instead of dividing apples over people, you want to divide €1000,- that you have cash equally over bank accounts. Only you can’t create a bank account because of some technical issue, so you have 0 bank accounts.
That doesn’t mean there isn’t any money, neither does that mean you have €0,- on your bank account, and neither does that mean you have €1000,- or any other amount on each bank account. It means you have no bank accounts, so you can’t put any money in them and so you can’t divide the money at all over the bank accounts.
You can’t divide 5 apples over 0 people because there are no people, and you can’t divide €1000,- over 0 bank accounts because you have no bank accounts. You can’t answer the question of how much apples/money each one would have, because the action of dividing by 0 itself is impossible.
You can’t divide by 0. That is the answer.
Seeing as someone else explained the physical aspect in a really good way, I’ll give you a more mathematical answer.
Think of the number 100.
Divide it by 10, and you have 100/10 = 10.
Divide it by 1, and you have 100/1 = 100.
Divide it by 0.1, and you have 100/0.1 = 1000.
By 0.01, and you have 100/0.01 = 10000.
As you keep making the number smaller and smaller, the result gets bigger and bigger. As you get closer and closer to 0, the result gets absurdly large, too large to compute or have any meaning whatsoever. In fact, it tends to infinity!
Now, think of dividing 100 by -10, -1, -0.1… and do the same logic for it. It goes -10, then -100, then -1000… It keeps getting smaller the closer the number you’re dividng it by gets to 0. When you start from the negative side, dividing by 0 tends to NEGATIVE infinity.
This would imply that dividing any number by 0 results in both positive and negative infinity at the same time, two values which contradict each other. It simply makes no sense!
you can’t divide by 0 because think about it this way: if you have 5 apples to divide between 5 people, you can give 1 to each person. but if you were to divide them between 0 people, you could give them the 5 apples, but since there is no person, you didn’t really give away the apples to anyone. you might as well give each person a billion apples, or 0.1, or pi apples. There are no people to receive them, so you can give away ANY amount of apples. But since that answer isn’t really valid, we say that we can’t divide by 0, because the answer isn’t defined
Another way to think about it is this.
Example: 5/1=5 or think about it like “What number added together 1 time makes 5? 5”
10/2 = 5 or “What number added together twice makes 10? 5”
Now how about you show me the equation for the word problem “What number added together 0 times makes 5?” There is no such number
Because 0 doesn’t go into anything any times.
You can not be a part of the zero people, if you were it now be one person. Now one person has the 5 apples.
Zero people=zero people YOU don’t get the apples. No one does.
She is the one person. So it would be dividing by one.
If your job is to equally distribute apples into a number of bags, and there are no bags. It is impossible to put the apples into the bags.
Multiplication and division is just “equal groups”
If you make 2 groups of 2 apples. You have 4 apples.
If you have 0 groups, of 2 apples, you have 0 apples.
So in division, if we divide 4 apples into two groups, we have 2 apples in each group.
So if we divide 4 apples into 0 groups it doesn’t matter if you just made applesauce, because there’s 0 groups to count.
If I ask you how many apples are in those baskets, and gesture at a room that has no baskets, how much time will you spend trying to count?
Division is like asking “How many equal groups of this size can you make?”
5 / 1 = 5 because you can arrange 5 apples into 5 groups of 1 apple each. 100 / 20 = 5 because you can arrange 100 apples into 5 groups of 20 apples each. You can’t distribute apples into groups of 0 apples each. it doesn’t work.
Division reverses multiplication.
When I say “I multiplied some number by 5 and got 20”, you can reverse-engineer my number by dividing 20 by 5.
But when I say “I multiplied some number by 0 and got 0”, that doesn’t work. Any number would result in 0. Multiplying by 0 destroys the information required to reverse it.
Division by 0 is impossible because reversing multiplication by 0 is impossible.
If you divide apples between 0 people or no-one, you didn’t divide at all.
You can cut an apple into five parts or even thousands of parts, but how do you divide it into 0 parts? That’s not possible, by the axiom that something is inherently not nothing.
Think of multiplication as adding the same number any number of times
If I want 4 to become 12, how many 4s do I add? 3
The problem with 0 though is that you can’t add 0 into any number and as such, the answer is 0. You add 0 0 times because it’s impossible.
It’s also why 0/0 is an error. How many 0’s do you need to add to get 0? Well it should be 1 but at the same time, you add 0 no amount of times. Thus you get a mathematical error where the answer is either 1 or 0.
>She says that if you have 5 apples and have no one to divide them to, your answer is ‘none’ which equates to 0 so 5 ÷ 0 = 0
No, “none” does not necessarily equal “0.” When dividing by 0, you get undefined. It’s a question that does not make sense.
How many airplanes does it take to change a lightbulb? Now, i’m sure there’s an engineer here that’s immediately thinking of ways to make this work. The point is, planes can’t change a lightbulb, so no answer you give it can properly answer the question. If you say “0 airplanes” that means that it doesn’t take any planes to change a lightbulb, and the lightbulb still gets changed. It doesn’t really make any sense, does it?
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Another way of thinking of it:
Dividing by a number is basically asking:
“How many times does this number fit into another number?”
Example:
10/2 = 5, and 2 fits into 10 exactly 5 times. You can reverse this too, so that 5 * 2 = 10.
10/0 = ?, and so how many times does zero fit into 10?
You could say “an infinite number of times” but then if you try to check your answer (multiply it back), it doesn’t work:
If 10/0 = infinity, then infinity * 0 = 10. But now we run into a problem. Anything * 0 = 0, so infinity * 0 must be 0? But isn’t, it has to equal 10, because 10/0 = infinity.
If we go by your sisters logic, then 10/0 = 0, because you can’t divide them at all. So going back to reversing the equation, we get 0 * 0 = 10? That obviously doesn’t make any sense.
Now just change 10 to be whatever number you want, and you’ve proven now that 0 * 0 = R (all real numbers), and that r/0 = infinity (R being all real numbers). We’ve essentially proven here that all real numbers have the same value.
So dividing by 0 just doesn’t lead to a consistent or logical answer, which is why it’s undefined.
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NOW, given that, in very high level mathematics, you can sometimes call x/0 = j. Similar to Sqrt(-1) = i. Although this is not standard mathematics, and as far as I know, doesn’t have many real applications (feel free to provide some if you know them!)
To put it simple: 12 ÷ x = 0. That means x × 0 = 12. That’s impossible to solve.
Ask Siri the question 0 divided by 0 it’s good
She’s right. If you have 5 apples and 5 people. They get 1 each. 5 divided by 5 is 1. The portion that each person is getting is 1.
If you have 5 apples and 0 people. The portion is zero because there is nobody to give them to.
Because division is repeated subtraction by equal groups.
21/7=3 as in you can subtract a group of 7 exactly 3 times. 21-7=14, 14-7=7, 7-7=0.
You CAN do that with zero, but it is infinite nonsense. 21-0=21, 21-0=21, 21-0=21, etc.
You have a pie with 8 slices you want to split it between 0 people. How much pie does each person get.
The best thing I have heard is that by dividing a number, how many times you can subtract a number from another number. Like 12÷3 means I can 4 times subtract it from 12 to reach zero.
But dividing by zero means you can infinitely times subtract 0 from that number but still you have that number so that is why dividing by zero gives Infinity.
One answer I dont see here goes back to more fundamental level of math – multiplication is just repeated addition, and division is repeated subtraction. As an example, divide 90 by 10 – you count the number of times you can subtract 10 from 90 without going below 0, and that is your answer. So if you divide 5 by 0, how many times can you subtract 0 from 5 before you hit 0?
If You’re keeping the five apples, ain’t you dividing it by one(yourself)?