Dividing a number by itself?

Question

Why is it that

3/3 = 1
2/2 = 1
1/1 = 1

but

0/0 is not equal to 1.

how many lots of zero go into 0: 0 or 1? that's what it hinges on regardless of what your calculator says.

if 1 * 0 = 0 doesn't it follow that 1 = 0/0?

okay. 2*0 = 0, 27 * 0 = 0 therefore 0/0 = 2 AND 0/0 = 27 AND if i want 0/0 = 1.

Are they not all true? Can't I define what I want the result of my division by 0 to be?

Answer 1

Let me give you a two part answer. The first part involves the concept of division, the second part involves a more 'formal' approach - though I have no intent of turning this response into a graduate thesis ;0)

First, think of what it means to divide something. If we divide three pizzas among twelve people, each person gets 1/2 (3 / 12 = 1/2) Similarly, we could divide six things by three people (6 / 3) = 2 per person. We could even divide 0 pizzas between 12 people. If you have 0 pizzas and 12 people everyone goes hungry. (each person gets 0/12 = 0).

Now, what would happen if you tried to divide 12 pizzas between 0 people. How much would each person get becomes a meaningless question because there are no people to divide it amongst. Similarly, extending the analogy, trying to divide no pizzas among no people is also meaningless in terms of having nobody to divide the contents of an empty pizza box amongst.

Second part: Consider that most division operations are reversible with multiplication. 12 / 6 = 2; and 2 * 6 = 12. So if we try 0/0 we have to ask ourselves what number times zero = 0. Well, 1 * 0 = 0. So does 2 *0, and 3 *0, and any other real number times 0 is zero. (this is called the annihilation property). Rather that say that 0/0 is every real number, we simply admit that there is no single answer and label it as undefined.

Answer 2

Any number divided by itself is 1, but 0/0 is undefined. In certain instances, such as limits, 0/0 may converge to an actual value but that value will vary from case to case. In terms of cross-multiplication, you can let 0/0 equal anything you want, because if you multiply both sides by 0 the equality remains. Hence, 0/0 is not given a value.

More generally speaking, division by 0 of any number is undefined, though when present in a limit it may converge. Sometimes it is convenient to define 1/0 = infinity, but even this informal definition is not used for 0/0

Answer 3

No the symbol 0 that we use to express nothing cannot add up to one when added subtracted divided or multiplied because it stands for nothing. 1 * 0 = 0 because that statement literally means that there are 0 1's, just like 50 * 0 = 0 because zero amounts of 50 still equals zero.

Answer 4

That's one ofthe conceptual problems of mathematics. To say 3/2, translated from the language of mathematics into english means "How many times can I fit the number 2 into the number 3?" - The answer is 1 1/2.
But with 0/0, you encounter a problem. If you fit 0 once into 0, you come up with a total of 0. So you can still add 0. Then you're up to 2x0=0, and you're still able to add 0, and so on. So that's why 0 presents a special problem.

Answer 5

As per mathematics any digit multiplied by 0 will be equal to 0 only.
Pl. follow the rule.

Answer 6

0/0 is not equal no one because any number divided by 0 is undefine. You can never divide a zero into anyone... How will you divide 0 when it has no value at all....

Answer 7

Sure. And then
5*0 = 0 => 5=0/0
27*0 = 0 => 27=0/0
In fact, 0/0 can be --anything-- you want it to be.
Which makes it an undefined value. Just like it says in your book.

--UNDEFINED--

Doug

Answer 8

0 is not a number...it is just a symbol for nothing or empty.
But sometimes, 0 is considered as a number because it's included in the number line..it is a rule and that's the rule!!

Answer 9

dividing anything by 0 is impossible. answer is beyond infinite. so calculators by default show error. Math is rules and that's the rule.

however 0/1 = 0

Answer 10

of direction, c because of the fact any time whilst a selection is split via itself it gets the quotient one.for e.g.- 4/4=a million,5/5=a million yet 0/0 isn't equivalent to a minimum of one because of the fact 0 would not have any multiple different than 0. sparkling Now.