Jami asked in Science & MathematicsMathematics · 4 months ago

Why is division by 0 undefined?

Explain in your own words why division by 0 is undefined. Why is 9/0 undefined? Why is 0/0 undefined?

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• Jim
Lv 7
4 months ago

If a/b = c then a =bc

let's see if that works

9/0 = x,

so 9 = 0*x but we know any number times 0 is 0, and we end up with

9 = 0 which doesn't work for me!

• 4 months ago

The simplest answer, which doesn't rely on any mathematical understanding other than the most basic, real-life concepts:

I have 10 cookies.  I share them between five people.  How many do they each receive?  --- Two each, obviously.

I have 10 cookies, I share them between no people.  How many do they each receive? --- There is no answer because the question makes no sense.  There are no people there to receive the cookies, so how can we answer a question about how many they each receive?  Although it is tempting to say that they get zero cookies each, there is no 'they'.

So, 10 divided by 5 equals 2.

But, 10 divided by 0 has no answer because they question makes no sense.

• D g
Lv 7
4 months ago

Because it is the divsion is making something into prices a certain size

You are dividing something by a certain size 0 is nothing you can't divide something into prices of nothing

Take the reverse operation multiply 0 by 12 = 0

So the division operation makes no sense for ,0

• Zirp
Lv 7
4 months ago

There are at least a dozen videos on youtube explaining it better than I can

• 4 months ago

I like to use this explanation.

Let's say you have 1 pizza that are cut into 8 pieces.

If you take a slice, you take 1/8 of it, leaving 7/8 behind.  You can continue to take 7 more pieces until the pizza is gone.

This is the same as saying 1 divided by 1/8 is 8:

1 / (1/8)

1 * 8

8

The smaller this fraction is, the more pieces you are able to take.  cut into 1/24th?  You'll get 24 slices before  you run out:

1 / (1/24)

1 * 24

24

But if you cut them infinitely small so you remove 0 from the pizza, the pizza is still intact.  No matter how many times you repeat this process, the pizza will never be consumed.

1 / 0 = undefined.

It's not like the other fractions where eventually ran out of pizza after a certain number of slices removed.  You can remove an infinite number of "0" sized slices and never consume the pizza.

• Mark
Lv 7
4 months ago

Because it can be ANY number.  Does 0 = 2?

• 4 months ago

If you have a number to be divided, and you have nothing to divide it(no denominator), How can you divide that number when there is nothing to divide it with.

Hence division by zero(0) is described as 'undefined'.

• 4 months ago

0/0 is indeterminate rather than undefined.

Other than that,

suppose 9/0 = x

9/0 = x

0 * 9/0 = 0 * x

9 = 0x

No value of x makes the last equation true so 9/0 is undefined.

• 4 months ago

Division by zero is an operation for which you cannot find an answer, so it is disallowed. You can understand why if you think about how division and multiplication are related.

9 divided by 0 is x would mean that

0 times x = 9

But no value would work for x because 0 times any number is 0. So division by zero doesn't work.

Why is 0/0 undefined ?

There's a special word for stuff like this, where you could conceivably give it any number of values. That word is "indeterminate." It's not the same as undefined. It essentially means that if it pops up somewhere, you don't know what its value will be in your case. For instance, if you have the limit as x->0 of x/x and of 7x/x, the expression will have a value of 1 in the first case and 7 in the second case. Indeterminate.