# Why can zero not be divided by any other number ?

justaguide | College Teacher | (Level 2) Distinguished Educator

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Zero can be divided by another number. When zero is divided by any number the result is the same, zero.

This division is equivalent to you having no chocolates and trying to distribute them among your friends. No matter how many friends you have each is not going to get any chocolates.

It is the division of a number by zero that is not defined, and is taken to equal infinite. If you divide any number A by a number B, you will see that the result increases as B decreases in value. Now zero is the extreme case, and B cannot go lower than zero in magnitude. At B equal to zero, A / B is equal to an infinitely large number.

iluvubabes | Student, Grade 9 | (Level 1) eNoter

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If you have zero apples and divide it by 3 it is impossible.  If you have nothing you can't divide it because you have nothing to devide.

neela | High School Teacher | (Level 3) Valedictorian

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100/5 = 20.30/6 = 5. 18/6 = 3.

Like that 0/2 = 0. 0/3 = 0. 0/100 = 0.

So zero divided by any number other than zero is zero.

Now we consider what happens if we divide a number by zero:

First we consider 10/x, where x is approaching zero from the positive side. We make the denominator x smaller and smaller approaching zero as below:

10/ 5 = 2. 10/4 = 2.5. 10/1= 10. 10/0.1 = 100. 10/0.01  = 1000....

We see that when the denominator becomes smaller (but not negative), the result is a larger positive number. There is no end to the largeness. So what is then 10/0 it is limitless  unbounded. The moment you say it is a number, you can find still bigger number.

Now we consider the number 10/x. Now we allow x to (increase) approach zero from the left side of zero in the number line:

10/-5 = -2. 10/-4 = -2.5. 10/-2 = -5. 10/-1 = -10. 10/-0.1 = -10. 10/-0.01 = -100.  10/0.001 = -1000.....

We see that as the denominator approach zero from the negative side, the result of division becomes a negative large number and there no limit for the largeness of the number.

If you plot the graph, we see that the 10/x is  continuous graph everywhere for all x> 0 and x <0.

But at x = 0, 10/x leaves a big gap or jump of - infinityto +infinity. So there is great discontinuity.

From the above we, conclude that 10/x is undefined for x= 0. Or 10/0 is undefined. So unlike other numbers, say10/4 = 2.5, we do not have any consistent answer for 10/0, or any number/0.