**Division by 0 is NOT ALLOWED in ***mathematics***. Reason :-**

Let's see the following scenario :-

5/0=?

Let the answer be x.

Thus 5/0=x , = 5=0×x, = 5=0.

See! What** **we proved! 5=0** **! Impossible.

Here the value of the answer (x) is also not defined because there is no such number which gives the answer 5 when multiplied by 0 (0×x=5; in this case x doesn't exist).

**Thus, division by 0 is not allowed and undefined.**

*Hope you understand***.**

Thanks for the A2A!

Well, you can define it, but when you do, you lose some important features. For example, there was a time when complex numbers didn’t exist. Well, people decided to define [math]\sqrt{-1}[/math], and they gained lots of important things, but they also lost things, like the fact that [math]\sqrt{ab}=\sqrt{a}\sqrt{b}[/math] for all numbers and that numbers can be ordered, but the pros outweighed the cons. This is why complex numbers are taught in school curriculums. On the other hand, people have defined division by [math]0[/math], but in that case, the cons outweighed the pros, so division by [math]0[/math] isn’t usually taught, unless you get to higher math.

[math]1 \div 1 = 1, 1 \div 2 = 0.5, 1 \div 3 = 0.\overline{3}, 1 \div 4 = 0.25[/math]

[math]1 div 5 = 0.2, 1 \div 6 = 0.1\overline{6}, 1 \div 7 = 0.\overline{142857}[/math]

[math]1 \div 8 = 0.125, 1 \div 9 = 0.\overline{1}, 1 \div 10 = 0.1, ….[/math]

[math]\frac{1}{100} = 0.01, \frac{1}{1000} = 0.001, \frac{1}{10000} = 0.0001….[/math]

Now, think of the other cases:

[math]0.1 \div 1 = 10, 0.01 \div 1 = 100, 0.001 \div 1 = 1000[/math],

[math]0.0001 \div 1 = 10000, 0.00001 \div 1 = 100000[/math]….

As the value of grows, [math]\frac{1}{0} = \infty[/math]

Use the relative properties to define the properties of the number Zero.

the resulting number would be divisible by 9.

Based on the above, Two properties of Zero can be defined.

The easiest way to answer this is to turn it around:

If [math]\dfrac{1}{0}=x[/math] then [math]1=0x[/math].

For what value of [math]x[/math] can you multiply it by [math]0[/math] and get [math]1[/math]? You say that there are no such values? There you go; that's why division by zero is usually undefined.

There is one exception: if the numerator is also zero.

If [math]\dfrac{0}{0}=x[/math] then [math]0=0x[/math].

For what value of [math]x[/math] can you multiply it by [math]0[/math] and get [math]0[/math]?

All of them.[math]\frac{0}{0}[/math] isn'tundefined(no valid answers); it'sindeterminate(everything is a valid answer).