Question

0/2=0why plz prove it
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Answer 1

First let us clear what is division.

If a number (dividend) is divided by another number (divisor), then the number we obtain (quotient) actually tells that how many times we will have to repeat the divisor to get the dividend.

Suppose, 108 is divided by 12. The quotient is 9. This means that when 12 will be added 9 times, (or 12 × 9), then the result will be 108.

[Here we are not taking case of remainders]

So, if 0 is divided by 2, we need a number, say q, such that when 2 is multiplied by q, the result is 0

So, we get 2q = 0

Now, the only value which suits here for q is 0. Hence, 0/2 = 0

Why only 0 suits here?

An example would explain you better!

1 + 1 = 1 × 2 = 2

3 + 3 = 3 × 2 = 6

999 + 999 = 999 × 2 = 1998

Applying the same rule,

0 + 0 = 0 × 2 = 0

This shows that any number when multiplied by 0, gives 0.

Hence, 2q = 0 will be possible only if q = 0.

This further verifies that when 0 is divided by any number, it gives 0.

NOTE :- Any number when divided by 0, gives undefined result. That is, 1/0, 2/0, 0/0 ..... are undefined.