We have all known since childhood that dividing any number by zero is not possible. The result we get after dividing by zero is not defined. But why is it so? Why can’t it be possible to divide by such a basic number like zero?
If you keep dividing any number by smaller numbers, the value of the result keeps increasing. For example,
20 ÷ 20 = 1
20 ÷ 10 = 2
20 ÷ 5 = 4
20 ÷ 1 = 20
20 ÷ 0.8 = 25
20 ÷ 0.5 = 40
20 ÷ 0.4 = 50
20 ÷ 0.2 = 100
20 ÷ 0.1 = 200
From these results, we can conclude that if we divide 20 with any number that tends towards zero, the answer will tend towards infinity. But that does not mean that 20 divided by zero equals infinity.
When we divide 20 by any number, it also means how many times of that number we are adding together to get 20. For example, if we add 10 with itself two times, we’ll get 20. If we add 0.5 with itself 40 times, we’ll get 20, and so on.
Dividing by a number is the same as multiplying its reciprocal. Let’s say we multiply 20 with any number x and get the result 20x. There exists a number (1/x) which is called the multiplicative inverse of x. The product of any number and its multiplicative inverse is always 1. As you can see in our example, if we multiply x with (1/x), the answer equals 1.
If we want to divide any number with zero, we have to find the multiplicative inverse of zero first. Let's say that the multiplicative inverse of zero is (1/0). Multiplying this number with zero should result in 1. But anything multiplied by zero always equals zero. So multiplying the multiplicative inverse of zero with zero can never result in 1.
(multiplicative inverse of 0) × 0 = supposed to be 1, but results in zero instead
Hence the multiplicative inverse of zero does not exist. But there must be a multiplicative inverse of a number if you want to divide it by something. Since zero does not have that, it is not possible to divide by zero.
