Question

Fill in the blank:
The multiplicative inverse of $ 0 $ ________________

Answer 1

Hint: In mathematics, the multiplicative inverse means the reciprocal. Let us suppose that “x” be any number then its multiplicative inverse can be expressed as $ $ $ \dfrac{1}{x}{\text{ and }}{{\text{x}}^{ - 1}} $ Here we will find the multiplicative inverse of and will fill in the blank the required answer.

Complete step-by-step answer:
Always remember that when the number zero is multiplied with any number gives resultant value as the zero. Also, when any number is divided by zero gives the resultant value as undefined or the infinity.
We know that multiplicative inverse of any fraction can be expressed for –
Let us assume that $ \dfrac{a}{b} $ is the given number then the multiplicative inverse of the given number can be given by - $ \dfrac{b}{a} $
Now, we are asked to find the inverse of
It can be written as $ \dfrac{0}{1} $
Now, the multiplicative inverse of the above fraction can be given as $ \dfrac{1}{0} $
Since, we know that anything divided by zero lasts for infinity and cannot be defined.
Hence, the multiplicative inverse of zero does not exist and can be said as undefined.
So, the correct answer is “undefined”.

Note: Know the difference between additive inverse and the multiplicative inverse and apply it accordingly.
Additive inverse: Additive inverse can be defined as the number which when added to the original number gives zero as the resultant value. For example; Additive inverse of
Fraction: Fractions are the part of the whole. Generally it represents any number of equal parts and it describes the part from the certain size.