Question

Find the additive inverse of: $0$

Answer 1

Hint: Assume the additive inverse of $0$ to be any variable. Then find the sum of $0$ and its inverse and equate it to $0$. By adding or subtracting numbers from both sides, find the value of the variable.

Complete step-by-step solution:
Let us consider the additive inverse of $0$ be \[x\].
The additive inverse of a number is the number which when added to the given number yields $0$.
So, we have to find the sum of $0$ and its inverse.
Since we assumed the additive inverse of $0$ to be \[x\]
So, we can write the sum of $0$ and \[x\] will be $0 + x = x$.
Now we can equate the sum to $0$
Then we get $x = 0$

So, the additive inverse of $0$ is $0$

Additional Information: Additive inverse simply means changing the sign of the number and adding it to the original number to get an answer equal to 0.
As we say followed the properties of additive inverse, based on negative of the primary number
1. $ - \left( { - x} \right) = x$
2. ${\left( { - x} \right)^2} = {x^2}$
3. $ - \left( {x + y} \right) = \left( { - x} \right) + \left( { - y} \right)$
4. $ - \left( {x - y} \right) = y - x$
5. $x - \left( { - y} \right) = x + y$
6. $\left( { - x} \right) \times y = x \times \left( { - y} \right) = - \left( {x \times y} \right)$
7. $\left( { - x} \right) \times \left( { - y} \right) = x \times y$

Note: An additive inverse of a number is defined as the value, which on adding with the original number results in zero value.
It is the value we add to a number to yield zero.
If the additive inverse will be minus of \[a\], then \[a\] is the primary number.
So we can write it as, $a + \left( { - a} \right) = a - a = 0$.
Example:
Additive inverse of $10$ is $ - 10$, as $10 + \left( { - 10} \right) = 0$.
Additive inverse of $ - 9$ is $9$, as $\left( { - 9} \right) + 9 = 0$.
Additive inverse is also called the opposite of the number, negation of number or changed sign of original number.