Question

If $x+0=0+x=x$, which is rational number, then $0$ is called

• A. identity for addition of rational numbers
• B. additive inverse of $x$
• C. multiplicative inverse of $x$
• D. reciprocal of $x$

Answer 1

The correct option is A

identity for addition of rational numbers

Explanation for correct option:

Option (A): Concept of additive identity - It says that when a number is added to zero, the result is the same. The identity element is zero (also known as additive identity)

When we add any integer with zero, the outcome is the same number. This is true for any real, complex, or imaginary number.

Suppose, $x$ is any real number, then

$x+0=x=0+x$

For example, $120+0=0+120=120$, where $0$ will be the additive identity.

Hence, option (A) identity for the addition of rational numbers is correct answer.

Explanation for incorrect options:

Option (b) - Additive inverse of $x$ - What you add to $x$ to make the total of zero is called the additive inverse of $x$.

Suppose, $x$ is any real number, then

$x+(-x)=0$

Here $-x$ is the additive inverse of $x$.

Hence, option (B) is incorrect.

Option (C): Multiplicative inverse of $x$ - The multiplicative inverse of an integer is a value that equals 1 when multiplied by the original number.

Suppose, $x$ is any real number, then

$x\times \frac{1}{x}=1$

Here $\frac{1}{x}$is the multiplicative inverse of $x$

Hence, option (C) is incorrect.

Option (D): Reciprocal of $x$ - Reciprocal of $x$ is similar to the multiplicative inverse of $x$.

So,

$x\times \frac{1}{x}=1$

Here $\frac{1}{x}$is the reciprocal of $x$

Hence, option (D) is incorrect.

Therefore, option (A) is the correct answer.