Question

What is the additive inverse of ${\displaystyle \frac{a}{b}}$ ?
a.${\displaystyle \frac{-a}{b}}$
b.${\displaystyle \frac{b}{a}}$
c.${\displaystyle \frac{-b}{a}}$
d.${\displaystyle \frac{-b}{a}}$

Answer 1

Hint: Just find the negation by putting ${}^{\prime }{-}^{\prime }$ sign before the fraction ${\displaystyle \frac{a}{b}}$.

Complete step-by-step answer:

In the question we have to find the additive inverse of ${\displaystyle \frac{a}{b}}$.
First, we understand what is additive inverse.
In mathematics, the additive inverse of a number ‘a’ is a number that, when added to ‘a’, yield zero. This number is also known as the opposite number, sign change or negation. For a real number, it reverses its sign: the opposite to positive number is negative number and vice versa. Zero is the additive inverse of itself.
The additive inverse is defined as its inverse element under the binary operation of addition, which allows a broad generalization to mathematical objects other than numbers. As for any inverse operation, double additive inverse has no effect: $-(-x)=x$.
For a number, generally the additive inverses are found or calculated using multiplication by $-1$ ; that is $-n=-1\times n$. Example: integers rational and real numbers.
Additive inverse are closely related to subtraction which can be viewed as an addition of the opposite:
$a-b=a+(-b)$
Conversely, additive inverse can be thought of subtraction from zero:
$-a=0-a$
Hence, unary minus sign notation can be seen as a shorthand for subtraction with the”0” symbol omitted, although the correct typography there should be no space after unary ${}^{″}{-}^{″}$.
So, the additive inverse of ${\displaystyle \frac{a}{b}}$ is ${\displaystyle \frac{-a}{b}}$.
Hence, the correct option is ‘a’.

Note: We can find just by multiplying the number with $(-1)$ or by subtracting from 0 to get the desired result or answer.