Question

What is the additive inverse of \[\dfrac{a}{b}\] ?
(A) \[\dfrac{a}{b}\]
(B) \[\dfrac{b}{a}\]
(C) \[\dfrac{-b}{a}\]
(D) \[\dfrac{-a}{b}\]

Answer 1

Hint: First of all, assume that the additive inverse of the given number \[\dfrac{a}{b}\] is equal to \[x\] . We know the property that when a number is added to its additive inverse then it becomes equal to zero. Now, use this property and solve it further to get the value of \[x\] .

Complete step by step answer:
According to the question, we are given a number and we have to find its additive inverse. Also, we are given four options and we have to pick the correct option after calculating the additive inverse of the given number.
The given number = \[\dfrac{a}{b}\] ………………………………….(1)
First of all, let us assume that \[x\] is the number which is the additive inverse of the given number …………………………………………….(2)
We know the property that when a number is added with its additive inverse equal to zero …………………………………………..(3)
Therefore, we need to add the number \[x\] with the given number \[\dfrac{a}{b}\] in order to get its additive inverse ………………………………………(4)
Now, from equation (3) and equation (4), we can say that the addition of \[x\] and \[\dfrac{a}{b}\] must be equal to zero.
On adding, we get
\[\Rightarrow x+\dfrac{a}{b}=0\]
\[\Rightarrow x=-\dfrac{a}{b}\] ……………………………….(5)
In equation (2), we have assumed that \[x\] is the additive inverse of \[\dfrac{a}{b}\] and from equation (5), we have calculated the value of \[x\] .
Therefore, the value of the additive inverse for the given number \[\dfrac{a}{b}\] is \[\dfrac{-a}{b}\] .
Hence, the correct option is (D).

Note:
 In this question, one might make a silly mistake and assume that when a number is added to its additive inverse yields 1. This is wrong because when a number is added to additive inverse then it becomes equal to zero. Therefore, take this point into consideration.