Question

The sum of additive inverse and multiplicative inverse of 2 is ___________.
(a). \[\dfrac{3}{2}\]
(b). \[\dfrac{-3}{2}\]
(c). \[\dfrac{1}{2}\]
(d). \[\dfrac{-1}{2}\]

Answer 1

- Hint: We will first of all know what is an additive inverse and what is a multiplicative inverse. And then we will proceed to do further calculations to find the sum of additive inverse and multiplicative inverse of 2.

Complete step-by-step solution -

The definition of Additive inverse is a number that when added to a given number gives zero.
The word meaning of ‘inverse’ is something opposite in effect. So, the multiplicative inverse of a number is a number that nullifies the impact of the number to identity 1. Thus, the multiplicative inverse of a number is a number by which the multiplication results in 1.
We have to find the additive inverse of 2. And 2 is an integer and integers have -2 as an additive inverse.
Therefore, we have the additive inverse of 2 as -2.
Now we will proceed to calculate the multiplicative inverse of 2.
If we have “a” as an integer then \[\dfrac{1}{a}\] is the multiplicative inverse of a.
2 is an integer then the multiplicative inverse of 2 is \[\dfrac{1}{2}\].
Hence, we obtained the additive inverse of 2 is -2 and the multiplicative inverse of 2 is \[\dfrac{1}{2}\].
The sum of both is given by,
\[-2+\dfrac{1}{2}=\dfrac{-3}{2}\].
Therefore, we get the answer as \[\dfrac{-3}{2}\], which is option (b).

Note: The possibility of error in these types of questions can be at the point where you have to calculate the value of multiplicative inverse of 2. Be careful while calculating the multiplicative inverse of any integer a, it is given by \[\dfrac{1}{a}\].