Question

Write the negative (additive inverse) of each of the following: - $${\displaystyle \frac{-2}{5}}$$.

Answer 1

Hint: Understand the definition of additive inverse of a number. Assume ‘x’ as the additive inverse of the given number: - $${\displaystyle \frac{-2}{5}}$$. Take the sum of x with the given number and equate it with 0. Assume this as a linear equation in x and solve for the value of x.

Complete step by step answer:
Here, we have to find the additive inverse of the given number $${\displaystyle \frac{-2}{5}}$$. First, let us know the definition of the term ‘additive inverse’.
In Mathematics, the additive inverse of a number x is the number that, when added to x, yields zero. This number is also known as the opposite (number), sign change and negation. For a real number, it reverses its sign. The opposite to a positive number is negative and the opposite to a negative number is positive. Zero is the additive inverse of itself. Let us take some examples: -the additive inverse of 5 is -5 because their sum is 0. Similarly, the additive inverse of -0.9 is 0.9.
For a number, the additive inverse can be calculated using multiplication by -1. For example: the additive inverse of 100 will be $$(-1)\times 100=-100$$.
Now, let us come to the question. We have to find the additive inverse of $${\displaystyle \frac{-2}{5}}$$.
Let us assume the additive inverse as ‘x’, therefore, the sum of x and $${\displaystyle \frac{-2}{5}}$$ must be zero. So, we have,
$$\begin{array}{rl}& \Rightarrow x+\left({\displaystyle \frac{-2}{5}}\right)=0\\ & \Rightarrow x-{\displaystyle \frac{2}{5}}=0\\ & \Rightarrow x={\displaystyle \frac{2}{5}}\end{array}$$

Hence, the additive inverse of $${\displaystyle \frac{-2}{5}}$$ is $${\displaystyle \frac{2}{5}}$$.

Note: One may note that we can also find the additive inverse of the given number by multiplying it with -1. In this way also we will get the same answer because $$(-1)\times \left({\displaystyle \frac{-2}{5}}\right)={\displaystyle \frac{2}{5}}$$. You Must not get confused between the terms additive inverse and multiplicative inverse. These two terms have completely different meanings and we must remember their definitions to know the difference between them.