Question

Write additive inverse of $$\dfrac{2}{8}$$ and $$\dfrac{-6}{-5}$$.

Answer 1

Hint: In this question it is given that we have to write the additive inverse of $$\dfrac{2}{8}$$ and $$\dfrac{-6}{-5}$$. So to find the additive inverse we need to know that the additive inverse of a number is what you add to a number to create the sum of zero. So in other words, the additive inverse of x is y, where the sum of x + y=0. The additive inverse of x is equal and opposite in sign of x, i.e y=-x and vice versa.

Complete step-by-step solution:
Here the first number is given, $$x=\dfrac{2}{8}$$
Now let the additive inverse of x is y,
$$\therefore \left( x+y\right) =0$$
$$\Rightarrow \dfrac{2}{8} +y=0$$
$$\Rightarrow y=-\dfrac{2}{8}$$
Therefore, the additive inverse of $$x=\dfrac{2}{8}$$ is $$-\dfrac{2}{8}$$.

Now another value $$x=\dfrac{-6}{-5} =\dfrac{6}{5}$$
Now since as we know that the product of negative terms gives positive,
i.e, $$x=\dfrac{2}{8}$$
$$=-6\times \left(\dfrac{1}{-5} \right) $$
$$=-6\times \left( -\dfrac{1}{5} \right) $$
$$=6\times \dfrac{1}{5} = \dfrac{6}{5}$$
Similarly, if y be the additive inverse of $$x=\dfrac{6}{5}$$, then,
$$x+y=0$$
$$\Rightarrow \dfrac{6}{5} +y=0$$
$$\Rightarrow y=-\dfrac{6}{5}$$
Therefore we can say that the additive inverse of $$\dfrac{6}{5}$$ is $$-\dfrac{6}{5}$$.


Note: While finding the inverse you can reduce the step by taking the negative sign of the given number, like additive inverse of $$x=\dfrac{2}{8}$$ is $$-x=-\dfrac{2}{8}$$ but in the second part we see that the numerator and denominator is in negative form, so because of that you have to find the actual sign of the number by taking the signs outside the fraction, and after that one can able to find the negative of that number.