Question

Find the additive inverse of each of the following:
 $\dfrac{{ - 16}}{{ - 5}}$

Answer 1

Hint: In the given question, we have to find the additive inverse of the given number. To find the additive inverse of a number, we must know what the term additive inverse actually means. The additive inverse of x is a number which when added to x gives zero as result. So, to find the additive inverse of the given number, we first equate the sum of the number and its additive inverse as zero. Then, we solve the mathematical equation obtained using the transposition method to find the value of the variable.

Complete step by step answer:
So, the number given to us is $\dfrac{{ - 16}}{{ - 5}}$.
Let us assume the additive inverse of the number to be x. Then, the sum of $\dfrac{{ - 16}}{{ - 5}}$ and x should be equal to zero. So, we get,
$x + \left( {\dfrac{{ - 16}}{{ - 5}}} \right) = 0$
Cancelling the negative sign present in both numerator and denominator, we get,
$ \Rightarrow x + \left( {\dfrac{{16}}{5}} \right) = 0$
Now, we use the transposition method to find the value of variable x in the equation above. So, shifting the constant to the right side of the equation, we get,
$ \Rightarrow x = - \dfrac{{16}}{5}$
So, we obtain the value of x as $ - \dfrac{{16}}{5}$.
Hence, the additive inverse of \[\dfrac{{ - 16}}{{ - 5}}\] which is equivalent to \[\dfrac{{16}}{5}\] is $ - \dfrac{{16}}{5}$.

Note:
We can see that the additive inverse of the number is opposite in sign when compared to the original number. Thus, we can say that the additive inverse is actually the negation of the original number. This is true for every real number. We can use this trick directly to find the additive inverse of a number as this saves a lot of time and calculations.