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Last updated date: 04th Dec 2023
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MVSAT Dec 2023

Find the additive inverse of the following rational number: $\dfrac{-7}{-12}$.

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Hint: The additive inverse or one can say the opposite of a number is the number which when added to the number gives the sum of zero, that is, this number is equal in magnitude to the original number but opposite in sign. In our problem, both the numerator as well as the denominator contain negative digits in which these negative signs get cancelled out and the number becomes positive. So, the additive inverse of this number will be negative.

Complete step-by-step solution:
We have been given to find the additive inverse of a fraction. The fraction given to us is equal to: $\dfrac{-7}{-12}$. Here, we can see that both the numerator as well as the denominator contain negative digits. This implies that these “minus” signs will cancel each other out. Thus, our number is now equal to: $\dfrac{7}{12}$.
Now, the number given to us has been simplified and is equal to $\dfrac{7}{12}$. Let the additive inverse of this number be denoted by ‘p’. Then, we can calculate the value of ‘p’ as follows:
The sum of $\dfrac{7}{12}$ and ‘p’ should be equal to zero. Mathematically, this could be written as:
$\Rightarrow p+\left( \dfrac{7}{12} \right)=0$
Taking the constant side from the left-hand side of our equation to the right-hand side of the equation, we get the final result as:
$\Rightarrow p=-\dfrac{7}{12}$
Hence, the additive inverse of $\dfrac{-7}{-12}$ comes out to be $-\dfrac{7}{12}$ .

Note: Zero is the only number (among real and complex numbers) which is the additive inverse of itself. Also, one should not confuse the additive inverse of a number with its multiplicative inverse, which is actually the reciprocal of the original number. If only the term “inverse” is used then, we shall calculate the multiplicative inverse in that case.