Question

Write the additive inverse of the given rational number:
\[\dfrac{-2}{-3}\]

Answer 1

Hint: In this question, as we already know from the properties of real numbers, that additive inverse is the number whose sum with the given number gives zero which is given by \[a+\left( -a \right)=0\]. Now, we need to consider the additive inverse as some variable and add the given number to it. Then equate the sum to zero and simplify further to get the result.

Complete step by step solution:
Rational Numbers:
A number which can be written in the form of \[\dfrac{p}{q}\], where \[p,q\in Z\]and \[q\ne 0\], is called a rational number. a rational number can be expressed as decimal based, on which rational numbers are divided again into two types called terminating and non-terminating recurring.
Real Number:
Any number, which is either rational or irrational is called a real number and is denoted by the symbol R.
Now, from the properties of the real numbers we have that
Additive Inverse:
Additive inverse of a number is the number when added to the given number yields zero which is given by
\[a+\left( -a \right)=0\]
Now, the given number in the question is \[\dfrac{-2}{-3}\]
Let us now assume its additive inverse as some b
Now, from the additive inverse property we have
\[\Rightarrow b+\dfrac{-2}{-3}=0\]
Let us now rearrange the terms
\[\Rightarrow b=-\left( \dfrac{-2}{-3} \right)\]
Now, this can be further written as
\[\therefore b=\dfrac{-2}{3}\]
Hence, the additive inverse of \[\dfrac{-2}{-3}\] is \[\dfrac{-2}{3}\]

Note:
Instead of considering the additive inverse property if we consider the additive identity property then the result will be completely different. So, we need to be careful while considering the property and then should simplify accordingly.
It is important to note that there are negative signs in the numerator and denominator of the given number so when we find the additive inverse there should be a negative at the last. Because forgetting the sign gives incorrect results.