Question

If $\dfrac{2}{{ - 9}}$ is additive inverse of $\dfrac{2}{{q}}$ then $q$ is equal to.

Answer 1

Hint: We have given the equation in the form of a rational number the additive inverse of the number can be found by using additive inverse identity. In the given function additive inverse. Identity $x + y = 0$ is applied. In that way, we can find the General solution of the given function. To solve the question let us discuss in detail about rational numbers and additive inverse.

Complete step by step answer:
Rational numbers are those which can be in the form of $\dfrac{p}{q}$ whose $p$ and $q$ both are integers. But there is a condition that is $q$ does not equal to zero i.e. $q \ne 0$, in the Rational numbers.
$p$ is the numerator and $p$ can be a positive and negative number as well. The value of $p$ is also considered to be zero.
$q$ is the denominator and $q$ can be a positive and negative number as well. But $q$ does not equal to be zero.

Additive Inverse:- When we change the sign of a number is known as Inverse of a number.
Additive inverse of a number is that in which we added a number and it yields zero. If $x$ is a number then we added $ - 1$ to it like.
$x + ( - x) = 0$ then it becomes zero. So we called $ - x$ be the additive inverse of $x$.

We have given $\dfrac{2}{{ - 9}}$ where it is a rational number it is in the form of $\dfrac{p}{q}$ where $p$ is $2$ and $q$ is $ - 9$.

Apply the additive identity
$x + y = 0$ on the given function.
Let $x$ be $\dfrac{2}{-9}$ and let $y$ be the additive inverse of $x$ so,
The identity is $x + y = 0$. The value of additive inverse $y$ from given identity becomes.
$y = - x$

Now, substituting the value of $x$ in the above equation we get.
$y = - \left( {\dfrac{2}{{ - 9}}} \right)$
As there are two negative signs so, the value $\dfrac{2}{9}$ becomes positive
We have
\[y = \dfrac{2}{9}\]
As $\dfrac{2}{9}$ is the form of $\dfrac{p}{q}$ as $p$ is $2$ and $q$ is $9$.
 In that way we can find the value of $q$ is $9$

Note: In above question, it is based on the rational number and additive inverse Rational numbers are used in our real life. They are used by banks and in taxes also for buying and selling products for solving the given question. Identity of additive inverse is used. In that way we can find out the solution of the given problem.