Question

What is the opposite and reciprocal of $18$ ?

Answer 1

Hint: In the given question, we have to find the opposite and the reciprocal of the given number. We will first understand the meaning of the terms opposite and reciprocal. Then, we will form the equations for both the entities and find their values. Opposite of a number is also termed as additive inverse. Reciprocal of a number is also termed as multiplicative inverse.

Complete answer:
So, the number given to us in the problem is $18$.
Let us assume the opposite of the number to be a variable, let's say x. Then, the sum of $18$ and x should be equal to zero. So, we get,
$x + 18 = 0$
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 = - 18$
So, the value of x is $ - 18$. Hence, the opposite of the number $18$ is $ - 18$.
Now, let us consider the reciprocal of the number as y.
Then the product of $18$ and y should be equal to unity. So, we get,
$ \Rightarrow \left( {18} \right) \times y = 1$
Isolating y and shifting other terms to the right side of the equation. So, dividing both sides by $18$, we get,
$ \Rightarrow y = \dfrac{1}{{\left( {18} \right)}}$
Simplifying the value of x,
$ \Rightarrow y = \dfrac{1}{{18}}$
So, we obtain the value of y as $\dfrac{1}{{18}}$. Therefore, the multiplicative inverse of the number given to us in the problem itself, $18$ is obtained as $\dfrac{1}{{18}}$.

Note:
We can see that the additive inverse of the number is opposite in sign when compared to the original number. Thus, we can notice that the additive inverse of a number is actually the same as the negation of the number. Similarly, we can also notice that the multiplicative inverse of a number is reciprocal of the number. We can find the opposite and reciprocal through these techniques.