Question

How do you find the reciprocal of $\dfrac{-2}{3}$?

Answer 1

Hint:Here the basic concept which is going to be used is that when a number is multiplied by its reciprocal then the product is always unity. After that just simply calculate the reciprocal by using the above-given information.

Complete Step by Step Solution:
As we know that when we multiply a number by its reciprocal the product is always equal to unity i.e. 1
So, here the given number is $\dfrac{-2}{3}$
Let us consider the reciprocal of the given number as x
Given number X Reciprocal = 1
$\Rightarrow \left( \dfrac{-2}{3} \right)\times \left( x \right)=1$
Now, multiplying both sides by $\dfrac{-3}{2}$
$\Rightarrow \left( \dfrac{-3}{2} \right)\times \left( \dfrac{-2}{3} \right)\times \left( x \right)=1\times \left( \dfrac{-3}{2} \right)$
$\Rightarrow x=\dfrac{-3}{2}$

Hence the reciprocal of $\dfrac{-2}{3}$ is $\dfrac{-3}{2}$

Additional Information:
We can confirm that the reciprocal of a given number we got is correct or not by multiplying the given number with the reciprocal number we got. If we will get the product as 1 then it is reciprocal of that given number otherwise not.

Note:
There is an additional method to solve this
Whenever you want to find the reciprocal of a number, just place it in denominator having numerator as 1 always
In this question, we are given $\dfrac{-2}{3}$
So, its reciprocal will be
$=\dfrac{1}{\dfrac{-2}{3}}$
Rewriting above number
$=\dfrac{3}{-2}$
Which is simply $\dfrac{-3}{2}$ , reciprocal of $\dfrac{-2}{3}$.