Question

What is the reciprocal of \[\dfrac{{ - 2}}{3}\]?

Answer 1

Hint: Given is a fraction with numerator and denominator. We have to find the reciprocal of the given fraction. It means if A is any number of the form, then the reciprocal is given by \[\dfrac{1}{A}\] . Thus, we will use the same thing to solve the question above.

Complete step-by-step answer:
Given is a fraction \[\dfrac{{ - 2}}{3}\].
Now in order to find the reciprocal let \[A = \dfrac{{ - 2}}{3}\]
Then reciprocal is given by \[\dfrac{1}{A} = \dfrac{1}{{\dfrac{{ - 2}}{3}}}\]
But this is not the simplified form. We will shift the denominator of the denominator of the main fraction to the numerator and the minus sign is always on the numerator.
\[ = \dfrac{{ - 3}}{2}\]
This is the simplified and correct answer.
So, the correct answer is “\[ \dfrac{{ - 3}}{2}\]”.

Note: Note that inverse and reciprocal are the words that are frequently used in place of each other. Whereas the reciprocal is the special multiplicative inverse such that if a number and its reciprocal are multiplied then the result will be 1.
Also note that there exists an additive inverse in which the sum of that number and its additive inverse is always zero.
But the reciprocal of a fraction is we can say flipping of the numerator and denominator.