Question

What is the reciprocal of -3?
(a) -3
(b) \[\dfrac{-1}{3}\]
(c) \[\dfrac{1}{3}\]
(d) 3
(e) Undefined.

Answer 1

Hint: We solve this problem by using the definition of reciprocal. The reciprocal is more similar to the multiplicative inverse. In mathematical definition we take both as the same. The number \['x'\] is said to be the reciprocal of \['n'\] if
\[n\times x=1\]
By using the above condition we find the reciprocal of the given number.

Complete step by step answer:
We are asked to find the reciprocal of -3
Let us assume that the given number as
\[\Rightarrow n=-3\]
Let us assume that the reciprocal of given number as \['k'\]
We know that the reciprocal is more similar to the multiplicative inverse.
We also know that the number \['x'\] is said to be the reciprocal of \['n'\] if
\[n\times x=1\]
By using the above definition onto given number we get
\[\Rightarrow n\times k=1\]
By substituting the required values in above equation we get
\[\Rightarrow -3\times k=1\]
Now by taking the constant term in the above equation to other side we get
\[\Rightarrow k=-\dfrac{1}{3}\]
Therefore, we can conclude that the reciprocal of -3 is \[-\dfrac{1}{3}\]

So, the correct answer is “Option b”.

Note: We have another method for finding the reciprocal of a number.
The reciprocal of a number \['n'\] is given as \['\dfrac{1}{n}'\]
We are asked to find the reciprocal of -3
Let us assume that the given number as
\[\Rightarrow n=-3\]
Let us assume that the reciprocal of given number as \['k'\]
By using the formula of reciprocal we get
\[\Rightarrow k=\dfrac{1}{n}\]
By substituting the required values in above equation we get
\[\begin{align}
  & \Rightarrow k=\dfrac{1}{\left( -3 \right)} \\
 & \Rightarrow k=-\dfrac{1}{3} \\
\end{align}\]
Therefore, we can conclude that the reciprocal of -3 is \[-\dfrac{1}{3}\]
So, option (b) is the correct answer.