Question

Write the reciprocal of $ - 5$.

Answer 1

Hint: This problem deals with the basic mathematical concepts, which includes the topic of the reciprocation, or with finding the inverse of any given number. In order to solve this problem we need to be familiar with types of numbers such as natural numbers, whole numbers and integers etc.Reciprocal of a given number is the inverse of the number.

Complete step-by-step solution:
The reciprocal of any given number is nothing but the inverse of that particular given number.
Given that a number which is -5, which is a negative integer.
Integers are the nothing but the whole numbers including zero, and also the negative of the whole numbers.
The integers set contains the numbers which are negative numbers as well as the positive numbers including zero.
The integers set is denoted by the letter $Z$, which is given below;
$ \Rightarrow Z = \left\{ {..... - 6, - 5, - 4, - 3, - 2, - 1,0,1,2,3,4,5,6....} \right\}$
So the integers set consists of negative whole numbers which are to the left of the zero, and the positive whole numbers which are to the right side of the zero.
Zero is a whole number, and hence it is an integer too.
Now given the number -5, which is an integer, also a negative integer because of the negative sign before the number 5.
Hence -5 is a negative integer.
Now we know that the reciprocal of a number is the inverse of the number.
Inverse of any number is the reciprocal of that number which is obtained by the fraction of which its numerator will be 1, and the denominator of the fraction will be the given number.
So the reciprocal of any given number is a fraction, with its numerator to be 1, and the denominator to be the given number.
Now finding the reciprocal of -5, as given below:
$ \Rightarrow \dfrac{1}{{ - 5}} = - \dfrac{1}{5}$

The reciprocal of -5 is $\dfrac{{ - 1}}{5}$.

Note: While solving the above problem please keep this in mind that all whole numbers are integers and since zero is also a whole number, thus zero is also an integer.
The whole number set is the set of natural numbers including zero, which would be : $\left\{ {0,1,2,3....} \right\}$.
While the set of natural numbers would be starting from 1, which would be : $\left\{ {1,2,3,4,....} \right\}$
Here natural numbers are also called as the counting numbers.