Question

How do you find the absolute value of $- 6$?

Answer 1

In this particular type of question, use the concept that absolute value of the integers is the modulus of the integers and use that there are two types of integers present in the physical world either positive or negative except $0$ as it is neither of the both but it is an integer so use these concepts to reach the solution of the question.

Complete step by step solution:
(i) As we all know that the integers are those numbers which are written in the form of a number which does not contain any decimal or fraction.

They are of mainly two types, positive integers and negative integers, except $0$ which is neither positive nor negative.

On the number line, positive integers are in the right direction with $0$ while the negative integers are in the left direction with $0$.

Now, to find the absolute value of the given number, first we must know what is meant by absolute value. So, absolute value means the distance of the number from $0$ in any direction on the number line.

Mathematically, we express the absolute value of a number as its modulus i.e., absolute value of
$x$ is $\left| x \right|$.

So, here we are asked to find the absolute value of $- 6$. So, we will have to find its mod i.e., $\left| { - 6} \right|$.

(ii) As we know that, in the mod function, if the value of the number is $0$ or greater than $0$ which means positive then we take the value of the number as it is as its absolute value. Whereas, if the value of the number is less than $0$ which means negative, then we take the negative of that number as its absolute value.

So, as we know that $- 6$ is a negative integer, we will take the negative of $- 6$. Therefore,
$- ( - 6) = 6$

Therefore, $\left| { - 6} \right| = 6$

Hence, the absolute value of $- 6$ is $6$.

Note: Always remember that since the absolute value is the distance of the number from $0$ on the number line, it can never be a negative value as distance is never negative. Also, the only time the absolute value becomes $0$ is when the number itself is $0$. For any other number, the absolute value will be greater than $0$.