Question

How do you simplify $\left| -13 \right|$ ?

Answer 1

Hint: We have been given an expression which consists of an integer -13, enclosed in an absolute value function. We have to simplify and find how integer -13 will be modified on removing the absolute value function. Thus, we shall focus upon the mathematical meaning of an absolute value function and analyze how this function changes the expression within it.

Complete step by step solution:
Let us first look at the structure of a number line.
In a number line, the integer 0 is placed in the middle of the line which has all positive real numbers upto infinity on its right side and has all the negative real numbers up to negative infinity on its left side. From here, we understand that both the positive and negative values of a particular integer which are on the right and left sides of zero, are equidistant from zero.
The absolute value function is a function that gives its output equal to this distance of any positive or negative real number from zero on the number line.
Since the distance of integer -13 from 0 is 13 units on the number line, thus, we get
$\left| -13 \right|=13$

Therefore, the simplified value of $\left| -13 \right|$ is 13.

Note: We have understood that the absolute value function is used to represent the distance of any number both on the right side and the left side of zero on the number line. Therefore, we can also say that even if integer 13 would have been put within the absolute value function instead of integer -13, the output value of this function would not have changed and remained the same, that is, 13.