Question

Explain why the absolute value of a number is never negative.

Short answer

Absolute value of a number represents the distance of the number from 0 on the number line and distance cannot be negative.

Step-by-step solution

Step-1 – Absolute value of a number

Absolute value of any positive or negative number is always positive and equal to the magnitude of the number. The absolute value of a number N is denoted by $\left|N\right|$.

For example, the absolute value of 3 is denoted by $\left|3\right|$and is equal to 3.

And the absolute value of $-4$is denoted by $\left|-4\right|$and is equal to 4.

Step-2 – Apply the concept of Distance

The distance between any two points is always positive. Distance is never measures in negative quantity.

Step-3 – Explanation of absolute value of a number

Absolute value of a number represents the distance of the number from 0 on the number line. If the number is positive then the distance is on right side on the number line from 0 to that number. And if the number is negative, the distance is measure to the left of 0 to that number.

Since the absolute value of a number is the distance of the number from 0 on the number line, and the distance is always positive.

So, the absolute value of a number is never negative.