Mathwarehouse Logo

Meaning of Absolute value

The formal definition of absolute value goes something like the following: "the magnitude of a real number without regard to its sign".

What the heck does that mean?

In plain "English", this means "how far from Zero" a number is, and the simplest way to understand this concept is by looking at some graphs!

Diagram 1 picture of absoltue value of 2 on number line

Diagram 1 above shows the $$ |2| $$ on a number line. As you can see, both $$-2$$ and $$2$$ satisfy the $$ |2| $$ because both of those numbers are '2' units from zero!

Example 2
Diagram 2 picture of absoltue value of 4 on number line

Diagram 2 above shows the $$ |4| $$ on a number line. As you can see, both $$-4$$ and $$4$$ satisfy the $$ |4| $$ because both of those numbers are '4' units from zero!

General Formula and Graph

general formula graph absolute value
Problem 1

What number can replace the question mark? (Can you figure out what absolute value that the number line graph below represents?)

'3' because $$ -3$$ and $$ 3 $$ are both the same distance from zero.

absolute value
Problem 2

What number can replace the question mark? (Can you figure out what absolute value that the number line graph below represents?)

There is no number that satisfies this . Because $$ 5 \ne 4 $$ . And the distance form zero must be the same.

absolute value
Next to Number line maker