Absolute value

Whether you walk 5 steps left or 5 steps right, the distance covered is the same, namely 5. Only the direction differs. The absolute value of a number captures exactly this idea: it tells how far you are from zero, no matter the direction.

Absolute value means distance from zero

You write absolute value with two vertical bars. So $|{-}5| = 5$ and equally $|5| = 5$, because both numbers sit the same distance from zero. On the number line the absolute value is simply the length of the path from the number to zero.

Never negative

A distance can never be negative, so an absolute value is never negative either. It is zero only for the number zero itself and otherwise always positive. So between the bars a negative number loses its minus sign, while a positive number stays exactly as it is.

Absolute value in practice

Absolute values show up wherever only the size of a difference matters, not its direction. If the temperature falls from 5 degrees to minus 6 degrees, start and end lie $|5 - ({-}6)| = 11$ degrees apart. So the absolute value of a difference always tells you how far two values sit from each other.