# Absolute numbers

What does it mean when a variable is between two vertical lines, like this: |x|?

## Absolute numbers

Maria is out for a walk. First, she walks one kilometer east, to Lina. Then she walks two kilometers west, to Leon. And then she walks three kilometers east, all the way to the beach. How far did Maria walk?

There are two different answers to this question. If we mean "how far away is Maria from her house?" Then you get the answer by taking the first distance, A... minus the second distance, B... plus the third distance, C. One minus two plus three.

Maria is two kilometers away from her house. But if we mean "How many kilometers did Maria cover?", the answer will be different. It is A, plus B, plus C. Maria walked 1 plus 2 plus 3, six kilometers in total. In the second calculation we changed the negative variable, B, to the same value, but a positive one.

The variables that were already positive we left as they were. In mathematics, this is called finding the absolute value of variables. The absolute value of a negative number is the same number, but positive! We write it like this: The absolute value of A, plus the absolute value of B, plus the absolute value of C. The vertical lines on each side of A, B, and C tell us that we deal with the absolute values of the three variables.

Here, we don't need to know which direction Maria walked. Regardless of whether A, B and C are negative or positive numbers, the absolute values are positive. Another way of looking at absolute values is like this: The absolute value of a number tells you how many steps away from zero it is on the number line. Five is five steps from zero. Minus five is also five steps from zero.

The absolute value of five is five. The absolute value of minus five is also five. So if you have to calculate the absolute value of X, you know it must be equal to or greater than zero. Two vertical lines before and after a variable mean absolute value. You get the absolute value of a negative number by removing the minus sign.

If X is a positive number, the absolute values of X and minus X are the same. The absolute value is always equal to or greater than zero.