Home > Pre-Algebra > Absolute Value > Subtracting Absolute Value

## Subtracting Absolute Value

#### Introduction

Absolute value is a way to measure how far a number is from zero on the number line. Because absolute value measures distance, and not direction, all absolute values are positive. Absolute value is written with the symbols | | either side of the number.

+3 is 3 units away from 0 on the number line, so:

$|3| = 3$

-3 is also 3 units away from 0 on the number line, so:

$|-3| = 3$

As a quick way to remember how to do absolute values, for positive numbers, the absolute value is the same. For negative numbers, simply remove the negative sign.

#### Terms

Absolute Value - The distance of a value from 0 on a number line.
Positive - Any value greater than zero.
Negative - Any value less than zero.

## Lesson

To subtract absolute values, you will need to first calculate the absolute values in the problem.

Take the following problem:

$|10| - |-8| = ?$

To solve this, we use order of operations to first calculate what the absolute value of each of the figures.

10 has a distance of 10 units from 0 and therefore has an absolute value of 10. For positive numbers, the absolute value is the same as the regular value.

$10 - |-8| = ?$

-8 is 8 units away from 0, and therefore has an absolute value of 8. For negative numbers, you can quickly calculate the absolute value by removing the negative sign.

$10 - 8 = ?$

The problem is now a simple subtraction question. 10 – 8 is 2, so this is the answer.

$10 - 8 = 2$$|10| - |-8| = 2$

Using absolute values in calculations requires you to solve the absolute values first, before proceeding on with the numbers as normal.

## Examples

#### Negative Absolute Value

$|20| - |5|$
$|20| = 20$
$|5| = 5$
$20 - 5 = 15$

#### Negative Absolute Value

$|-4| - |3|$
$|-4| = 4$
$|3| = 3$
$4 - 3 = 1$