Adding Absolute Value

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Introduction

Absolute value is defined as a number’s distance in units from 0 on the number line. The number 3 is 3 units away from 0 on the number line, so has an absolute value of 3. -3 is also 3 units away from 0 on the number line, so also has an absolute value of 3.

For positive numbers, the absolute value is the same as the number’s value. For negative numbers, the absolute value is the same as the number without the negative sign. Absolute values are always positive numbers.

Absolute values are represented by the use of | | either side of the number. The absolute value of x is written as $|x|$ .

For example:

$|-3| = 3$

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 add two absolute values, you need to first work out the absolute values individually, then proceed with the equation as a normal addition problem.

For example, using the question below:

$|8| + |-5| = mathord{?}$

First, you would write out the absolute values for the two terms in the equation. Since 8 is a positive value, its absolute value is the same, so that remains the same.

$8 + |-5| = mathord{?}$

For $|-5|$ you will need to calculate the absolute value. –5 is 5 units away from 0, so the absolute value is 5. (Another way to do this is just to remove the negative sign).

$8 + 5 = mathord{?}$

Now we just complete the equation as normal. The total of 8 and 5 is 13, so the answer is 13.

$8 + 5 = 13$

$|8| + |-5| = 13$

Just remember to work out the absolute values first in the order of operations, and you can then solve the equations like regular addition equations.

Examples

Positive Absolute Value

|4| + |7|

|4| = 4

|7| = 7

4 + 7 = 11

Negative Absolute Value

|2| + |-1|

|2| = 2

|-1| = 1

2 + 1 = 3

Negative Absolute Value

|2| + |-1| + |5| + |2|

|2| = 2

|-1| = 1

|5| = 5

|2| = 2

2 + 1 + 5 + 2 = 10