Home > Pre-Algebra > Absolute Value > Multiplying Absolute Value

Multiplying Absolute Value


Absolute value in Math is a way that we can measure how far a number is from 0, without taking into account the direction (whether the number is positive or negative). We denote absolute value by using the symbols | | either side of the number. The absolute value of x is written as | x |.

To find the absolute value of a positive number is simple because the values are the same. The number 7 is 7 units away from 0 on the number line, so:

7=7|7| = 7

To find the absolute value of a negative number you count how far it is from 0 in units. Another way to do this is just to remove the negative sign. –7 is 7 units away from 0 on the number line, so:

7=7|-7| = 7


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.


In order to multiply an absolute value, you need to first work out the absolute terms. Take the following example:

6x3=?|6| x |-3| = ?

In order to solve this, we first need to work out the absolute values of the figures.

The absolute value of 6 is the distance of 6 from 0. 6 is 6 units away from 0. For positive numbers, their absolute value is the same as their non-absolute value, so we can keep that the same:

6x3=?6 x |-3| = ?

Next, we need to find the absolute value of | -3 |. -3 is 3 units distant from 0, and therefore has an absolute value of 3. For negative numbers, a quick way to calculate the absolute value is to just remove the negative sign.

6x3=?6 x 3 = ?

That leaves a regular multiplication problem. 6 x 3 is 18, and so the answer is:

6x3=186 x 3 = 186x3=18|6| x |-3| = 18

The trick with absolute value is to solve the absolute value first in the order of operations, before completing the rest of the problem.


Multiplying Absolute Value Worksheets (PDF)

Multiplying Absolute Value Worksheet 1

Multiplying Absolute Value Worksheet 2

Multiplying Absolute Value Worksheet 3