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Multiplying Absolute Value

Introduction

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:

$|7| = 7$

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:

$|-7| = 7$

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

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

$|6| x |-3| = ?$

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:

$6 x |-3| = ?$

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.

$6 x 3 = ?$

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

$6 x 3 = 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.