Absolute Value

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The absolute value of a number describes the distance of the number on the number line from 0. It does not consider which direction from 0 the number lies. The absolute value of a number is always positive.

The absolute value of 3 is 3 which means that its distance from 0 is 3 units

The absolute value of −3 is also 3 which means that its distance from 0 is 3 units

The symbol for absolute value is two straight lines || (called bars) surrounding the number or expression for which you wish to indicate absolute value.

For example:	\| 6 \| = 6 which means the absolute value of 6 is 6. \| − 6 \| = 6 which means the absolute value of -6 is 6.
	\| 3 − 7 \| = \| −4 \| = 4
	\| 6 + 3(−5) \| = \| 6 − 15 \| = \| −9 \| = 9

Have a look at the following videos for more examples on absolute values:

It is important to note that the absolute value bars do NOT work in the same way as parentheses. Recall that − (−5) = (−1) × (−5) = +5.

However, for the absolute value it is done by removing the absolute bar and then performing the sign operation.
−| −5 | = −(+5) = (−1) × (+5) = −5

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For example:	\| 6 \| = 6 which means the absolute value of 6 is 6. \| − 6 \| = 6 which means the absolute value of -6 is 6.
	\| 3 − 7 \| = \| −4 \| = 4
	\| 6 + 3(−5) \| = \| 6 − 15 \| = \| −9 \| = 9