Definition:

• The absolute value of a number is its distance from 0 on a number line, regardless of direction.
• It is always a non-negative number.

Notation:

• The absolute value of a number aaa is denoted as ∣a∣|a|∣a∣.

Examples:

• ∣5∣=5
• ∣−5∣=5
• ∣0∣=0

Properties:

• ∣a∣≥0|a| for any real number aaa.
• ∣a∣=0 if and only if a=0.
• ∣a×b∣=∣a∣×∣b∣|.

Opposite Integers

Definition:

• Two integers are opposites if they are the same distance from 0 on a number line but in opposite directions.
• The opposite of aaa is −a-a−a.

Examples:

• The opposite of 7 is -7.
• The opposite of -3 is 3.
• The opposite of 0 is 0.

Properties:

• aa and −a-a have the same absolute value: ∣a∣=∣−a∣.
• Adding opposite integers results in 0: a+(−a)=0

Practice problems

What is the opposite of –3?	The opposite of –3 is 3.
What is the opposite of –5?	The opposite of –5 is 5.
What is the opposite of 20?	The opposite of 20 is -20.
What is the opposite of 65?	The opposite of 65 is -65.
What is the opposite of -11?	The opposite of -11 is 11.
What is the absolute value of 4?	The absolute value of 4 is 4.
What is the absolute value of 3?	The absolute value of 3 is 3.
What is the absolute value of –3?	the absolute value of –3 is 3.
What is the absolute value of 8?	the absolute value of 8 is 8.
What is the absolute value of -1?	the absolute value of -1 is 1.

Learn with an example

Try some practice problems!