Absolute value and opposite integers
Key Notes:
- 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
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. |
What is the absolute value of –7?
key idea: Absolute values are positive or zero.
solution:
The absolute value of a number is its distance from 0.
Find the distance between –7 and 0 on a number line.

The distance between –7 and 0 is 7 .
So, the absolute value of –7 is 7.
Learn with an example
➡️ What is the opposite of 2?
The opposite of 2 is –2.
➡️ What is the opposite of 5?
The opposite of 5 is –5.
➡️ What is the absolute value of –3?
The absolute value of a number is its distance from 0.
Find the distance between –3 and 0 on a number line.

The distance between –3 and 0 is 3 .
So, the absolute value of –3 is 3.
Try some practice problems!