Absolute value and opposite integers

Key Notes:

  1. 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.
  2. Notation:
    • The absolute value of a number aaa is denoted as ∣a∣|a|∣a∣.
  3. Examples:
    • ∣5∣=5
    • ∣−5∣=5
    • ∣0∣=0
  4. Properties:
    • ∣a∣≥0|a| for any real number aaa.
    • ∣a∣=0 if and only if a=0.
    • ∣a×b∣=∣a∣×∣b∣|.

Opposite Integers

  1. 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.
  2. Examples:
    • The opposite of 7 is -7.
    • The opposite of -3 is 3.
    • The opposite of 0 is 0.
  3. 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!