Below are the main properties of the modulus of a real number (i.e. positive, negative and zero).
Property 1
The modulus of a number is the distance, which cannot be negative. Therefore, the modulus cannot be less than zero.
|a| ≥ 0
Property 2
The modulus of a positive number is equal to the same number.
|a| = aAt a > 0
Property 3
The module of a negative number is equal to the same number, but with the opposite sign.
|-a| = aAt a <0
Property 4
The absolute value of zero is zero.
|a| = 0At a = 0
Property 5
The modules of opposite numbers are equal to each other.
|-a| = |a| = a
Property 6
The absolute value of a number a is the square root of a2.
Property 7
The modulus of the product is equal to the product of the modules of the numbers.
|ab| = |a| ⋅ |b|
Property 8
The modulus of a quotient is equal to dividing one modulus by another.
|a : b| = |a| : |b|