Law of Signs

Set of laws that govern basic operations on real numbers.

Properties

The addition of real numbers is carried out according to the following rules, where a and b are positive numbers :

(+a) + (+b) = (a + b)
(+a) + (–b) = (a – b) if a ≥ b and (+a) + (–b) = –(b – a) if a < b
(–a) + (–b) = –(a + b)
(–a) + (+b) = –(a – b) if a ≥ b and (–a) + (+b) = (b – a) if a < b

The subtraction of real numbers is carried out according to the following rules, where a and b are positive numbers :

(+a) – (–b) = (a + b)
(+a) – (+b) = (a – b) if a > b and (+a) – (+b) = –(b – a) if a < b
(–a) – (+b) = –(a + b)
(–a) – (–b) = –(a – b) if a > b and (–a) – (–b) = (b – a) if a < b

The multiplication of two real numbers is carried out according to the following rules :

(+a) × (–b) = (–a) × (+b) = –ab
(+a) × (+b) = (–a) × (–b) = ab

The division of two real numbers is carried out according to the following rules :

[latex]\dfrac{(+a)}{(+b)} = \dfrac{(–a)}{(–b)} = \dfrac{a}{b}[/latex]
[latex]\dfrac{(+a)}{(–b)} = \dfrac{(–a)}{(+b)} = – \dfrac{a}{b}[/latex]