Algebraic Operation

Operation that follows certain rules regarding signs.

The expression "law of signs" is often used to refer to these algebraic operations.

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