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 :
- \(\dfrac{(+a)}{(+b)} = \dfrac{(–a)}{(–b)} = \dfrac{a}{b}\)
- \(\dfrac{(+a)}{(–b)} = \dfrac{(–a)}{(+b)} = – \dfrac{a}{b}\)