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 :

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