# Algebraic Operation

## 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) = (ab) if ab and
(+a) + (–b) = –(ba) if a < b
• (–a) + (–b) = –(a + b)
• (–a) + (+b) = –(ab) if ab and
(–a) + (+b) = (ba) if ab

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) = (ab) if a > b and
(+a) – (+b) = –(ba) if a < b
• (–a) – (+b) = –(a + b)
• (–a) – (–b) = –(ab) if a > b and
(–a) – (–b) = (ba) if ab

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 :

• $$\dfrac{(+a)}{(+b)}$$ = $$\dfrac{(–a)}{(–b)}$$ =$$\dfrac{a}{b}$$
• $$\dfrac{(+a)}{(–b)}$$ = $$\dfrac{(–a)}{(+b)}$$ = – $$\dfrac{a}{b}$$