What are the addition rules for rational numbers?

Answer 1

The set of rational numbers form an Abelian group under addition. That is, if x, y and z are any rational numbers, then

• x + y is a rational number (closure)
• (x + y) + z = x + (y + z) (associative property), and this means that either can be written as x + y + z
• there is a rational number, 0, such that x + 0 = x = 0 + x (existence of identity)
• for any x, there is a rational number x' such that x + x' = 0 = x' + x (existence of additive inverse). x' is denoted by -x.
• x + y = y + x (commutative or Abelian property).