Laws of Arithmetic

There are three laws of arithmetic: The associative law, the commutative law, and the distributive law. These laws are:

• Associative law:
  • For addition: (a + b) + c = a + (b + c)
  • For multiplication: (ab)c = a(bc)
• Commutative law:
  • For addition: a + b = b + a
  • For multiplication: ab = ba
• Distributive law: a(b + c) = ab + ac

You may also see these referred to as the "ACD laws of arithmetic," after the first initial of each of the laws.

The laws of arithmetic apply to the natural numbers, integers, rational numbers, real numbers, and even to complex numbers.