Arithmetic operations. Numerical identities

Arithmetic operations (addition, subtraction, multiplication, division) are binary operations on numbers. Numerical identities are equalities that hold for all numbers, such as $a + 0 = a$ (additive identity) and $a imes 1 = a$ (multiplicative identity).

Important properties

• Additive identity: $a + 0 = a$

• Multiplicative identity: $a imes 1 = a$

• Commutativity: $a + b = b + a$, $a imes b = b imes a$

• Associativity: $(a + b) + c = a + (b + c)$, $(a imes b) imes c = a imes (b imes c)$

• Distributivity: $a imes (b + c) = a imes b + a imes c$