Branch of mathematics that deals with the properties of
Initially it dealt only with the counting numbers, but its definition has broadened to include all {{link=real number">real number s. The most important arithmetic properties (where a and b are real numbers) are the commutative law s of addition and multiplication, a + b = b + a and a b = b a ; the associative law s of addition and multiplication, a + (b + c) = (a + b) + c and a (bc) = (ab) c ; and the distributive law , which connects addition and multiplication, a (b + c) = a b + a c . These properties include subtraction (addition of a negative number) and division (multiplication by a fraction ).