ASSOCIATIVE LAWS, two laws relating to numbers, one with respect to addition and the other with respect to multi plication. These laws may respectively be defined symbolically as follows : a+ (b + c) = (a + b) + c, and a(bc) _ (ab) c; that is, the terms or the factors may be associated in any way we choose. (See also COMMUTATIVE LAWS.) The numbers may be either positive or negative, integral or fractional, rational or irrational, and real or imaginary. The laws do not hold through out the entire range of mathematics, however. For example, the associative law of addition does not hold for certain divergent series. (See SERIES.)