 Congruence modulo formula_1 (for a fixed formula_1) is compatible with both addition and multiplication on the integers.That is,

if

then

The corresponding addition and multiplication of equivalence classes is known as modular arithmetic.From the point of view of abstract algebra, congruence modulo formula_1 is a congruence relation on the ring of integers, and arithmetic modulo formula_1 occurs on the corresponding quotient ring.