Several methods are expressed by multiplication: for example, five threes are added, 5x3 =15; Four 3+3+3+3, written as 3×4. Multiplication is a shortcut to add up the same numbers. The result of its operation is called product, and "X" is the symbol of multiplication. From the philosophical point of view, multiplication is the result of qualitative change caused by additive quantity. The multiplication of integers (including negative numbers), rational numbers (fractions) and real numbers is a systematic summary of this basic definition.

Law of multiplication operation

Integer multiplication meets the following requirements: exchange law, association law, distribution law and elimination law.

With the development of mathematics, the object of operation has developed from integer to more general group.

Intra-group multiplication is no longer needed to satisfy the commutative law. The most famous noncommutative example is the quaternion group discovered by Hamilton. But the law of association is still satisfied.