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.
Multiplication can also be seen as calculating the objects arranged in a rectangle (integer) or finding the area of a rectangle with a given side length. The area of the rectangle does not depend on which side is measured first, which shows the exchange property. ?
Extended data:
Multiplication algorithm
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.