The origin history of multiplication: multiplication comes from addition, which is a quick calculation of addition. When multiple identical numbers are added, multiplication is introduced to improve the calculation efficiency. 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. The product of two measured values is a new type of measurement, for example, multiplying the length of two sides of a rectangle to get its area, which is the theme of size analysis.