Multiplication calculates objects arranged in a rectangle (integer), or finds 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.
Extended data:
This problem is a solution of multiplication.
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.
The Egyptian integer and fraction multiplication method recorded in Ames papyrus is continuous addition and doubling. For example, to find the product of 13 and 2 1, 2 1 must be multiplied by 2 to get 2×2 1 = 42, 4× 2 1 = 2× 42 = 84, 8× 2/kloc.
13×2 1 =( 1 + 4 + 8)×2 1 =( 1×2 1)+(4×2 1)+(8×2 1)= 2 1 + 84 + 168 = 273。