1, when two numbers are multiplied, one factor is expanded (or reduced) by n times, and the other factor is unchanged, then their product is also expanded by n times. (n is a non-zero natural number).
2. If a factor is amplified by a factor and a factor is amplified by b times, the product is amplified by a*b times.
When two numbers are multiplied, one factor is enlarged by n times and the other factor is reduced by n times, so their products remain unchanged.
Summary: The law of product change refers to the change of product caused by the change of factors. If one factor is enlarged by n times, and the other factor remains unchanged, the product is also enlarged by n times. If one factor is enlarged by n times and the other factor is reduced by n times, the product remains unchanged.
Expand one's knowledge
The basic definition in elementary arithmetic is the number or quantity obtained by multiplying two or more numbers or quantities. Sometimes called products. Product is the name of many different concepts in mathematics. In arithmetic, the result of multiplication of two or more numbers is called their product or product.
When the multiplied numbers are real numbers or complex numbers, the order of multiplication has no effect on the product, which is called commutativity. When the product is a quaternion or matrix, or an element in some algebraic structures, the order will affect the result of the product. This shows that the multiplication of these objects is not commutative.
Product of algebraic objects
Objects with various algebraic structures can get different products by defining different binary operations. For example, a plane vector can define a point product, and a three-dimensional vector can define a cross product and a mixed product. Common products include: the inner product of two vectors in vector space, the product of matrix in matrix set, Hadamard product of matrix, Kroneck product of matrix, outer product of tensor, tensor product of tensor and point-by-point product of two functions.
Product of algebraic structure
The concept of product of algebraic structure is often used when studying algebraic structure in abstract algebra. The product of two algebraic structures is generally defined as a new algebraic structure in which the elements in the two algebraic structures correspond to a new element through a binary mapping, and then the new element is formed through appropriate rules.
If the number of elements of two algebraic structures is limited, then the number of elements of their product will be the product of their respective elements. This is one of the reasons why this new algebraic structure is called product.