What are the formulas of commutative law, associative law, distribution rate, multiplicative commutative law, associative law and distribution rate?

1, multiplication method of substitution: In the multiplication of two numbers, according to the calculation order from left to right, two factors are multiplied, and the position of the exchange factor remains unchanged.

The formula of multiplicative commutative law: a× b = b× a.

2. Multiplication and association law: three numbers are multiplied, that is, the first two numbers are multiplied and then multiplied, or the last two numbers are multiplied and then multiplied, and the product remains unchanged.

The formula of multiplicative associative law (a×b)×c=a×(b×c)

3. Multiplication and distribution law: the sum of two numbers is multiplied by one number. You can multiply them by this number first, and then add up the products.

The formula of multiplication and distribution law is: (a+b) × c = a× c+b× c.

Extended data

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.

References:

Baidu encyclopedia-multiplication