(1) additive commutative law: a+b = b+a.

(2) Additive associative law: (A+B)+C = A+(B+C)

(3) Multiplicative commutative law: ab=ba

(4) multiplicative associative law: (ab)c=a(bc)

(5) Multiplication and distribution law: A (B+C) = AB+AC.

Extended data:

Division algorithm:

The property that the quotient of (1) is invariant is that the dividend and divisor are multiplied or divided by a number (except zero), and the quotient is invariant. a/b=(a*n)/(b*n)=(a/n)/(b/n)

(2) The sum (difference) of two numbers is divided by a number, which can be used to divide two numbers respectively (in the case of divisibility), and then the sum (difference) of two quotients can be found.

(a+b)/c = a/c+b/c； (a-b)/c=a/c-b/c

Properties of removing brackets in multiplication and division mixed operation

(1) The product of a number divided by two numbers is equal to the number divided by two factors of the product in turn.

a/(b*c)=a/b/c

(2) The quotient of a number divided by two numbers is equal to the number multiplied by the dividend in the quotient and the divisor in the divisor.

a/(b/c)=a/b*c