1, additive commutative law: Two addends are interchanged, and the sum is unchanged. This is called additive commutative law. Expressed in letters: a+b = b+a.

2, the law of addition and association: three numbers are added, first add the first two numbers, or add the last two numbers first, and the sum is unchanged. This is the so-called law of additive association. Expressed in letters: (a+b)+c = a+(b+c).

3. Multiplicative commutative law: two factors exchange positions and the product remains unchanged. This is the so-called multiplication commutative law. Expressed in letters: a× b = b× a.

4. Multiplication and association law: When three numbers are multiplied, the first two numbers are multiplied first, or the last two numbers are multiplied first, and the product remains unchanged. This is the so-called law of multiplication and association. Expressed in letters: (a×b)×c= a ×( b×c).

5. 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 them up. This is the so-called law of multiplication and division. Expressed in letters: (a+b) × c = a× c+b× ca× (b+c) = a× b+a× c.

6. The nature of subtraction 1: If a number subtracts two numbers continuously, the sum of the two subtractions can be subtracted. Expressed in letters: A-B-C = A-(B+C) A-(B+C) = A-B-C.

7. The essence of subtraction 2: One number subtracts two numbers continuously, and you can subtract the second subtraction first and then the first subtraction. Expressed in letters: a-b a-b-c = a-c-b c-b.

8. The nature of division 1: A number is divided by two numbers continuously and can be divided by the product of these two divisors. Expressed in letters: a ÷ b ÷ c = a ÷ (b× c) a ÷ (b× c) = a ÷ b ÷ c c.

9. Nature of Division 2: A number is continuously divided by two numbers, which can be divided by the second divisor first and then by the first divisor. Expressed in letters: a ÷ b ÷ c = a ÷ c ÷ b