1, the addition rule of rational numbers

Add two numbers, take the same sign, and then add the absolute values.

Add two different symbols with different absolute values, take the symbol with the larger absolute value, and subtract the symbol with the smaller absolute value from the larger absolute value.

Two opposite numbers add up to zero.

Add a number to zero and you still get the number.

2. Arithmetic of rational number addition

Additive commutative law: When two numbers are added, the position of the addend is reversed and the sum remains the same. That is, a+b = b+a.

Law of addition and association: when three numbers are added, the first two numbers are added, or the last two numbers are added first, and the sum is unchanged. That is, (a+b)+c=a+(b+c).

3, rational number subtraction rule: subtracting a number is equal to adding the reciprocal of this number. That is, a-b=a+(-b).

4, the multiplication rule of rational numbers

Multiply two numbers, the same sign is positive, the different sign is negative, and then multiply by the absolute value.

Any number multiplied by 0 is 0.

Two numbers whose product is 1 are reciprocal.

Concepts of monomial and polynomial

1, monomial: In an algebraic expression, if only multiplication (including power) operations are involved. Or algebraic expressions that contain division but do not contain letters in division are called monomials.

2. The coefficient and times of single item: the non-zero numerical factor in single item is called the numerical coefficient of single item, which is simply referred to as the coefficient of single item; When the coefficient is not zero, the sum of all the letter indexes in the single item is called the number of times of the single item.

3. Polynomial: The sum of several monomials is called polynomial.

4. Number and degree of polynomials: the number of monomials contained in a polynomial is the number of polynomial terms, and each monomial is called a polynomial term; In polynomial, the degree of the term with the highest degree is called the degree of polynomial.