1, algorithm and properties:

(1) additive commutative law: When two numbers are added, the positions of addends are interchanged, and the sum remains unchanged. That is, a+b = b+a.

(2) law of addition and association: when three numbers are added, the first two numbers are added first, and then the third number is added; Or add the last two numbers first and then add them to the first number, and their sum remains the same. That is, (a+b)+c=a+(b+c).

(3) Multiplication and exchange law: When two numbers are multiplied, the position of the exchange factor remains unchanged. That is, a× b = b× a.

(4) Multiplication and association law: multiply three numbers, first by the first two numbers, and then by the third number; Or multiply the last two numbers first, and then multiply them with the first number, and their products remain unchanged. That is, (a×b)×c=a×(b×c).

(5) Multiplication and distribution law: the sum (difference) of two numbers is multiplied by a number, and the two numbers can be multiplied by this number respectively, and then the two products are added (subtracted). That is, (a+b) × c = a× c+b× c.

(6) Quotient invariance: The dividend and divisor are expanded (multiplied) or reduced (except 0) by the same multiple at the same time, and the quotient remains unchanged.

(7) The essence of subtraction: a number subtracts two numbers continuously, and the sum of these two numbers can be subtracted by this number, and the difference remains unchanged.

(8) Nature of division: A number is divided by two numbers continuously, and this number can be used to divide the product of the last two numbers.

2. An equation with an unknown number is called an equation.

3. The value of the unknown that makes the left and right sides of the equation equal is called the solution of the equation.

4. The side length of a square is represented by A, the area by S and the circumference by C. ..

5. Equation is different from arithmetic: arithmetic is a formula, which consists of operation symbols and known numbers, and it represents unknowns. An equation is an equation, and the unknown in the equation can participate in the operation. Only when the unknown is a specific numerical value can the equation be established.

6. The range of solving application problems by column equation:

(1) General application problems.

(2) Sum times and difference times.

(3) Calculation of the perimeter, area and volume of geometric shapes.

(4) Fraction and percentage application questions.

(5) ratio and proportion application questions.

7. Solving equations: The process of solving equations is called solving equations.

8. The significance of solving application problems with equations: the method of solving application problems with equations to find the unknown quantity of application problems.

9. Steps of solving application problems by column equation (setting, column, solution and answer)

(1) Hypothesis: Find out the meaning of the problem, determine the unknown quantity, and express it with X..

(2) Column: Find out the equivalence relation between the quantities in the question, and column the equations according to the equivalence relation.

(3) Solution: Solve the equation.

(4) Answer: Check or check and write the answer.