Writing Method of Recursive Equation in Grade Three Mathematics: In elementary arithmetic, the calculation process is expressed by equations in turn according to the operation order, and each step should be aligned with the equal sign. The two lines of the equal sign should be parallel, and the length of the equal sign line should be about half a centimeter.

First, the operation sequence of mathematical recursion

Recursive equations generally refer to elementary arithmetic, in which addition and subtraction are called first-level operations and multiplication and division are called second-level operations. When calculating at the same level, calculate from left to right in turn; Two-stage operation, first multiply and then divide, then add and subtract.

When there are brackets, count the inside of brackets first, and then count the outside of brackets; When there are multiple brackets, count the brackets first, then the brackets inside, then the braces inside, and finally the brackets outside. When performing mixed operations, the numbers in parentheses are calculated first, and the parentheses are from small to large. If there is a power, calculate the power first, and then from high to low.

Second, the recursive equation calculation

Formula calculation is a recursive equation calculation, which is an operation to write out the calculation process completely, that is, vertical calculation. When calculating mixed operations, it is usually to calculate an expression step by step. The equal sign cannot be written on the original formula, but the process of each step should be written. Generally speaking, the equal sign should go forward and not be aligned with the first line.

Properties of recursive operation:

1, the properties of addition operation

From additive commutative law's associative law, it can be concluded that when several addends are added, the positions of addends can be exchanged at will; Or add a few addends first and then add them with other addends, and the sum remains the same. For example: 34+72+66+28 = (34+66)+(72+28) = 200.

2. The nature of subtraction operation

(1) A number minus the sum of two numbers is equal to subtracting each addend in the sum from this number in turn. For example:134-(34+63) =134-34-63 = 37.

(2) A number minus the difference between two numbers is equal to this number minus the minuend in the difference first and then minus the minuend. For example: 100-(32-15) =100-32+15 = 68+15 = 83.

(3) Subtract a number from the sum of several numbers. You can choose any addend to subtract this number, and then add it with the rest addends. For example: (35+17+29)-25 = 35-25+17+29 = 56.

3. The nature of multiplication operation

(1) Multiply several numbers by the product of a number, so that any factor in the product can be multiplied by this number and then multiplied by other numbers. For example: (25×3 × 9)×4=25×4×3×9=2700.

(2) Multiply the difference between two numbers by a number, so that the minuend and the minuend are multiplied by this number respectively, and then subtract the products. For example: (137-125) × 8 =137× 8-125× 8 = 96.

4. The nature of the division operation

(1) If a number is divided by (or multiplied by) a number and then multiplied by (or divided by) the same number, the number remains the same. For example: 68÷ 17× 17=68 (or 68× 17÷ 17=68).

(2) A number divided by the product of several numbers can be divided by the factors in the product in turn. For example: 320÷(2×5×8)=320÷2÷5÷8=4.

(3) The quotient of a number divided by two numbers is equal to the number divided by the dividend in the quotient and then multiplied by the divisor in the quotient. For example: 56÷(8÷4)=56÷8×4=28.