1. Multiplication and distribution law: Multiplying one number with the sum of the other two numbers is equivalent to multiplying this number with these two numbers respectively and then adding them. For example: a× (b+c) = a× b+a× c.
2. Multiplication and association law: the operation in brackets is performed first, and then the multiplication operation is performed. For example: (a×b)×c=a×(b×c).
3. Multiplication and exchange law: when two numbers are multiplied, the position of the exchange factor remains unchanged. For example: a× b = b× a.
4. The essence of division: the dividend and divisor are multiplied or divided by the same number at the same time, and the quotient remains unchanged. For example: a÷b=(a×c)÷(b×c).
5. Square difference formula: the square of the sum and difference of two numbers is equal to the sum of the squares of these two numbers MINUS twice the product of these two numbers. For example: (a+b)(a-b)=a_-b_.
6. Complete square formula: the square of a number is equal to twice this number plus the square of half this number. For example: a_=2ab+b_.
7. Cubic difference formula: the cubic difference of two numbers is equal to the cube of these two numbers and the cube of the product of these two numbers. For example: (a_-b_)=a_+b_-3ab(a+b).
8. Cubic sum formula: the cubic sum of two numbers is equal to the cubic difference of these two numbers plus the cubic product of these two numbers. For example: (a_+b_)=a_-b_+3ab(a+b).
9. Power: the power of a number is equal to the power of this number multiplied by the power of this number. For example: (a _) _ = a _× a _× a _× a _× a _× a _ a _
10. Addition and subtraction of scores: directly add and subtract the scores after converting them into the same denominator; Or after the fraction is converted into decimal, add and subtract, and finally convert the result back to fraction.
By mastering these quick calculation skills, students can solve complex problems more quickly and accurately and improve the efficiency of solving problems. At the same time, these skills are also helpful to cultivate students' logical thinking ability and spatial imagination ability.