1. Using the law of multiplication and distribution: 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: 2×(3+4)=2×3+2×4.
2. Use the law of multiplicative association: first carry out the operation in brackets, and then carry out the multiplication operation. For example: 2×(3+4)=2×3+2×4.
3. Use the multiplication exchange law: change the order of factors in the multiplication formula, and the product remains unchanged. For example: 2×3=3×2.
4. Use the nature 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: 12÷6= 18÷9.
5. Use the nature of the fraction: multiply or divide the numerator and denominator of a fraction by the same number at the same time, and the size of the fraction remains unchanged. For example: 3/4=9/ 12.
6. Use the properties of integers: decompose an integer into the product of prime factors, and then use the properties of prime factors to calculate. For example, 12=2×2×3, which can be decomposed into the square of 2 times 3 for easy calculation.
7. Use the nature of multiple: a number multiplied by a multiple is equivalent to this number multiplied by this multiple and then divided by this multiple. For example:12× 3 =12× (3 ÷1).
8. Use the nature of divisor: divide the numerator and denominator of a fraction by their greatest common divisor at the same time to get the simplest fraction. For example: 8/ 16= 1/2.
9. Using the property of arithmetic progression: the difference between any two terms in arithmetic progression is constant, which can be used for calculation. For example, 2, 5, 8, 1 1 is a arithmetic progression, and the difference between two adjacent terms is 3, which can be calculated by using this property.