1. Quotient invariance: In division, the dividend and divisor expand or shrink by the same multiple (except 0) at the same time, and the quotient remains unchanged. This is the unchangeable nature of business.

2. Basic properties of decimals: add or remove zero at the end of decimals, and the size of decimals remains unchanged.

3. The basic nature of the fraction: the numerator and denominator of the fraction are multiplied or divided by the same number (except 0) at the same time, and the size of the fraction remains unchanged.

4. The nature of the ratio: the first term and the last term of the ratio are multiplied or divided by the same number (except 0) at the same time, and the ratio remains unchanged, which is called the basic nature of the ratio.

5. Basic properties of the equation:

Add (subtract) the same number on both sides of the equation, and the equation remains unchanged; Both sides of the equation are multiplied (divided) by the same number that is not 0, and the equation remains unchanged.