First, the meaning of positive and negative numbers:

1, direction indication: you can use positive and negative numbers to indicate the direction. Positive numbers can mean right, up or other positive directions, and negative numbers can mean left, down or other negative directions. This is very useful in physics, geometry and engineering.

2. Temperature representation: The temperature can be represented by positive and negative numbers. In the Celsius or Fahrenheit scale, a positive number indicates that the temperature is higher than the fixed temperature, and a negative number indicates that the temperature is lower than the fixed temperature. Such a representation can conveniently describe the degree of heat and cold.

3. Debt and liabilities: Negative numbers can be used to express the concept of debt or debt. When we borrow money from others, the amount borrowed can be expressed in negative numbers. This usage can also be extended to other financial fields, such as account balance and negative assets.

4. Coordinate representation: In mathematics, positive numbers and negative numbers are also used to indicate the position in the coordinate system. For example, in a plane rectangular coordinate system, a positive number represents the upper right of the origin and a negative number represents the lower left of the origin.

5. Measure differences: positive and negative numbers can be used to measure differences or changes. Negative numbers mean decrease, loss or decline, and positive numbers mean increase, profit or rise. This is often used in statistics, economics and scientific research.

Second, the nature of positive and negative numbers:

1, inverse: every positive number has a corresponding inverse with the same absolute value but opposite sign.

2. Additive nature: When numbers with the same sign are added, the absolute values are added, and the same sign is kept. When the numbers of different symbols are added, the absolute value is subtracted and the symbol with larger absolute value is retained.

3. Subtraction property: subtracting a number is equal to adding the reciprocal of this number.

4. Multiplication property: when the same number is multiplied, the product is positive. When numbers of different signs are multiplied, the product is negative. Nature of division: Divide by a non-zero number, numbers with the same sign will be divided into positive numbers, and numbers with different signs will be divided into negative numbers.

5. Number axis representation: the number axis can be used to represent positive numbers and negative numbers, where zero is at the origin, positive numbers are on the right side of the origin, and negative numbers are on the left side of the origin.

The significance of mathematics

1. Problem solving: Mathematics is a systematic tool for thinking and solving problems. It provides a logical and accurate way of analysis and reasoning, and helps us to solve various practical problems, from simple arithmetic calculation to complex engineering and scientific calculation.

2. Develop logical thinking: Learning mathematics can cultivate and develop logical thinking ability. Mathematics requires us to reason, abstract, logically infer, think clearly, accurately and reasonably. This kind of logical thinking ability is beneficial in other disciplines and daily life.

3. Model and prediction: Mathematics provides a method to build models, analyze laws and predict the future. Through mathematical modeling, we can reveal the mathematical laws behind natural and social phenomena, and use these laws to predict and optimize.