In our life and production, we often encounter quantities with opposite meanings. For example, 3 degrees above zero and 6 degrees below zero; 6 meters forward and 6 meters backward; The elevation of Mount Everest and Turpan on the map for primary schools. It is not enough to express these quantities learned in primary school, so there are positive numbers and negative numbers to express the opposite meanings of these quantities. The positive and negative numbers in this section are the most used quantities in our future study, and they are also the basis of learning junior high school mathematics. First, the breakthrough of knowledge points

Knowledge point 1: the definition of positive and negative numbers

Positive numbers and negative numbers represent quantities with opposite meanings. If the East is defined as positive, then the West is negative. Note: 1. The "-"before a negative number cannot be omitted, otherwise it will become a positive number.

2. For positive numbers and negative numbers, it cannot be simply understood that good numbers with "+"are positive numbers and numbers with "-"are negative numbers. For example, -a is not necessarily a negative number.

Knowledge point 2: the meaning of 0

In primary schools, "0" only means "none" or "blank". But after the introduction of negative numbers, "0" has a richer meaning. For example, "0" can be the dividing line between positive and negative numbers.

Knowledge point 3: positive numbers and negative numbers indicate the application of quantities with opposite meanings in practice.

Because in real life, we need to express some quantities with opposite meanings concisely, then we will set a standard, in which greater than the standard is positive and less than the standard is negative. Note: the title does not specify which quantity is represented by a positive number and which quantity is represented by a negative number. It is customary to regard "forward, upward, income, above zero, increase, exceed, more" and other quantities with opposite meanings as negative numbers.

1.

Positive numbers and negative numbers are actually needed.

Positive numbers and negative numbers are generated according to actual needs. With the broadening of knowledge, the natural numbers, fractions and decimals in primary school can no longer meet the actual needs, such as some quantities with opposite meanings, such as 200 yuan expenditure 100 yuan, 6℃ above zero, 4℃ below zero, and so on. They not only have opposite meanings, but also represent a certain amount. How to express them? We define one meaning as positive and another quantity with the opposite meaning as negative, thus producing positive numbers and negative numbers.

2.

The concepts of positive and negative numbers

(1) like 5,

..... such a number is called a positive number.

such as

Equal numbers are all positive numbers.

Numbers preceded by "-"(pronounced negative) are called negative numbers.

such as

Wait a minute. They are all negative numbers.

(2) Zero is neither positive nor negative, it represents the boundary between positive and negative numbers.

3.

Some Concepts of Rational Numbers

(1) Integers and fractions are collectively called rational numbers.

Note: Integers can also be regarded as fractions with denominator of 1, but for the convenience of research, the fractions in this chapter refer to fractions without integers.

(2) Integers include positive integers, zero and negative integers.

(3) Scores include positive and negative scores.

4.

Rational number classification

(1) According to the relationship between positive number, negative number and 0:

(2) According to the relationship between integer and fraction:

(1) Rational numbers are divided into integers and fractions. Integers are divided into positive integers, zero and negative integers. Scores are divided into positive scores and negative scores. Namely: