First, the definition of negative numbers is 1. All the numbers I learned before (except 0) are positive numbers, which means that the "+"in front of positive numbers can be omitted! 2. Definition of negative number: adding "-"before positive number is negative number. 3. Negative numbers must start with "-". If there is no "-"in front of it (there can be no sign or "+"), it is all positive numbers (except 0). 4.0 is neither positive nor negative, it is the dividing line between positive and negative numbers. Exercise: 1, classify the following numbers as required: 511.25, -7, 3, 3.01...,-5, 0, 2,-.

Positive number 2. Write the negative numbers of the following numbers.

negative number

natural number

Nonpositive number

3 1 7 、 7、、 3 、 + 2 + 0.33……、 5 3 19

Second, the role of negative numbers 1, negative numbers appear under the premise of artificially specifying the positive direction. 2. Negative numbers are usually used to represent quantities with opposite meanings to positive numbers. 3. When choosing whether to use a positive number or a negative number, first look at whether the positive direction is specified. 4. Generally, the quantity with positive meaning is represented by a positive number, and the quantity with negative meaning is represented by a negative number. Example: 5 above zero is represented by +5℃; 5 degrees below zero means -5℃. The income of 2000 yuan is represented by +2000 yuan; Expenditure in 500 yuan is expressed in 500 yuan. Exercise: 1 If -20% means an increase of 20%, what does -20% mean? One night, the temperature in Huangshan dropped by 7 degrees Celsius from 2 degrees Celsius above zero in the morning. That night, the temperature in Huangshan is 3 degrees. The normal water level is 0, the water level is 0.2 _ _ _ _ _ _ _ _ _ _, and the water level is _ _ _ _ _ _ _ when it is 0.3m below the normal water level.

The normal water level is 5 meters, and the current water level is 6.3 meters, 2.5 meters lower than the normal water level.

Centigrade.

4. Answer as required: The students prove that the teacher's request to move forward is correct. (1) Take two steps forward and record it as _ _ _ _ _ _ _ _ _ _ _. (2) Take five steps back and record it as _ _ _ _ _ _ _ _ _ _ _ _ _. (3) How should he take the "six steps"? How about "marked as -4 steps"?

5. Look at the picture and answer the questions

Tokyo time is earlier than Beijing time 1 hour, which is recorded as+1 hour; Paris time was 7 hours later, and it was recorded as -7 o'clock. Displays the time in other time zones based on Beijing time. Sydney time: _ _ _ _ _ _ _ _ _ _ London time: _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _

(3) If the profit 1000 yuan is recorded as+1000 yuan, then the loss 200 yuan can be recorded as -200 yuan ((4) The temperature of 0℃ means that there is no temperature ().

)

7. The meaning of the common negative number (1) on the map: On the topographic map of China, we can see that there is a world's highest peak-Mount Everest in China, marked as 8848, and there is a Turpan basin in the northwest, marked as-155 meters. Can you tell me what 8848 meters and-155 meters mean respectively? Who are these two levels based on? (2) Revenue and expenditure: 2,600 yuan; (3) Education expenditure: 300 yuan (3) Entertainment expenditure: 500 yuan (3). (3) What is the meaning of negative -3 floor in the elevator room? Who is the standard? 8. Starting from school, going east is positive, and going west is negative. Xiaoming walks +50m from school,-100m. At this time, the distance between Xiao Ming and the school is (). 9. Food packages often say: "The net weight is 500.5g, which means the standard quality of food is" () Actually, there are no bags at most, () there are at least (). Third, the reading and writing method of negative number 1 Reading method: add "negative" before reading. 2. Writing method: put "-"before the written number. Practice: 16 degrees Celsius MINUS 3 degrees Celsius above zero. 4. Know the number axis 1, the elements of the number axis: positive direction (indicated by arrow), origin (0 scale 2. Positive direction: according to the meaning of the question, the positive direction is determined, generally upward or right. 3. Origin: the position of the number 0, which is generally determined according to the distribution of the number. If the difference between the positive and negative numbers to be represented is not equal, the origin is in the middle of the number axis; If there are more positive numbers than negative numbers, the origin is left; If there are more negative numbers than positive numbers, the origin is on the right. 4. Unit length: The distance between scales is determined by the size of the number to be represented. If the quantity is too large, the scale distance can be appropriately smaller, if the quantity is too small, the scale distance can be appropriately larger. The unit length is not necessarily 1 for each scale. Example:

forward direction

Writing: (writing: (

) or ()

)

Reading: reading:

-4

-3

unit length

-2

- 1

1

2

three

four

five

origin

5. Represents the number 1 on the number axis. Representing numbers on a given axis: Draw numbers on the corresponding scales according to the numbers. 2 2. For the representation of non-integers: further subdivide the scale. For example, if the line segment between 0 and 1 needs to be divided into three equal parts, then this number is divided into two equal parts. 3 3. Representation of negative numbers: All negative numbers are on the left of 0 and all positive numbers are on the right of 0. For example, +3.5 is between 3 and 4, and -3.5 is between -3 and -4.

Exercise: 1 The following numbers are represented on the number axis: 1 1.75 -4 3.

1

3 4

five

-3.2

2. Write the numbers A B -8 -6 -4 represented by the following points.

Carbon-2 compound

D 0 2

E 4

F 6 8

G 10

6. According to the comparison number 1 on the number axis, the number to the left of 0 is negative and the number to the right of 0 is positive; All positive numbers are greater than negative numbers; All negative numbers are less than positive number 2, the number on the right side of the number axis is larger, and the number on the left side is smaller; 3. If the negative number is large, the negative sign is not considered, and the number with large number is small; 4.0 is greater than all negative numbers and less than all positive numbers. Exercise: 1, compare size -6.5 -6.6 1.5 4 7 0 9 7 -9.8

3 2

negative number

0 3 8

-0.05 3 5 0.5

-2.75 1 10 5 8

+2.75 -0. 1

-2.5

-3.5

-

- 10. 1

1.0 1

-0.5

0.625

2. Represent the following numbers on the number axis and arrange them in descending order: 5-3.552-1.751.250-21.2.

3. Fill in the appropriate numbers in the brackets. ① 5,2,- 1,-4,( ),( ) )

② - 10,-5,0,5, 10,(

),(

Unit 1 self-test questions

1. Fill in the blanks with 1. Write down the temperatures displayed on the thermometer below and read them out.

2. For a building, the five floors above ground are marked as +5, the second floor underground is marked as (), and the first floor underground is marked as (3. The car forward 36 meters is +36 meters, and backward 10 meters is () meters. 4. The deepest Mariana Trench in the world is11034m below sea level, which is recorded as () m and pronounced as ().

) layer.

5. The following is the record of reservoir water level change. If the rise of 7 meters is recorded as +7 cm, please show the remaining 4 records. Up 7 cm +7 cm 6. Qingqing walked 80 meters east from the school, marked as +80 meters, and then walked west 100 meters. At this point, her distance from the school is marked as (). 7. Do you know that if the water in life freezes, it means that the temperature is below ()℃ and the boiling temperature of water is ()℃. 2. Judging whether it is true or false (tick "√" for the right and "×" for the wrong)1.0 is a positive number. () 2.+4, +9,+12 is positive, -3, -7, -2 1 is negative, and 5 is neither positive nor negative. () 3. Negative numbers are all less than 0. () 4. If Tingting walks 50 meters east, it is +50 meters, then she walks north 100 meters is-100 meters. The height of lakes in the world is definitely below sea level, and their heights are all expressed by negative numbers. () Third, multiple-choice questions. 1. The freezing temperature of water is (). A.0℃ B. 100℃ C.- 1℃ 2。 Generally speaking, the water temperature suitable for fish life is () a.70℃ B.-10℃ C.10℃ 3. As shown on the right, each small square represents 60. A. 24 B. 20 C. 22 4 When two numbers are added, the sum must be (). A. positive number B. negative number C. unable to determine 5. The number A is 18, which is four times smaller than the number B. The correct formula for finding the number B is (). A. (18-4) ÷ 2b. (18+4) ÷ 2c.18× 2-4 Fourth, the operation problem Xiaodong starts from the school, walks 2,800 meters along the east-west street, and walks in the north-south direction/kloc-0. Where did you go after "+1500m"? And fill in the corresponding positive and negative numbers in the chart. 3 cm up, 4 cm down, 5 cm down, 4 cm up.

5. By observation or measurement, which of the following figures is equal in area to Figure ①?

6. Short answer questions 1. Xiaodong and Xiaoming are having a quiz. According to the rules of the game, a * * * answers five questions, with one score+10 correctly and one score-10 incorrectly. If there is no answer, the winner is the one with the highest score. The following is the record of the competition: (1) Xiao Ming got the question _ _ _ _ right and the question _ _ _ wrong. (2) If Xiaodong wants to hit Xiao Ming, he must at least answer the question _ _ _ _ _ correctly, and Xiao Ming answers the question _ _ _ _ incorrectly.

Xiaoming question 1 question 2 question 3+10—10+10

Xiaodong+10+ 10- 10

2. Last week, the borrowing records of the school library are as follows (more than 50 books are recorded as positive, and less than 50 books are recorded as negative):

Monday 0

Tuesday +8

Wednesday +6

Thursday -2

Friday to 7 th

How many books were lent out last Friday? How many more books did you borrow last Tuesday than last Friday? (3) How many books were lent out on average every day last week? 3. A bus departs from the starting station, passes through five stops and finally reaches the terminal. The following table records the changes in the number of passengers on this bus. Starting station +25 intermediate station 1 0+12 intermediate station 2-3+6 intermediate station 3-5+8 intermediate station 4- 10+7 intermediate station 5- 13 0.

Number of people getting on and off at each station (1) How many people get on the bus in the middle of 5 stations?

terminal

—27

(2) How many people got off at the first five stops?

(3) At which station did no one get off? At which station did no one get on the bus?