Chapter 1 Rational Numbers

1. 1 positive and negative numbers

Basic detection

At 1. There are both positive and negative numbers.

2. If the water level changes to +5m when the water level rises 5m, it changes to m when the water level drops 3m, and it changes to m when the water level does not rise or fall.

3. The meaning of quantities expressed by positive numbers and negative numbers respectively in the same problem.

4.20 10 The national average annual precipitation decreased by 24 ㎜ compared with the previous year. In 2009, it increased by 8 ㎜ compared with the previous year. In 2008, it decreased by 20㎜. Positive and negative numbers indicate the growth of the average annual precipitation in China in the past three years compared with the previous year.

Expansion and improvement

5. The following statement is true ()

A. zero is a positive number, not a negative number. B. zero is neither positive nor negative.

C. zero is both positive and negative. D. Non-positive numbers must be negative numbers, and non-negative numbers must be positive numbers.

6. March eastward -30 meters means ()

A. head east for 30 meters. B month-30 meters to the east

C. March 30 meters west. D month-30 meters west.

7. Both Party A and Party B start from place A at the same time. If they walk 48 meters south, they will be marked as +48 meters, and then Party B will walk 32 meters north, which will be marked as the distance between them is meters.

8. The instructions of a drug indicate that the storage temperature is (20 2)℃, so it is appropriate to store it in the range of℃ to℃.

9. If an object moves 5m to the right as -5m, what does it mean that the object moves +5m again? How far is the object from its position before it moved twice?

1.2. 1 rational number test

Basic detection

1, _ _ _ _ _ _ _ _ _ and _ _ _ _ are collectively called integers; _ _ _ _ _ and _ _ _ are collectively referred to as scores; _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ and _ _ _ _ are collectively referred to as non-negative numbers; _ _ _ _ _ _ and _ _ _ _, collectively referred to as non-positive numbers; _ _ _ _ _ _ and _ _ _ are collectively referred to as non-positive integers; _ _ _ _ _ _ and _ _ _ are collectively called non-negative integers.

2, the following is not a positive rational number ()

a 、-3. 14 B、0 C、D、3

3, both a fraction and a positive number is ()

a 、+2 B 、- C、0 D、2.3

Expansion and improvement

4, the following statement is correct ()

A, positive numbers, 0 and negative numbers are collectively called rational numbers B, and fractions and integers are collectively called rational numbers.

C, positive rational number and responsible rational number are collectively called rational number d, and none of the above is correct.

5.-a must be ()

A, positive number b, negative number c, positive number or negative number d, positive number or zero or negative number

6, in the following statement, the wrong is ()

(1) is negative; ② 1.5 is not an integer; ③ Non-negative rational numbers do not contain 0; ④ Integers and fractions are collectively called rational numbers; ⑤0 is the smallest rational number; 6- 1 is the smallest negative integer.

a， 1 b，2 c，3 d，4

7. Fill in the following figures in the corresponding brackets:

Natural number set {...};

Integer set {…};

Positive fraction set {…};

Non-positive set {…};

8. Short answer questions:

Is there a negative number between (1)- 1 and 0? If yes, please list.

(2) Is there a negative integer between -3 and-1? What are the integers between -2 and 2?

(3) Is there a negative integer greater than-1? Is there a positive integer less than 1?

(4) Write three rational numbers greater than-105 and less than-100.

1.2.2 axis

Basic detection

1, draw the number axis, indicating the following rational numbers:

2. The point representing -4 on the number axis is located at the edge of the origin, and the distance from the origin.

It's a unit length.

3. Compare the sizes and fill in ">" and ".

1 0; 0 - 1; - 1 -2; -5 -3; -2.5 2.5.

Expansion and improvement

4. There is a point on the number axis that is 5 away from the origin, indicating that the number is.

5. it is known that x is an integer and -3 < x < 4, then all possible values representing x on the number axis are.

6. On the number axis, point A and point B represent -5 and 2 respectively, so the length of line segment AB is.

7. Starting from the point representing-1 on the number axis, move two unit lengths to the left to point B, then the number represented by point B is, and then move two unit lengths to the right to reach point C, then the number represented by point C is.

8. Point A on the number axis represents -3. Move point A to the right by 7 unit lengths, and then to the left by 5 unit lengths, so that the distance from the end point to the origin is one unit length.

1.2.3 reciprocal

Basic detection

1 and the reciprocal of -(+5), namely-(+5) =;

The inverse of -(-5), that is -(-5)=.

The reciprocal of 2 and -2 is; The reciprocal of is; The reciprocal of 0 is.

3. Simplify the following figures:

-(-68)= -(+0.75)= -(- )=

-(+3.8)= +(-3)= +(+6)=

4, the following statement is correct ()

A, positive and negative numbers are opposite; B, the antonym of any number is different from itself.

C, any number has its reciprocal d, and the numbers represented by two points on both sides of the origin on the number axis are reciprocal.

Expansion and improvement:

5. The reciprocal of-(-3) is.

6. It is known that the numbers represented by A and B on the number axis are opposite, the distance between two points is 6, and point A is to the left of point B, so the numbers represented by point A and point B are respectively.

7. Given that A and B are reciprocal, B and C are reciprocal, and c=-6, then a=.

8. The reciprocal of the number A is non-negative, so the relationship between this number A and 0 is

A zero.

9. On the number axis, point A represents -3, point B and point C represent the opposite number, and the distance from point B to point A is 2, so the number represented by point C should be.

10, the following conclusion is correct ()

(1) Any number is not equal to its inverse; ② Numbers with opposite signs are opposite to each other; ③ The distance between two opposite points is equal to the origin; (4) If rational numbers A and B are opposite, then A+B = 0; ⑤ If rational numbers A and B are opposite, their signs must be different.

a，2 B，3 C，4 D，5。

1 1. If a=-a, where is the point representing A on the number axis?

1.2.4 absolute value

Basic detection:

The absolute value of 1 -8 is recorded.

2. The absolute value is equal to 5.

3. If ︱a︱= A, then A

The absolute value of 4 is 2004, and the absolute value of 0 is.

The absolute value of a number refers to the point on the graph that represents this number.

The distance to.

6. if x < y < 0, then ︱ x ︱ y ︱.

7.︱ x- 1 ︱ = 3, then x =

8. If ︱ x+3 ︱+y-4 ︱ = 0, then x+y =.

9. the positions of rational numbers a and b on the number axis are shown in the figure, then a and b,

︱a︱ ︱b︱。

10.︱x ︱ b > c, find the value of a+b+C b+c.

7. If 1 < a < 3, then.

8. Calculation:

9. Calculation:

(+ 1)+(-2)+(+3)+(-4)+…+(+99)+(- 100)

10. 10 bags of rice, with 50 kilograms per bag as the standard: the excess kilograms are positive, and the shortage kilograms are negative. The weighing records are as follows: +0.5, +0.3, 0, -0.2, -0.3,+1. 1,-.

10 bag of rice * * * How many kilograms is overweight? How many kilograms is the total weight?

1.3.2 subtraction of rational numbers

Basic detection

1、( 1)(-3)-________= 1 (2)________-7=-2

2. Calculation:

( 1) (2)

(3) (4)

3, the following operation is correct ()

A、

B,

C,

d、

4. Calculation:

( 1) (2)

(3)

Expansion and improvement

5, the following can be written as a-b+c is ()

a、a-(+b)-(+c) B、a-(+b)-(-c)

c、a+(-b)+(-c) D、a+(-b)-(+c)

6. If _ _ _ _ _ _.

7, if x < 0, it is equal to ()

a 、-x B、0 C、2x D 、-2x

8, the following conclusion is incorrect ()

A, if a > 0 and b < 0, a-b > 0 b, if a < 0 and b > 0, a-b < 0.

C, if a < 0 and b < 0, then a-(-b) > 0.

D, if a-b>0, b < 0, a-b > 0.

9. The results of Red Star team in four football matches are: 3: 1 in the first game, 2: 3 in the second game, 0: 0 in the third game and 2: 5 in the fourth game. What is the total goal difference of Red Star in four games?

10. A patient needs to measure his blood pressure every afternoon. The table below shows the change of hypertension in this patient from Monday to Friday. The patient's highest blood pressure last Sunday was 160 units.

Monday, Tuesday, Wednesday, Thursday and Friday.

High pressure change

(Compared with the previous day), it increased by 25 units, decreased by 15 units, increased by 13 units and decreased by 20 units.

(1) When is the patient's blood pressure? When is the blood pressure the lowest?

(2) Compared with last week, did the blood pressure rise or fall this Friday?

1.4. 1 rational number multiplication

Basic detection

1, fill in the blanks:

The reciprocal of (1)-7 is _ _, the reciprocal is _ _, and the absolute value is _ _;

The reciprocal of (2) is _ _, and the reciprocal of -2.5 is _ _;

(3) The rational number whose reciprocal equals itself is _ _.

2. Calculation:

( 1) ; (2)(-6)×5× ;

(3)(-4)×7×(- 1)×(-0.25); (4)

3, the product of rational number and its inverse ()

A, the sign must be positive B, and the sign must be negative.

C, not greater than zero d, not less than zero.

4, the following statement is wrong ()

A any rational number has a reciprocal b, and the product of the two reciprocal is 1.

C the reciprocal d with the same sign, 1 and-1 are negative reciprocal.

Expansion and improvement

The reciprocal of 5 is _ _.

6. Two rational numbers A and B are known. If AB < 0 and A+B < 0, then ()

A, a > 0, b > 0 b, a < 0, b > 0 c, a and b are different symbols, and the absolute value of negative numbers is large.

7. Known values.

8. If A and B are reciprocal, C and D are reciprocal, and the absolute value of M is 1, then the value of.