Example 1: Find the absolute value of 3, -6, 9, 0.

Intention: Let students fully understand the meaning of absolute value: The distance between the point representing the number A on the general number axis and the origin is called the absolute value of the number A (where the number A can be positive, negative or 0).

Answer: =3 =6 =9 =0

Reflection: Through this example and the definition of absolute value, we can know that the absolute value of a positive number is itself; The absolute value of a negative number is its reciprocal; The absolute value of 0 is 0.

When a is a positive number, =a

When a is negative, = a.

When a is 0, =0.

Exercise: Write down the absolute values of the following numbers.

1 , 5 , —2.4 , , , 99 ,0

Example 2: Compare the following logarithms.

(1)-(- 1) and -(+2)(2)- and (3)-(-0.3) and

Solution: (1) Simplify first, -(- 1) = 1, -(+2)

Because positive number is greater than negative number,1>; —2

(2) This is the comparative size of two negative numbers. First, find their absolute values.

= , ==

because

namely

So->

Simplify first, -(-0.3) =, =0.4

Because 0.3

So -(-0.3)

Reflection: when the different numbers of two symbols are relatively large, we should consider their positive and negative; When two numbers with the same sign are relatively large, their absolute values should be considered.

Exercise: Compare the sizes of the following logarithms.

—3 and—5; —2.5 and—;

Example 3: Calculation Problem

( 1) 16+(—25)+24+(—35)

(2)(—20)+(+3)—(—5)—(+7)

(3)(-5)x(-3)X6

Solution: (1)16+(-25)+24+(-35)

= 16=24+(—25)+(—35)

=40+(—60)

=—20

Reflection: additive commutative law and the law of association can simplify the operation. It is of great significance to understand the operation law.

.

(2) Analysis: There are addition and subtraction in this formula. It can be changed to (-20)+(+3)+(+5)+(-7) according to the rational number subtraction rule.

Turn the problem into the addition of several rational numbers.

(—20)+(+3)—(—5)—(+7)

=(—20)+(+3)+(+5)+(—7)

=[(—20)+(—7) ]+[(+3)+(+5)]

=( —27)+(+8)

=— 19

(3) Analysis: This formula has positive and negative multiplication, and the answer can be obtained according to the rational number multiplication rule.

(-5)x(-3)X6

= 15x6

=90

Reflection: multiply rational numbers, first determine the size of the product, and then determine the sign of the product.

Exercise: (1) 23+(- 13)+24

(2)(—7)—(+3)+(—6)—(— 18)

(3)—2.4+3.5—4. 1+3.2

(4)x(—7)x()

(5)(—)x36

One: Basic training

1. The temperature in Changshu city was 5℃ in the morning and rose by 3℃ at noon. In the afternoon, affected by the cold air from the south, it dropped by 9℃ at night, and the temperature at night was℃.

2. In the rational numbers -3, 0, 20,-1.25, 1,-,-(-5), the positive integer is _ _ _ _ _ _ _.

Negative integer is, positive fraction is, and non-negative number is.

3. The following statement is true ().

A, rational numbers are divided into positive rational numbers, 0, negative rational numbers, integers and fractions.

Rational numbers are either positive or negative.

C. rational numbers can be integers or fractions.

D, none of the above statements are correct

4, if it is a rational number, and, then there must be ().

A. the fourth century BC.

5. Write down the opposite numbers of the following numbers and their absolute values:

3,-8,0, 100,-3.9,

6,,, position, as shown in the figure.

rule

7. Comparison size: (1)-2+6; (2) 0 - 1.8 ; (3)_____

8. If,,, then the correct one in the following relationship is ().

A.B.

C.d。

9. Calculation of rational number:

( 1)23— 17+6—22 (2) 1—4+3—0.5 (3)

(5)33. 1- 10.72-(-22.9) (6)( 1- 1-+)×(—24)

10. Among the following variants of commutative addend, the correct one is ().

A, B,

C, D,

1 1, if, then

12、…=_________

Second, improve training.

1 1, if, and are reciprocal and the absolute value is 2, then the value of the algebraic expression is ().

12, if =2, then x must be equal to 2? Why? If =0, what is x? If x =-x, what is x?

13, use ">" "< or" = "to fill in the blanks.

If a person

(2) If a>0 and b<0, then A&B _ _ 0, _ 0.

(3) If

(4) If a=0 and b≠0, then ab _ _ 0, _ 0.

14, observe the following equation; ; ; ; ; ; ; Through observation, the number of units determined by the law you found is ().

15, observe the following equations in sequence:

9× 0+ 1 = 1, 9× 1+ 1 = 10, 9× 2+3 = 2 1, 9× 3+4 = 3 1, 9×

16. Fill in-15,-12, -9, -6, -3, 0, 3, 6, 9 in the small box below to make the sum of the three numbers of the big box equal. (4 points)

Reference answer:

- 1

5 ; -3; -; 1; 0

C

B

-3、3; 8、8; - 100、 100; 39、39; 、;

c-b _

& lt& gt& lt

D

- 10; -0.5; ; 45.28; seven

D

- 100

three

Not necessarily, but -2 is also; 0 ; 0

& lt& lt； & lt& lt； & gt& gt； = =

eight

10n+ 1

-6 9 - 12

-9 -3 3

6 - 15 0

Knowledge expansion

Nowadays, in industrial production, standard specifications are designed for the size and quality of products, but generally in actual processing, it is impossible for every product to be exactly the same as the standard specifications. Usually, within a certain range, as long as it does not affect the use, products that are slightly larger or smaller than the standard are qualified, and products beyond this range are unqualified.

Usually, on the production drawings, the qualified scope of each product is clearly defined. For example, if the drawing indicates that the diameter of a part is (30±0.02)mm, then the maximum diameter of the actual product can be (30+0.02)mm and the minimum diameter can be (30-0.02)mm, and all products within this range are qualified.

There are also positive numbers and negative numbers to represent the range of life. For example, the instructions of a drug indicate that the storage temperature is (25 3)℃, so it is appropriate to store it in the range of _ _ _ _ _ _ _ _.

At present, the world's most accurate clock NIST F- 1 has an error of 1 second within 20 million years. Do you know its accuracy?

Can you give other examples of ranges expressed by positive numbers and negative numbers?

This is definitely a process.

1 If | x-4 | = 3 and -y = 3, the value of x-y is equal to.

2 if-ABC & gt； 0, and the numbers of b and c are different, then a _ _ 0 (use ">" or "

3 If m is a rational number, simplify m-|m|/|m|.

4( 1)

If the polynomials x 4y-3x 2-1and-x 2m+1+2xy+5 are homogeneous polynomials; Find the value of m

(2) It is known that the polynomial ax 2+2bxy+x 2-x-2xy+y about x and y does not contain quadratic terms, so find the value of 5a-8b.

5( 1) Given (-a+ 1/3b) 2+| 3b-9 | = 0, find the value of 3a+ 1/2b.

(2) Given | a-2 |+(b+5) 2+| c+3 | = 0, find the value of (b-c) a.

Best answer

1 If | x-4 | = 3 and -y = 3, the value of x-y is equal to 4 and 10.

2 if-ABC & gt； 0, and the numbers of b and c are different, then a _ _ >；; _0 (use ">" or "

3 If m is a rational number, simplify m-|m|/|m|=m- 1.

4( 1) If the polynomials x 4y-3x 2-1and-x 2m+1+2xy+5 are homogeneous polynomials; Find the value of m

If your topic is the power of (2m+ 1), it is 2m+ 1 = 4, and m = 3/2.

If your topic is 2m power, it is 2m=4 m=2.

(2) It is known that the polynomial ax 2+2bxy+x 2-x-2xy+y about x and y does not contain quadratic terms, so find the value of 5a-8b.

If the polynomial ax 2+2bxy+x 2-x-2xy+y contains no quadratic term. Then a=- 1 b= 1.

5a-8b=-5-8= 13

5( 1) Given (-a+ 1/3b) 2+| 3b-9 | = 0, find the value of 3a+ 1/2b.

(-a+ 1/3b)？ =0 a= 1/3b

3b-9=0 b=3 a= 1

∴3a+ 1/2b=3+3/2=9/2

(2) Given | a-2 |+(b+5) 2+| c+3 | = 0, find the value of (b-c) a.

a-2=0 b+5=0 c+3=0

∴ a=2 b=-5 c=-3

(b-c)^a=[-5-(-3)]？ =(-2)? =4