Mathematical problems of 100 mixed operation of addition, subtraction, multiplication and division

-38)+52+ 1 18+(-62)=

(-32)+68+(-29)+(-68)=

(-2 1)+25 1+2 1+(- 15 1)=

12+35+(-23)+0=

(-6)+8+(-4)+ 12 =

27+(-26)+33+(-27)

12+35+(-23)+0=

39+[-23]+0+[- 16]=

[- 18]+29+[-52]+60=

[-3]+[-2]+[- 1]+0+ 1+2=

[-30 1]+ 125+30 1+[-75]=

[- 1]+[- 1/2]+[+3/4]+[- 1/4]=

[-7/2]+[+5/6]+[-0.5]+4/5+ 19/6=

[-26.54]+[-6. 14]+ 18.54+6. 14=

1. 125+[- 17/5]+[- 1/8]+[-0.6]=

Rational number exercise

Exercise1(level b)

(1) Calculation problem:

( 1)23+(-73) (2)(-84)+(-49) (3)7+(-2.04) (4)4.23+(-7.57) (5)(-7/3)+(-7/6) (6)9/4+(-3/2) (7)3.75+(2.25)+5/4 (8)-3.75+(+5/4)+(- 1.5)

(2) Calculate by a simple method:

( 1)(- 17/4)+(- 10/3)+(+ 13/3)+( 1 1/3) (2)(- 1.8)+(+0.2)+(- 1.7)+(0. 1)+(+ 1.8)+(+ 1.4)

(3) It is known that X =+ 17 (3/4), Y =-9 (5/ 1 1) and Z =-2.25.

Find the value of: (-x)+(-y)+z.

(4) if ">" and "0" are used, then a-ba (c) if ba (d) if a.

(2) Fill in the blanks:

(1) zero minus the inverse of a, the result is _ _ _ _ _ _ _ _; ② if a-b >; A, then B is _ _ _ _ _ _ _ _ _ _ _; (3) subtract-π from -3. 14, and the difference should be _ _ _ _ _ _ _ _; (4) The minuend is-12(4/5), with a difference of 4.2, so the minuend should be _ _ _ _ _ _ _ _ _ _ _ _; (5) If B-A

(3) True or false:

(1) When a number subtracts a negative number, the difference is less than the minuend. (2) When a number subtracts a positive number, the difference is less than the minuend. (3) Subtract any number from 0, and the difference is always equal to the reciprocal of this number. (4) If X+(-Y)=Z, then X=Y+Z (5) If 0, b|b|, then a-b >; 0

Exercise 2 (Level B)

(1) calculation: (1) (+1.3)-(+17/7) (2)-(+2/3) (3) | (-7.2)-(-6.

(2) If |a|=4, |b|=2, and |a+b|=a+b, find the value of a-b. 。

(3) If A and B are rational numbers and | a |

(4) If |X- 1|=4, find x and observe the distance between the point representing the number x and the point representing 1 on the number axis.

Exercise 3 (Level A)

(1) Multiple choice questions:

The correct pronunciation of (1) formula -40-28+ 19-24+32 is () (a) minus 40, minus 28, plus 19, minus the sum of 24 and 32, and (b) minus 40 plus/kloc-0. 0, then () (a) At least two of the three numbers are negative (b) Only one of the three numbers is negative (c) At least one of the three numbers is negative (d) Two of the three numbers are positive or two are negative (3) If m

(2) Fill in the blanks:

The general steps of (1) rational number addition and subtraction mixed operation are: (1) _ _ _ _ _ _ _; (2)_________; (3)________ _______; (4) _ _ _ _ _ _ _ _ _ _ _. (2) When b0, (a+b)(a- 1) >; 0, there must be () (A)b with the same number as A (B)a+b with the same number as A-1(c) A > 1 (D)b 1 (6) The product of a rational number and its opposite number () (a) The sign must be positive (b) The sign must be negative (c) It must not be less than zero (d) It must not be greater than zero (7) If | a-1|||.

(2) Fill in the blanks:

The multiplication rule of (1) rational number is: multiply two numbers, Use the same symbol _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _. (4) Calculation: (4a) * (-3b) * (5c) *1/6 = _ _ _ _ _ _ _ _ _ _ _; (5) Error in calculation: (-8) * (1/2-1/4+2) =-4-2+16 =10 is _ _ _ _ _. (6) Calculation: (-1/6) * (-6) * (17) * (-7/10) = [(-16) * (-6)].

(3) True or false:

(1) If the product of two numbers is positive, then both numbers must be positive; (2) If the product of two numbers is negative, then the signs of the two numbers are different; (3) Multiply several rational numbers, and when there are even factors, the product is positive; (4) Multiplying several rational numbers, when the product is negative, there are odd negative factors; (5) The product ratio is greater than each factor.

Exercise (4) (Level B)

(1) Calculation problem:

( 1)(-4)(+6)(-7) (2)(-27)(-25)(-3)(-4) (3)0.00 1*(-0. 1)*( 1. 1) (4)24*(-5/4)*(- 12/ 15)*(-0. / kloc-0/2) (5)(-3/2) (-4/3)(-5/4)(-6/5)(-7/6)(-8/7) (6)(-24/7)( 1 1/8+7/3-3.75)*24

(2) Calculate by a simple method:

( 1) (-7 1/8) * (-23)-23 * (-73/8) (2) (-7/ 15) * (- 18) * (-45/65448)

(4) Given1+2+3+...+31+32+33 =17 * 33, calculate the following formula.

The value of 1-3+2-6+3-9- 12+ ... +3 1-93+32-96+33-99.

Exercise 5 (Level A)

(1) Multiple choice questions:

(1) It is known that A and B are two rational numbers. If their quotient a/b=0, then () (A)a=0 and b≠0 (B)a=0 (C)a=0 or b=0 (D)a=0 or b≠0. -1 and-1; 0 and 0; -2/3 and -3/2, where the reciprocal is () (a) only (b) only (c) only (d) both are (3) If a/|b|(b≠0) is a positive integer, then () |b| is the divisor of a (. B, then there must be () (a) A)A+b & gt；; a(B)a-B & gt； a(C)2a & gt； ab(D)a/b & gt； 1

(2) Fill in the blanks:

(1) When |a|/a= 1, a _ _ _ _ _ _ 0; When |a|/a=- 1, a _ _ _ _ _ _ 0; (fill in > 0, then a _ _ _ _ _ _ 0; (1 1) If ab/c0, then B _ _ _ _ _ _ 0; (12) if a/b >; 0，b/c(-0.3)4 & gt； - 106(B)(-0.3)4 >； - 106 >(-0.2)3(C)- 106 & gt； (-0.2)3 & gt； (-0.3)4(D)(-0.3)4 & gt； (-0.2)3 & gt； -106 (4) If A is a rational number and A2 >；; A, then the value range of A is () (a) A.

(2) Fill in the blanks:

(1)23, 3 is _ _ _ _ _, 2 is _ _ _ _ _ _, and the power is _ _ _ _ _ _ _ _; If 3 is regarded as a power, its cardinal number is _ _ _ _ _ _ _ _,

The index is _ _ _ _ _ _ _ _; (2) According to the meaning of power: (-2)3 stands for _ _ _ _ _ _ _ multiplication; (-3)2v represents _ _ _ _ _ multiplication; -23 means _ _ _ _ _. (3) The rational number whose square equals 36/49 is _ _ _ _ _ _ _; The cubic number equal to -27/64 is _ _ _ _ _ _ _ (4) Write a positive number greater than 10 as a* 10n (n is a positive integer), where the range of a is _ _ _ _ _ _ _ _, where n is an integer.

The number of digits is less than _ _ _ _ _ _, which is called scientific notation; (5) Write down the following numbers by scientific notation: 4000 = _ _ _ _ _ _ _ _ _ _ _ _; 950000=________________; earth

The mass is about 49800 ... 0g (28 bits), which can be recorded as _ _ _ _ _ _ _ _; (6) What are the numbers recorded by scientific notation, namely105 = _ _ _ _ _ _ _ _ _ _ _; 2* 105=______________; 9.7 *107 = _ _ _ _ _ _ 9.756 *103 = _ _ _ _ _ (7) The following numbers are natural numbers. 7* 106 is 3.78* 107 is _ _ _ _ digits; 10 10 is _ _ _ _ _ digits; (8) If rational number m 0, B0 (b) a-| b | > 0 (c) A2+B3 > 0 (d) A <; 0 (6) The minimum value of algebraic expression (a+2)2+5 is () (a) A = 0 (b) A = 2 (c) A =-2 (d) A0 (b) B-A >; 0 (c) A and B are reciprocal; (D)-ab (C)a

(5) The approximate value 1.20 obtained by rounding method represents the range of the exact number a ().

(A) 1. 195≤A & lt； 1.205(B) 1. 15≤a & lt； 1. 18(C) 1. 10≤a & lt； 1.30(D) 1.200≤a & lt； 1.205 (6) The following statements are correct: (a) The accuracy of similarity number 3.80 is the same as that of similarity number 38; (b) The number of significant digits of similarity number 38.0 is the same as that of similarity number 38. (c)3. 14 16 has three significant digits 3, 1 4 after being accurate to the percentile; (d) Write 123* 102 as 1.23* 104 with four significant digits.

(2) Fill in the blanks:

(1) Write the precision and significant figures of the following rounded approximations: (1) Approximate number 85 is accurate to _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ (3) The divisor of 5.2 million is accurate to _ _ _ _ _ _ _ _, and the effective number is _ _ _ _ _ _ _ _; (4) The approximate value of 0.20 is accurate to _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _.

The divisor 2.7 183 is accurate to _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _.

(3) True or false:

(1) The approximate value of 25.0 is exactly a dash, and the significant digits are 2,5; (2) Similarity number 4000 is as accurate as similarity number 4000; (3) The divisor 4000 is as accurate as the divisor 4 * 10 3; (4) The approximate value of 9.949 accurate to 0.0 1 is 9.95.

Exercise 8 (Level B)

(1) Use rounding method to approximate the following figures (three significant figures are required): (1) 37.27 (2) 810.9 (3) 0.0045078 (4) 3.079.

(2) Use rounding method to approximate the following numbers (accurate to thousands): (1) 37890.6 (2) 213612.4 (3)1906.57.

(3) Calculation (the result is reserved with two significant figures): (1) 3.14 * 3.42 (2) 972 * 3.14 *14.

Exercise 9

(a) look-up table evaluation:

( 1)7.042 (2)2.482 (3)9.52 (4)2.00 12 (5) 123.42 (6)0. 12342 (7) 1.283 (8)3.4683 (9)(-0.5398)3 ( 10)53.733

(2) Given that 2.4682=6.90 1, we can find the values of 24.682 and 0.024682 without looking up the table.

(3) 5.2633= 145.7 is known, so we don't look it up.

( 1)0.52633 (2)0.05263 (3)52.632 (4)52633

(4) Given 21.762 2 = 473.5, what is the approximate value of 0.002 1762 with three significant digits?

(5) Look-up table calculation: the surface area of a ball with a radius of 77cm (the area of the ball =4π*r2).

Rational number exercise

In view of the fact that some schools may hold the selection examination for the entrance experimental classes, it may involve some contents of Grade One. We specially selected this exercise of rational numbers for students to practice, which may be more difficult than some topics in the elective examination (rational numbers part). This exercise can also be used as a rational number after studying in senior one.

fill (up) a vacancy

The reciprocal of 1 -(-) is _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _.

2. If |x|+|y|=0, then x = _ _ _ _ _ _ _ _ _ and y = _ _ _ _ _ _ _.

3. If |a|=|b|, then A and B _ _ _ _ _ _ _ _ _

4. Because the number of points with equal distance from point 2 to point 6 is 4, there is such a relationship, then the number with equal distance from point 100 to point 999 is _ _ _ _ _ _ _ _ _ _ _ _; The number represented by a point with the same distance from the point is _ _ _ _ _ _ _ _ _; The number represented by points with equal distance from m to -n is _ _ _ _ _ _ _ _.

5. Calculation: = _ _ _ _ _ _.

6. Known, then = _ _ _ _ _ _.

7. If = 2, then X =.

8. The rational number represented by a point 4 units away from point 3 is _ _ _ _ _ _ _ _.

9. The rational number within the range of _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _

10. A positive integer less than 3 is _ _ _ _.

1 1. If m 0, | m | > | n|, then m+n _ _ _ _ _ _ 0.

12. Can you work it out quickly?

In order to solve this problem, we study the square of a positive integer with a unit number of 5. Any positive integer with a unit number of 5 can be written as 10N+5 (n is a positive integer), that is, the value of sum. Try to analyze these simple cases, 2, 3 ... and explore their laws.

(1) Explore the law through calculation:

Can write;

………………

Can be written as _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _

2 According to the above rules, try to calculate =

13. Observe the numbers in the following column and write them on the horizontal line according to the law.

- ; ; - ; ; ; ; ……; The number of 2003 is.

14. Fill in the following numbers in the corresponding set.

Integer set: {...}

Negative set: {...}

Music score setting: {...}

Nonnegative set: {...}

Positive rational number set: {...}

Negative score set: {...}

Either-or problem

15.( 1) The following statement is true ()

(a) The greater the absolute value, the greater the number;

(b) The greater the absolute value, the smaller the number;

(d) The absolute values of two numbers are equal.

16. Known

A.-3a+b+c b . 3a+3 b+ c c c a-b+2c d .-a+3 B- 3c

17. The following conclusion is correct ()

A divisor 1.230 is the same as the significant number 1.23.

B. The approximate value of 79.0 is a number accurate to one place, and its significant figures are 7 and 9.

C. The approximate value 3.0324 has five significant figures.

D. The approximate value of 5,000 has the same accuracy as the approximate value of 5,000.

18. Add two rational numbers. If the sum is less than either addend, then two addends ().

(a) all positive numbers; (b) All negative numbers; (c) The opposite number; Different signs.

19. If rational number ()

A. When ...

D. None of the above statements is true.

20. The sum of two nonzero rational numbers is positive, so these two rational numbers are ().

(a) Both are positive numbers; (b) At least one of them is positive.

(c) Positive number is greater than negative number (d) Positive number is greater than the absolute value of negative number, or both are positive numbers.

Three calculation problems

2 1. Find the following values (-48)÷6-(-25)×(-4)

(2)5.6+[0.9+4.4-(-8. 1)];

(3) 120×( );

(4)

22. The income and expenditure of a unit in a week are as follows: +853.5 yuan, +237.2 yuan, -325 yuan,+138.5 yuan, -280 yuan, -520 yuan,+103 yuan. So, is this stock a profit or a loss this week? How much is the surplus or loss?

Tip: In this question, a positive number means income and a negative number means expenditure. Add up seven days' income or expenses, and the sum is positive, which means surplus, and the sum is negative, which means loss.

23. The table below records the daily maximum and minimum temperatures in a certain place for a week. When is the temperature difference maximum and when is the temperature difference minimum?

Monday one two three four five six seven

Maximum temperature 10? C 1 1？ C 12？ C 9？ C 8？ C 9？ C 8？ C

Minimum temperature 2? C 0？ C 1？ C - 1？ What about C2? C -3？ C - 1？ C

24. In the formal volleyball match, there are strict rules about the weight of the volleyball used. Check the weight of five volleyball balls, and the number of grams exceeding the specified weight is positive, and the number of grams below the specified weight is negative. The inspection results are as follows:

+ 15 - 10 +30 -20 -40

Point out which volleyball is of better quality (that is, the weight is closest to the specified weight)? How to illustrate this problem with the absolute value knowledge you have learned?

25. Known; ;

(1) guess and fill in the blanks:

(2) Calculation ①

②23+43+63+983+……+ 1003

26. Explore the law and arrange the continuous even numbers 2, 4, 6, 8, … in the following table:

2 4 6 8 10

12 14 16 18 20

22 24 26 28 30

32 34 36 38 40

… …

(1) What is the relationship between the sum of the five numbers in the cross box and the sum of the intermediate number 16?

(2) Let the middle number be x, and use algebraic expression to represent the sum of five numbers in the cross box.

(3) If you move the cross box up and down, left and right, you can box out five more digits. Can the sum of the other five digits be equal to 20 1? If yes, write down these five numbers, if not, explain the reasons.

27. let y=ax5+bx3+cx-5, where a, b and c are constants. It is known that when x= -5, y=7 and x=5, the value of y is found.

Rational number exercise reference answer

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1.4,-,. Hint: Although the questions are simple, such conceptual questions are almost compulsory in the seventh grade exam.

2.0,0. Hint: |x|≥0, |y|≥0. ∴x=0,y=0.

3. Equal or opposite numbers. Tip: The absolute values of mutually opposite numbers are equal.

4.549.5. Tip: The midpoint of a number with two equal points on the number axis is equal to half of the sum of these two numbers.

5.0. Tip: The sum of every two adjacent items is 0.

6.-8. Hint: 4+a=0, a-2b=0, and the solution is: a= -4, b= -2. = -8.

7. x-3 = 2. x = 3 2, X = 5 or x= 1.

8.- 1 or 7. Tip: The rational number represented by point 3, which is 4 units away, is 3 4.

9.3.1415-3.1424. Tip: According to the rounding rule.

10. 1, 2. Tip: An integer greater than zero is called a positive integer.

1 1.& lt0. Hint: the sign of rational number addition depends on the number with large absolute value.

12.=5625= 100×5×(5+ 1)+25; =7225= 100×8×(8+ 1)+25;

= 100× 10×( 10+ 1)+25= 1 1025.

13.,,. Hint: the nth item of this column number can be expressed as (-1) n.

14. Hint: (1) set refers to the sum of a class of things with certain characteristics. Be careful not to leave out the number 0. There are only a few numbers in the title, so ellipsis is usually added.

(2) Non-negative numbers refer to all rational numbers that are not negative numbers, but should be positive numbers and zero. What does non-positive numbers mean? (A: Negative numbers and zero)

Answer: Integer set: {...}

Negative set: {...}

Music score setting: {...}

Nonnegative set: {...}

Positive rational number set: {...}

Negative score set: {...}

Either-or problem

15.d. Hint: For two negative numbers, the smaller absolute value is larger, so A is wrong. For two positive numbers, the number with the larger absolute value is larger, so B is wrong. The absolute values of two opposite numbers are equal.

16. A hint:-a+b-(-c)-(a+b)+(b+c)-(a+c) =-3a+b+c.

17.c. Tip: The definition of a valid number is from the first non-zero number on the left to the last number on the right. 18.B

19.c tip: when n is odd,

20. D. Tip: Two rational numbers should be added, and the sign of the obtained number is determined by the number with the largest absolute value.

Three calculation problems

2 1. Find the following values.

( 1)- 108

(2) 19. Tip: Remove the brackets first, and then calculate.

(3)- 1 1 1. Hint: 120× ()

120×( )

= 120×(- )+ 120× - 120×

= - 1 1 1

(4). Prompt;

= 1- +

22. Hint: In this question, a positive number means income and a negative number means expenditure. Add up seven days' income or expenses, and the sum is positive, which means surplus, and the sum is negative, which means loss.

Solution: (+853.5)+(+237.2)+(-325)+(+138.5)+(-520)+(-280)+(+103).

=[(+853.5)+(+237.2)+(+ 138.5)+(+ 103)]+[(-325)+(-520)+(-280)]

=(+ 1332.2)+(- 1 125)

=+207.2

Therefore, this week, the unit has a surplus of 207.2 yuan.

23. Tip: Find the temperature difference by subtraction, that is, the difference of the highest temperature, and then compare their sizes.

Solution: Monday temperature difference: 10-2 = 8 (? c)

Temperature difference on Tuesday:11-0 =11(? c)

Temperature difference on Wednesday:12-1=11(? c)

Temperature difference on Thursday: 9-(- 1) = 10 (? c)

Temperature difference on Friday: 8-(-2) = 10 (? c)

Temperature difference on Saturday: 9-(-3) = 12 (? c)

Sunday temperature difference: 8-(- 1) = 9 (? c)

So the temperature difference is the largest on Saturday and the smallest on Monday.

24、

Solution: The second volleyball is of better quality. The absolute value of these data is used to judge the quality of volleyball. The smaller the absolute value, the closer to the specified weight, so the better the quality.

25.

( 1) (2)①25502500; Tip: Original Type =

② Original formula =

=23× 13+23×23+23×33+23×43+23×53+……+23×503

=23( 13+23+33+43+53+……+503)

=8×

= 13005000

26.

(1) The sum of the five numbers in the cross box is equal to five times that in the middle.

(2)5 times

(3) No, suppose 5x=20 1.x=40.2. It is not an integer, so there is no such x.

27.y = ax5+bx3+CX-5, y+5 = ax5+bx3+CX, when x=-5, y+5= 12.