52, a number is 2, it is ().

53.A number is 20% less than B number, and B number is ()% more than A number.

54 and 78 are a number, and this number is (). 55 and 45 kilograms are ()% of 1 ton.

56, 15 meter is () meter.

57, 50 is greater than 40 ()%; 40 is less than 50 ()%.

58. There are 80 boys in the sixth grade, and 20 girls are less than boys. Girls are boys (), and boys are about ()% of girls.

59. The number A is the number B, and the number A is () times that of the number B.

60. Put 4g salt into 12g water, and the salt accounts for ()% of the salt water.

The germination test was carried out with 6 1 200 seeds, among which 4 seeds did not germinate and the germination rate was ()%.

62. A train from A to B takes 3 hours to complete the journey, accounting for () of the remaining distance.

63. 25% of a certain number is 100, and this number is ().

64. A book has 120 pages. Those who read the book on the first day and the book on the second day should start reading from page () on the third day.

65, planting trees in spring, the first team belongs to the second team, and the second team is more than the first team ()%.

66, a cup of milk, drink 20%, add water and stir well, and then drink 50%, so bad pure milk accounts for ()% of the cup capacity.

Add 20g sugar to100g water, and the sugar content of sugar water is about ()%.

There are 48 students in Class 6 (2), including girls 18, and later transferred to () girls. At this time, the number of girls accounted for 40% of the class.

68. The weight of a pile of coal is equal to its 100 tons. This pile of coal weighs () tons.

69. The difference between two simplest fractions with the same denominator is that the quotient of these two molecules is that these two fractions are () and () respectively.

Second, the application problem

1. This glass factory 10 produced 2000 cases of glass in October, more than in September. How many boxes of glass were produced in September?

2. A textile factory has 3500 foreskin cotton. How many bags were used for the first time and the second time?

3. The original cement 1200 tons in a warehouse on a construction site, 30% for the first time, and the same amount for the second time. How many tons of cement are there in the warehouse?

4. Factory shipped 12 tons of steel, which was used up for the first time and used up for the second time. How many tons more than the first time?

The school planted 45 trees, including paulownia and poplar. How many trees are there?

6. Of the 350 machines produced by Dahua Machinery Factory, 4 were found to be unqualified. Please inquire about the qualification rate of these machines.

7. Type a manuscript, 36 pages on the first day, and complete 60% of the task. How many pages do you need to type to complete this task?

8. A pile of grain was shipped for the first time, 2 10 tons was shipped for the second time, and the rest was shipped. How many tons is this pile of grain?

9. 60% of a bag of cement is used, and the remaining part is less than the used part 10 kg. How many kilograms did you use?

10, a car goes straight from a to b; Another 50 kilometers will be 6 kilometers less than the whole journey. How many kilometers is it between A and B?

1 1. Xiaohong's mother bought a national construction bond with a term of 3 years and 20,000 yuan. If the annual rate of return is 6. 15%, what will be the principal and interest at maturity?

12. The turnover of an insurance company in the first half of this year was 33.6 million yuan. If the business tax is paid at 5%, how much business tax will be paid in the first half of this year?

13. Uncle Wang deposited 4500 yuan in the bank for a fixed period of 5 years. If the annual interest rate is 4. 14%, individual income tax will be paid at 20% of the due interest. How much personal income tax does Uncle Wang have to pay?

Fourth, the application of engineering problems

[evaluation objective]

Be able to identify the application problems of "engineering problems", analyze the quantitative relationship in engineering problems, and answer practical problems correctly.

[knowledge review]

1, characteristics of engineering application problems

Engineering problem is a typical application problem of fractions and percentages. It mainly studies the relationship among total workload, work efficiency and working hours. Its characteristic is that it often does not give the specific number of total workload, but only puts forward words such as "a project", "a job", "a road" and "a book". When answering, the total workload should be "1", but

2. The basic relationship of engineering problems.

Work efficiency × working hours = total workload.

Total amount of work ÷ work efficiency = working hours

Total workload ÷ working time = working efficiency

The engineering problems we contact are all the same, so it has the following relations:

Total workload ÷ work efficiency = cooperation time

3. Problems that should be paid attention to in solving engineering application problems.

The application of engineering problems is generally around the problem of finding work efficiency. Engineering problems mainly study the three quantitative relationships of total work, work efficiency and working time. Pay attention to the corresponding relationship of three quantities when solving problems. That is to find out whose working hours, we must find out the corresponding total work and work efficiency. For example:

A workload, a working time = a working efficiency.

B workload ÷ B working hours = B working efficiency.

C workload, c working hours = C working efficiency.

Total workload ÷ cooperation time = work efficiency and

[test analysis]

[Example 1] For a project, team A 12 days completed the task, team B 15 days completed the task, team A completed it alone, and the rest were completed by both parties. How many days did it take to complete the task?

Analysis: The rest needs to be done by both parties, and it will take several days to complete. We must first find out the sum of the remaining work and the work efficiency of both parties. According to "The remaining work was done by team A alone and by both parties", we can find out that the remaining work is (1-). According to "Team A completed the task alone in 12 days", we can learn something about it. According to "Team B completes the task alone 15 days", it can be found that the working efficiency of Team B is. It can be found that the work efficiency of both teams is (+).

Column synthesis formula calculation:

( 1- )÷( + )

= ÷

=6 (days)

A: The rest will be finished by Team A and Team B in six days.

[Example 2] For a project, it takes 20 days for Team A to do it alone and 30 days for Team B to do it alone. Now the two teams have worked together for a few days, and the remaining B team 10 days will be completed. How many days did Team A and Team B work together?

Analysis: How many days will it take for Team A and Team B to finish? First of all, we ask for the sum of the total workload and work efficiency of Team A and Team B. According to "Team A needs 20 days to finish it alone", we can find that the work efficiency of Team A is; According to "Team B needs to be alone for 30 days", the efficiency of Team B can be obtained. According to "the remaining team B needs 10 days to complete", the workload of team B in 10 days can be obtained, that is, × 10 =, from which the total workload of team A and team B can be obtained as 1-× 10.

Column synthesis formula:

( 1- × 10)÷( + )

=( 1- )÷

=8 days

Answer; It took Team A and Team B eight days to finish it.

[Example 3] A job was completed in 6 days by itself and 8 days by team B. Now that team C has completed all the projects, the rest will be handed over to teams A and B. How many days will it take to complete this task?

Analysis: According to "one job is completed by Party A in 6 days and Party B in 8 days", the work efficiency of Party A is (+), and from "all projects have been completed by Group C", all projects still have (1-), and the remaining workload is divided by the sum of the work efficiency of both parties.

Column synthesis formula calculation:

( 1- )÷( + )

= ÷

=3 days

A: It will take three days to finish.

[Example 4] A pool has three water pipes, A, B and C. A single pipe can fill the empty pool in 6 hours, B pipe in 4 hours and C pipe 12 hours. How many hours can three pipes fill an empty pool?

Analysis: If the full pool water is regarded as the unit of "1", pipe A will inject water every hour, pipe B will inject water every hour, pipe C will release water every hour, and all three pipes will be opened at the same time, then water will be injected every hour.

+-=. According to the total workload ÷ total work efficiency = cooperation time, we can find out how many hours the three pipes are opened together to fill the empty pool with water.

Column synthesis formula:

1÷( + - )

= 1÷

=3 hours

Answer: Three pipes can fill an empty pool with water in three hours.

Exercise 4

Fill in the blanks

1. A project can be completed in 4 days by Party A, 8 days by Party B and () days by Party B. 。

Team a 10 days, team b 20 days, and both parties can complete a project in () days.

3. Party A and Party B jointly complete a project in 6 days, with Party A completing 15 days alone, Party A completing () days and Party B completing the remaining 5 days.

4. From Station A to bilibili, the bus takes 5 hours and the truck takes 6 hours. The speed of the bus is ()% faster than that of the truck.

5, processing a batch of parts, A single hour, B single hour, two people do () hours together.

6. Party A will finish a project in 6 days, and Party B will finish it in 0/2 days.

(1) Party A and Party B complete all the projects in one day ();

(2) Party A and Party B shall complete it within () days;

(3) Party A and Party B jointly complete the whole project within 3 days ();

(4) The ratio of work efficiency between A and B is ().

Second, answer the following questions

1, a pile of goods, car A needs to deliver in hours, and car B needs to deliver in hours. How many hours will it take if two cars are shipped together?

2. It takes six days for a person to do a job, and the efficiency of B is twice that of A. How many days do two people do it at the same time?

3. For work A, A will do it alone 15 days, B will do it alone 18 days, A will do it for 5 days first, and B will do the rest alone. How many days?

4. It takes 10 hour for Party A to produce a batch of parts, but Party B can only produce this batch of parts at the same time. How many hours does it take Party B to do this batch of documents alone?

5. For a job, Team A 12 days, Team B 15 days, Team A alone, and the rest are jointly completed by Party A and Party B. How many days does it take to complete the task?

6. Build a 30-kilometer expressway. Team a 10 day, team b 15 day. How many days can two teams work together?

7. For a project, it takes 8 days for team A to do it alone, and it takes 2 days for team B to do it alone/kloc-0. How many days does it take for Party A and Party B to cooperate in this project?

8. When the swimming pool is filled with water, the single open pipe A is filled for 10 hour, and the single open pipe B is filled for 8 hours. How many hours can the pool be filled if pipe A and pipe B are opened at the same time?

9. For typing a 5400-word manuscript, Party A will type it all in 3 hours, Party B will type it all in 2 hours, and both parties will type it together 1 hour. How many words does Party A type more than Party B?

10, it takes 30 days for Party A to do a job, and the time for Party B to do it alone is the time for Party A. If two people do it together, how many days will it take to complete the whole project?

Fourth, solve application problems with column equations.

[evaluation objective]

1, can analyze the equivalence relation in the topic and list the equations according to the equivalence relation.

2. Understand and master the methods and steps of solving application problems with column equations, and master the writing format of solving application problems with column equations.

3. You can check whether the results conform to the meaning of the problem according to the equivalence relation in the application problem.

[knowledge review]

Equation is an important part of mathematics, and many practical problems are solved by equation. Therefore, learning this part of knowledge well can not only further cultivate our ability of logical reasoning, analyzing and solving problems, but also lay a solid foundation for basic subjects such as mathematics in the future.

The key to enumerating equations to solve practical problems is to analyze the quantitative relationship in the problems. Only in this way can we list the equations correctly and solve the problem.

Analyzing the quantitative relationship of application problems includes two aspects: one is to clarify the relationship between known numbers and unknowns and express it with algebraic expressions; The second is to find out the relationship between quantity and quantity and list the equations.

The general steps to solve application problems with column equations are:

1, find out the meaning of the problem, and find out the relationship between the known number and the unknown number;

2. Use the letter χ to represent the unknown;

3. Find out the equivalent relationship between known number and unknown number, and list the equations;

4. Solve the equation and find the value of χ;

5. Test and write the answers.

[Main train of thought of column equation]

1, according to the calculation formula of geometric equation;

2. Establish an equation according to the meaning of proportion and the meaning of positive and negative proportion;

3. Establish an equation according to the meaning of scale;

4. Establish equations according to common quantitative relations;

5. According to the meaning of fractional multiplication, that is, the series equation of "how many fractions of a number are found", the problem of "how to find this number when how many fractions of a number are known" is solved.

[Case study]

[Example 1] The area of a trapezoid is 54 square centimeters, the upper bottom is 8 centimeters, and the lower bottom is 10 centimeters. What's your height?

Analysis: the equivalent relationship of this question is the area formula of trapezoid, that is,

S=(a+b )×h÷2

If the height is χ cm, you can replace the letters of the above formula with known numbers and list the equations.

Let the height of trapezoid be χ cm.

( 10+8)×χ÷2=54

( 10+8)×χ= 108

χ= 108÷ 18

χ=6

Answer: The height of this trapezoid is 6 cm.

[Example 2] The farm raises 2 16 pigs, of which the number of pigs is the number of sheep. How many sheep are there?

Analysis: According to the known condition in the problem that "the number of pigs is the number of sheep heads", an equivalence relation can be found:

Number of pigs × = Number of sheep ×

The number of pigs is 2 16. If the number of sheep is χ, the equation can be listed according to the above equivalence relation.

χ=2 16×

χ= 108

χ= 108÷

χ= 162

Answer; There are 162 sheep.

Example 3: Grade six students planted 72 fewer trees than Class Two. There are 45 people in class one, with an average of 8 trees per person, and there are 48 people in class two. How many trees per person?

Analysis: According to the known condition of "one class is 72 less than the second class", the equivalence relation can be found:

Grade 2-1 grade =72 trees

The number of trees planted in one class is (8×45). If Class Two plants χ trees, the total number of trees planted in Class Two is 48χ trees. According to the equivalence relation, the equation can be listed as follows:

Set up two classes and plant χ trees on average.

48χ-8×45=72

48χ-360=72

48χ=360+72

48χ=432

χ=9

Answer: Class Two plants an average of 9 trees per person.

A harvester can harvest 57 hectares of wheat in three days. According to this calculation, how many days will it take to harvest 133 hectares of wheat? (Use proportional solution)

Analysis: According to this calculation, the working efficiency is certain (that is, the efficiency is equal), so as long as the working efficiency is expressed twice, the equation can be listed (that is, the problem can be solved by proportional thinking).

It takes χ days to harvest 133 hectares of wheat.

=

57χ= 133×3

χ=

χ=7

A: It takes 7 days to harvest 133 hectares of wheat.

The farm has to harvest 550 hectares of wheat, and harvested 150 hectares three days ago. According to this calculation, how many days will it take to finish the rest?

[Solution 1]

Analysis: According to this calculation, the number of hectares of wheat harvested every day (that is, the working efficiency) is certain, that is, the efficiency is equal, so the equation can be listed as follows:

The rest will take x days to complete.

=

150χ=(550- 150)×3

χ=

χ=8

A: The rest will take eight days to complete.

[Solution 2]

If it takes χ days to harvest 550 hectares of wheat, it will take (χ-3) days for the rest.

=

150χ=550×3

χ=

χ= 1 1

χ-3= 1 1-3=8

A: The rest will take eight days to complete.

[Example 6] Spread a square brick on the floor of the house, and it costs 2000 yuan to use a square brick with a side length of 2 meters. If you use a square brick with a side length of 4 meters, how many pieces do you need?

Analysis: according to the meaning of the question, the area of the house is certain, and the area of each square brick is equal to the residual product of the number of blocks.

Set a square brick χ block with a side length of 4 decimeters.

(4×4)χ=(2×2)×2000

16χ=4×2000

χ=

χ=500

Answer: Change it to a square brick with a side length of 4 meters and ask for 500 yuan.

On the scale map, there is a rectangular land with a length of 3.2 cm and a width of 1.2 cm. What is the actual perimeter and area of this land?

Analysis: To ask the actual perimeter and area, you should ask the actual length and width. According to the meaning of scale, the length and width are solved by equation, and then the actual perimeter and area are calculated.

Solution: Let the actual length of this land be χ cm and the width be y cm.

=

χ=3.2×50000

χ= 160000

160000m =1600m

=

y= 1.2×50000

y=60000

60000 cm =600 m

Circumference: (1600+600) × 2

=2200×2

=4400 meters

Area:1600× 600 = 960,000 square meters

A: The actual perimeter of this land is 4,400 meters; The actual area is 960,000 square meters.

Can this problem be solved by arithmetic? Just try it.

Example 8: A and B are 540 kilometers apart, and two cars, A and B, leave from A and B at the same time. After 9 hours of meeting, it is known that the speed of car A is three times that of car B, so what are the speeds of car A and car B respectively?

Analysis: According to the meaning of the question, two equivalent relationships can be found:

The distance between garage A and garage B is equal to the distance between A and B; The sum of the speed of car A and the speed of car B multiplied by the travel time is equal to the distance between a and b, but it is better to set the unknown as χ and use this quantity to represent another quantity.

If car B travels χ km every hour, then the speed of car A is χ km.

The equation 1 is 3x9+x9 = 540.

Equation 2: (3 χ+χ) × 9 = 540.

Solve the above formula: χ= 15.

3χ= 15×3=45

Answer: A car is 45 kilometers per hour, and B car is 15 kilometers per hour.

[Example 9] A factory used 480 tons of water every month, less than originally planned. /kloc-how many tons of water was originally planned in October?

Analysis: According to "saving compared with the original plan", the original planned quantity is 1, and the unit quantity "1" should be set as χ, which is more convenient to express the saved quantity; Then according to the equation "planned water tonnage-water saving tonnage = actual water tonnage".

Assuming that the original planned water consumption is χ tons, χ tons will be saved.

χ- χ=480

χ=480

χ=540

A:/kloc-540 tons of water was saved in October.

I answered so many questions. Give it to me.