Typical examples of application problems of mathematical scores and percentages in sixth grade
(1) What percentage of one number is another?
The structural feature of this kind of problem is that two quantities are known, and the problem is the percentage between these two quantities.
Finding the percentage of one number to another number is essentially the same as finding the multiple or fraction of one number to another number, except that the calculation result is expressed by percentage, so when finding the percentage of one number to another number, it should be calculated by division.
The general rule of solving problems is: Let A and B be two numbers. When finding the percentage of b, the formula is a? B. When solving this kind of application problem, the key is to understand the meaning of the problem.
Examples are as follows:
Aunt Li, a professional pig farmer, raised 350 pigs last year. This year, she raised 60 more pigs than last year. What is the proportion of pigs she raises this year?
Thinking analysis:
The meaning of the question is: there are more pigs raised this year than last year, which is a few percent of last year. So should the number of pigs raised this year be more than last year? The number of pigs raised last year, and then convert the results into percentages.
(2) Find the fraction or percentage of a number.
Find the fraction or percentage of a number and calculate it by multiplication.
When answering such questions, we should start with the known conditions that reflect the multiple relationship between two numbers, and first determine the unit? 1? , and then determine the unit? 1? The fraction or percentage of.
(3) Find the fraction or percentage of a given number.
This kind of application problem can be solved by equation or arithmetic.
When solving by arithmetic, we should use division to calculate.
When solving this kind of application problems, we should also analyze the known conditions that reflect the multiple relationship between two numbers:
Determine the unit first? 1? , and then determine the unit? 1? What is the score or percentage of?
You can draw some slightly more difficult application questions to help analyze the quantitative relationship.
(4) Engineering problems
The engineering problem is to study work efficiency, working time and total work.
The characteristics of this kind of topic are:
The total amount of work does not give the actual amount. Think of it as? 1? Work efficiency is mostly used to express cooperation time.
Examples are as follows:
For a project, Team A needs 8 days to build and Team B needs 12 days to build. After four days of joint repair by the two teams, how many days will it take for the remaining tasks to be repaired by team B alone?
Thinking analysis:
Think of the workload of a project as? 1? The working efficiency of Party A is 1/8 and that of Party B is112.
It is known that the two teams have worked together for four days, so we can calculate the workload of joint repair and then calculate the remaining workload.
Divide the remaining workload by B's work efficiency, that is, it will take several days to complete.
Typical examples of mathematical proportion and proportional application in grade six
(A) the problem of scale application
This kind of application problem is to study the relationship between distance, actual distance and scale on the map.
When solving this kind of application problems, the most important thing is to understand the meaning of scale, that is:
Distance on the map? Actual distance = proportion
According to this relationship, if any two quantities between the three are known, the third unknown quantity can be found.
Examples are as follows:
On the map with the scale of 1: 300000, the distance from city A to city B is 8 cm. What is the actual distance from city A to city B?
Thinking analysis:
Write the scale in the form of fraction, set the actual distance as x, and substitute it into the relationship of scale to solve it. The name of the unknown unit of measurement should be the same as that of the known unit of measurement.
(2) Proportional distribution of application questions
This kind of application problem is characterized by dividing a quantity into two parts or several parts according to a certain proportion, and finding the number of each part.
This is the only problem that students come into contact with in primary school.
The law to solve this kind of application problem is:
First calculate the sum of the shares of each part, and then determine the scores of each part in the total. Finally, according to the fraction of a number, the number of each part is calculated by multiplication.
Proportional distribution can also be solved by normalization.
Examples are as follows:
A pesticide solution is prepared by adding water to medicinal powder, and the weight ratio of medicinal powder to water is1:100. How many kilograms of powder does 2500 kilograms of water need? How many kilograms of water does 5.5 kilograms of powder need?
Thinking analysis:
Knowing the number of parts of medicine and water, we can know the sum of the total parts of medicine and water, and we can also know how much medicine and water each account for the total parts. Knowing the scores, we can also calculate their respective relative quantities.
(3) Positive and negative proportion application questions
To solve this kind of application problem, the key is to judge whether the two related quantities in the problem are directly proportional or inversely proportional.
If the letters X and Y are used to represent two related quantities, and K is used to represent the proportion (certain), when two opposite related quantities are in direct proportion, the following formula is used:
Kx=y (sure).
If two related quantities are inversely proportional, they can be expressed by the following formula:
? Y=K (certain).
Examples are as follows:
June 1st Toy Factory will produce 2080 sets of children's toys. 960 units were produced in the first six days. According to this calculation, how many days will it take to complete all the tasks?
Thinking analysis:
Because of the heavy workload? Working hours = working efficiency, which is known to be certain, so the total amount of work is proportional to working hours.
The sixth grade mathematics score and percentage application exercises.
(A) Fractional application questions
1, a tank of water, used 1/2 and 5 barrels, with 30% left. How many barrels of water are there in this tank?
2. The length of a steel pipe is10m. Cut off 7/ 10 for the first time, and cut off the remaining 1/3 for the second time. How many meters are left?
3. After 2/3 of the expressway is completed, it is16.5km away from the midpoint. What is the total length of this highway?
4. The master and the apprentice made a batch of parts together, and the apprentice made 2/7 of the total, 2 1 less than the master. How many parts are there in this batch?
5. There is a batch of chemical fertilizers in the warehouse, and 2/5 of the total amount was taken out for the first time, and less than 1/3 of the total amount was taken out for the second time. At this time, there are 24 bags left in the warehouse. How many bags are taken out twice?
6. The distance between Party A and Party B is 1 152km. A bus and a truck leave from two places at the same time. Trucks run 72 kilometers per hour, 2/7 faster than buses. How many hours did it take for two cars to meet?
7. A coat is more expensive than a pair of trousers 160 yuan, in which the price of trousers is 3/5 of that of a coat. How much is a pair of trousers?
8. There are 60 black rabbits in the feeding group, and there are more white rabbits than black rabbits 1/5. How many white rabbits are there?
9. The school wants to dig an 80-meter-long sewer. 1/4 was dug on the first day, and 1/2 was dug on the second day. * * How many meters have you dug in two days? How many meters are left?
Answer:
1. There are 25 barrels of water in this water tank.
There are 2 meters left in this steel pipe.
This highway is 99 kilometers long.
There are 49 parts in this batch.
5. Take out 2 1 package twice.
6.9 hours later, the two cars met.
7, a pair of pants 240 yuan
8. There are 72 white rabbits
9. I dug 60 meters in two days, leaving 20 meters.
(2) percentage application problem
1. The output value of a chemical fertilizer plant increased by 20% this year, 5 million yuan more than last year. How much is this year worth?
2. The fruit company stores a batch of apples, and delivers them after selling 30% 160 boxes, which is more than the original apples110. How many boxes of apples are there?
3, a commodity, the original price is 20% less than the current price, the current price 1028 yuan, what is the original price?
The interest earned from the education savings is tax-free. Dad saved Xiao Xiao's education savings for three years, with an annual interest rate of 5.40%. Upon maturity, * * * received the principal and interest of 22,646 yuan. What is the principal of the education savings fund that Dad gave Xiao Xiaocun?
5. The clothing store bought two clothes at the same time, each of which earned 120 yuan, but one of them earned 20% and the other accompanied 20%. Did the two clothes sold by the clothing store make money or lose money?
6. The father is 43 years old and the daughter is 1 1 year old. A few years ago, my daughter was 20% older than my father.
6, less than 2/5 tons, 20% for () tons, () tons of 30% for 60 tons.
7, a 200-page book, read 20%, and left () pages unread. 40% of the number A is equal to 50% of the number B. The number A is 120 and the number B is ().
8. A factory used 5400 tons of water in the second half of April, saving 20% compared with the first half. How many tons of water were used in the first half of the year?
9. Zhang Ping has 500 yuan money and plans to deposit it in the bank for two years. There are two deposit methods. One is to save it for two years, with an annual interest rate of 2.43%. One is to save it for one year with an annual interest rate of 2.25%. When the first year expires, take out the principal and after-tax interest and deposit it for another year. Which method can I choose to get more after-tax interest?
10. Xiaoli's mother deposited 5,000 yuan in the bank for a year, with an annual interest rate of 2.25%. When withdrawing money, the bank withheld and remitted 20% interest tax. How much interest tax was paid at maturity?
1 1. The flour yield of a wheat is 85%. Grinding 13.6 tons of flour requires this kind of wheat.
Answer:
1. The output value this year is 30 million yuan.
2. At this time, there are 440 boxes of apples (originally there were 400 boxes of apples).
3. The original price is 822.40 yuan.
4. Deposit principal 19488+0 yuan.
5. I lost money selling these two clothes 10.
Six or three years ago, my daughter was 20% older than my father.
7, 0.32 tons; 200 tons
8. There are 160 pages left; The best number is 96.
9. The water consumption in the first half of the month was 6,750 tons.
10, the first method obtains more after-tax interest (19.44 yuan; 18. 16 yuan)
1 1, and the interest tax paid is 22.5 yuan.
Need 12, 16 tons of wheat.
Math ratio and proportion application exercises in sixth grade
1. The circumference of a rectangle is 24 cm, and the length-width ratio is 2: 1. How many square centimeters is the area of this rectangle?
2. The sum of sides of a cuboid is 96 cm, and the ratio of length, width and height is 3∶2 ∶ 1. What is the volume of this cuboid?
3. The total length of a cuboid is 96 cm, the height is 4 cm, and the length-width ratio is 3 ∶2. What is the volume of this cuboid?
4. There are 42 computer interest groups in a school, of which the ratio of male to female is 4 ∶3. How many boys are there?
There are two baskets of fruit, and the fruit in basket A weighs 32kg. After taking out 20% from basket B, the weight ratio of the two baskets of fruits is 4:3. How many kilograms were there in the original two baskets of fruit?
6. Make a 600g bean paste bun, and the ratio of flour, red beans and sugar is 3:2: 1. How many grams of flour, red beans and sugar do you need?
7. Xiaoming read a story book. On the first day, he read 1/9 of the book, and the next day, he read 24 pages. The ratio of pages read in two days to remaining pages is 1: 4. How many pages are there in this book?
8. The ratio of the three internal angles of a triangle is 2:3:4. What are the degrees of these three internal angles?
Answer:
The area of this rectangle is 32 square centimeters.
The volume of this cuboid is 384 cubic centimeters.
The volume of this cuboid is 384 cubic centimeters.
4. There are 24 boys
5, the original two baskets of fruit * * * have 62 kilograms.
6. Brown sugar needs 200g, and beans need 100g.
7. This book has 270 pages.