Key points of solving general application problems in sixth grade mathematics: starting with conditions? From the question
When analyzing the conditions, we should always pay attention to the problem of the topic.
When analyzing a problem, we should always pay attention to the known conditions of the topic.
Examples are as follows:
A workshop of a hardware factory wants to produce 1 100 parts, which has been produced for five days, with an average of 130 parts per day. If the average daily output is 150, how many days will it take to complete the rest?
Thinking analysis:
Known? It has been in production for five days, with an average of 130 pieces per day? , you can find the quantity that has been produced.
Known? Production 1 100 machine parts? And the quantity that has been produced, you know? The rest are generated on average every day 150? You will find that it will take several days to finish.
Thoughts on solving typical application problems in sixth grade mathematics (1) Finding average application problems
The law of solving the average value is: total amount? Total number of corresponding copies = average
Note: in this kind of application problems, to grasp the corresponding relationship, you can divide it into different sub-quantities according to the total amount, then find out their respective copies one by one according to the sub-quantities, and finally get the corresponding relationship.
Example 1 is as follows:
A rice mill, 4 hours in the morning 1360 kg, 3 hours in the afternoon 1096 kg. How many kilograms of rice is milled per hour on this day?
Thinking analysis:
How many kilograms of rice should be milled per hour on this day, and the following three problems need to be solved:
1. How many meters did you press this day? A day includes morning and afternoon.
2. How many hours did you work this day? (4 hours in the morning and 3 hours in the afternoon).
3. What is the total amount of this day? What's the total number of copies today? (In this way, the corresponding relationship is found and the problem is solved. )
(2) the problem of standardization
The title structure of standardization problem is:
The first part of the topic is known conditions, which is a set of related quantities;
The second half of the topic is a question and a set of related quantities, one of which is unknown.
The law of solving problems is to find the single quantity first, and then according to the problem, or how many times the single quantity is, or how much the single quantity is.
Examples are as follows:
Six tractors cultivated 300 acres of land in four hours. According to this calculation, how many acres of land can eight tractors cultivate in seven hours?
Thinking analysis:
First, the unit quantity, namely 1 tractor and 1 hour, is calculated, and then the mu of cultivated land of 8 tractors for 7 hours is calculated.
(3) the problem of the meeting
Refers to two moving objects moving in opposite directions from two places at different speeds.
The basic relationship when encountering problems is:
1, meeting time = distance apart (when two objects are moving)? Speed and.
The example is as follows: the distance between the two places is 500 meters. Xiaohong and Xiaoming came from two places at the same time. Xiaohong walks 60 meters per minute and Xiaoming walks 65 meters per minute. How many minutes did you meet?
2. Distance (when two objects move) = the sum of speeds? Meeting time
Examples are as follows: a bus and a truck set off from both parties at the same time, and met on the way 10 hours later. It is known that the average speed of trucks is 45 kilometers per hour, and the speed of passenger cars is 20% faster than that of trucks. How many kilometers is it between Party A and Party B?
3. Speed = separation distance (when two objects move)? Meet time-optimal speed
The example is as follows: a truck and a bus set off from two places 648 kilometers apart at the same time and met after 4.5 hours. The speed of the passenger car is 80 kilometers per hour, and how many kilometers per hour is the truck?
The question of meeting can vary a lot.
For example, two objects move in opposite directions from two places, but they don't start at the same time;
Or one of the objects pauses in the middle;
Or after two moving objects meet, they continue to walk for a certain distance. These should be analyzed in combination with the specific situation.
In addition, the problems encountered can be extended to engineering problems: ergonomics and? Joint working hours = total work.
The sixth grade math application problem 1 1. There is a batch of parts, 12 days for both parties to process, 9 days for both parties to process, 18 days for both parties to process and three people to process at the same time. How many days can it be finished?
Xiaoming can buy 12 pencils or 4 erasers with his money. He bought three pencils first, how many erasers can he buy for the rest?
3. Processing a batch of parts. On the first day and the second day, 2/9 of this batch of parts was completed. On the third day, 80 parts were processed, just finishing the processing task. How many parts are there in this batch?
This TV factory planned to produce 5000 TV sets in May, but actually produced 6000 TV sets. What percentage did it exceed?
5. The original price of a computer is 6800 yuan, and now it is reduced by 1700 yuan. What is the percentage reduction?
6. For a section of road, it takes 20 minutes for Party A to complete the journey, and 15 minutes for Party B to complete the journey. What's the Internet speed of Party A?
7. A manuscript was originally planned to be copied in five days, but it was copied in four days. What percentage has the actual work efficiency improved over the plan?
8. Take out 1/5 from the coal in pile A and give it to pile B. At this time, the weights of the two piles of coal will be equal. How much is the weight of raw coal in pile B less than that in pile A?
Class 9.6 (1) has 32 boys and 28 girls. Class 6 (2) is 95% of Class 6 (1). How many students are there in Class Six (2)?
10, a scarf, if sold at 100 yuan, you can earn 25%, if sold at 120 yuan, what percentage can you earn?
1 1, bought 55 footballs, and bought 20% less basketball than football. How many basketballs are there?
12, a pile of sand, the first time 40%. The second shipment is 30%, leaving 48 tons. How many tons is this pile of sand?
13. A flour mill can grind 13000 kg of flour with 20 tons of wheat. Find the flour yield of wheat?
14. In100g of water, add 25g of salt. What's the salt content of this brine?
15, the oil yield of a rapeseed is 33%, if you want to squeeze out 100 kg rapeseed oil. How many kilograms of rapeseed are there at least?
16,200 parts were processed in Li Shifu, and 4 parts were rejected after inspection. What's the pass rate? According to this calculation, how many parts are unqualified after processing 700 parts?
17, Xiaohong's father deposited 5,000 yuan into the bank's current savings with a monthly interest rate of 0.60%. How much after-tax interest did he get after four months? How much principal and interest can I get back
18, Mr. Wang's monthly salary 1450 yuan, and personal income tax will be levied at 5% for the part exceeding 1200 yuan. What is Mr. Wang's monthly salary after tax?
19. The original price of a basketball 180 yuan is now sold at 75% off the original price. What's the current price of this kind of basketball? How much cheaper is each?
Li Dan's family harvested 300 kilograms of corn last year and 249 kilograms the year before last. Last year, corn production increased by several percentage points over the previous year.
Sixth grade math application problem 1 answer:
1, it takes 8 days for three people to process at the same time.
2. You can also buy 3 erasers (12 pencils =4 erasers, which means 1 eraser =3 pencils).
3. There are 144 parts in this batch.
4, overfulfilled by 20%
5. Reduce the price by 25%
6. The speed of A is 75% of that of B.
7. The actual work efficiency is 25% higher than planned.
8. The weight of coal pile B is 40% lighter than that of coal pile A..
There are 57 students in Class Six (2).
10, answer in two situations (i.e. sales profit rate and cost profit rate):
(1) if it is 25% of the price, the profit is 100? 25%=25, so the cost should be 100-25=75.
When selling 120 yuan, the profit is 120-75=45, so the sales profit rate is 45? 120=37.5%
② If it is 25% of the cost: let the cost be X, then (100-X)? X=25%, X=80, so the cost is 80. When the price is 120, the profit is 120-80=40, so the cost profit rate is 40/80=50%.
1 1, there are 44 basketballs.
12, this pile of sand has 160 tons.
13, the flour yield of wheat is 65%.
14, the salt content of this brine is 20%.
15, at least 303kg rapeseed is needed.
16, the qualified rate is 98%; Of the 700, 14 failed.
17, 96 yuan can get after-tax interest; You can get back the principal and interest of 1 ***5096 yuan.
18, and teacher Wang's monthly after-tax salary is 1437.5 yuan.
19. The current price of this basketball is1one in 35 yuan, which is cheaper than that in 45 yuan.
Last year's corn output increased by 20% compared with the previous year.
The sixth grade math application problem 2 1. Mingming bought a calculator in the shop, and 68 yuan got a 15% discount. What is the original price of this calculator?
Xiaohua's family harvested 4000 kilograms of rice the year before last. Last year, due to pests, the output decreased by 35% compared with the previous year. How many Jin of rice did Xiaohua's family collect last year?
3. The current price of a commodity is 18 yuan, with a loss of 25%. How much is the loss? If you want to make a profit of 25%, how much should you sell it?
4.30 kg of salt water with a salt content of 10%. How many kilograms of salt can be added to make salt water with a salt content of 25%?
5. The original price of a leather coat is 1800 yuan, but now it has been reduced. What's the discount on products sold in 270 yuan?
6. The insurance company has 120 employees, of which male employees account for 50% of female employees. How many male employees are there in this insurance company?
7. An engineering team built 600 meters on the first day, 20% of the total length on the second day and 25% on the third day. At this time, 75% of the total length was repaired. What is the total length of this highway?
8. Xiaojun bought a set of discounted clothes at the price of 72 yuan, which was cheaper than the original price by 8 yuan. How much is the discount on this suit?
9.1520kg salt water has a salt content of 25%. How many kilograms of water need to be evaporated to turn these brine into brine with a salt content of 50%?
10, the toy store sells two kinds of toys at the same time, the price is 120 yuan, one can earn 25% and the other can lose 25%. If these two toys are sold at the same time, is it a loss or a profit? If so, how much will it cost? If so, how much will it cost?
1 1 .314m round fish pond. What is the area of this fish pond?
12. A round vegetable field with a diameter of 20 meters. Now, how many square meters of plastic film are needed to cover vegetable fields? If the film price per square meter is 0.5 yuan, how much do these films cost?
13 The outer diameter of the bicycle wheel is 70cm. If the wheels rotate 100 cycles per minute on average, it takes about 25 minutes to get from Wangzhigang Town to Baoying County. How many kilometers is it from Wangzhigang Town to Baoying County?
14. Build a canal with a length of 1800 meters. After five days' work, the repaired canal accounts for13 of the unrepaired canal. According to this schedule, how many days will it take for the canal to be completed?
15, the sixth grade math interest group activity, the students didn't participate in 3/7, and then 30 people participated, so the students didn't participate in 2/3, how many people were there in the sixth grade?
16, 5/6 of the school art group is just 5/8 of the science and technology group. It is known that there are 24 people in the art troupe. How many people are there in the science and technology team of this school?
17, transport a batch of chemical fertilizer 25% first, and then transport 18 tons. At this time, 45% did not ship. How many tons of chemical fertilizer are there?
18. The school enclosed a rectangular vegetable field with a 40-meter-long iron wire (excluding joints). The width of the rectangle is known as 1/4. What is the area of this vegetable field in the school?
Sixth grade math application problem 2 answer:
1, the original price of this calculator is 80 yuan.
2.600 kilograms of rice was harvested last year.
3. Lost 6 yuan (the cost price of this commodity is 24 yuan); If you want to make a profit of 25%, you should sell it as 30 yuan.
4. Add 6 kilograms of salt.
These goods are sold at a 15% discount.
This insurance company has 40 male employees.
The total length of this highway is 2000 meters.
This suit is sold at a 10% discount.
9. 760 kilograms of water needs to be evaporated.
10, this fish pond covers an area of 7850 square meters.
1 1, at least 3 14 square meters of membrane is needed, and the cost is 157 yuan.
12, about 5.5km.
13, it takes 10 days to complete the canal.
14, 6, 300 people.
15, 32 people in the science and technology group.
16, this batch of fertilizer has 60 tons.
17. The area of this vegetable field is 64 square meters.