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Wide angle mathematical problems in sixth grade mathematics 1. For any seven different natural numbers, the difference between at least two of them is a multiple of 6. Why? 2. In 1,2,3,..., 49,50, at least how many different numbers must be taken out to ensure that one of them can be divided by 5? 3. There are 63 students in a class. They all participate in extracurricular interest groups. The activities include mathematics, art, calligraphy and English. Each student can participate in one, two, three or four interest groups. How many students in the class participate in the same project? 4. Give 400 cards to several students, each of whom can get no more than 11 cards. Try to prove that at least 7 students get the same number of cards How many questions can I answer? I'm in a hurry. I'm in a hurry. I'm in a hurry. I'm in a hurry
Because there are six possible results of any natural number divided by 6: 0, 1, 2, 3, 4, 5, and there are seven numbers, which will produce seven residuals. Then at least two of the seven residuals are the same. If you find the difference between the two numbers, you can just subtract the residuals, and the result can be divided by 6
Who can help to solve the following problem (Grade 6)
There are 630 tons of sand in two piles. If two fifths of the sand in pile a is put into pile B, the sand in pile B is four times as much as that in pile A. how many tons of sand are there in each pile?
There is also a small question:
Find the rules and fill in the numbers
1/2 ,1/6 ,1/12 ,1/20 ,1/30 ,1/42 ,( ),( ),( )
Suppose: there were x tons of sand in pile a, then there were (630-x) tons of sand in pile B, 2 / 5x + (630-x) = 4 * 3 / 5xx = 210630-210 = 420 tons, so the sand in pile a was 210 tons, and the sand in pile B was 420 tons
A few sixth grade practical problems, the best distribution
1. The volume of an original book is 50.24 cubic meters, and the perimeter of its bottom is 15.7 meters. How high is the column?
2. A cuboid refrigerator, 4 decimeters long, 3 decimeters wide and 5 decimeters high, is filled with water. Pour the water into a cylindrical bucket, 12 decimeters high, with 2 / 5 of the space in the bucket. How many square decimeters does the cylindrical bucket cover?
3. The side of a cylinder is a rectangle with a length of 25.12 cm and a width of 5 cm. What is the maximum volume of the cylinder?
1. Radius of bottom circle: 15.7 △ 3.14 △ 2 = 2.5m
The area of bottom circle: 2.5 × 2.5 × 3.14 = 19.625m & sup2;
Height: 50.24 △ 19.625 = 2.56M
2. Water volume: 4 × 3 × 5 = 60dm & sup3;
Barrel volume: 60 △ 2 / 5 = 150dm & sup3;
The floor area of the barrel: 150 △ 12 = 12.5dm & sup2;
3. If the circumference of the bottom is 25.12cm, 5cm is the height of the cylinder
Bottom circle radius: 25.12 △ 3.14 △ 2 = 4cm
Cylinder volume: 4 × 4 × 3.14 × 5 = 251.2cm & sup3;
② Taking 5cm as the circumference of the bottom surface, 25.12cm is the height of the cylinder
Radius of bottom circle: 5 △ 3.14 △ 2 = 2.5 / 3.14cm
Cylinder volume: 2.5 / 3.14 × 2.5 / 3.14 × 3.14 × 25.12 = 50cm & sup3;
Because 251.2cm & sup3; > 50cm & sup3;
So the largest volume of this aid is 251.2cm & sup3;
RELATED INFORMATIONS
- 1. What are the wide angles of mathematics from the second volume of the first grade to the second volume of the sixth grade of PEP? Write clearly!
- 2. 1. There is a chain made of red, white and black beads in the order of five red, four white and three black beads, sharing 185 beads. How many are the black beads? What color is the 69th?
- 3. What is the probability that at least two of n people have the same birthday?
- 4. The probability of two out of 50 having the same birthday 365 days
- 5. What is the probability that at least two people born in March will have the same birthday? A（30×29）/31² B 1-（30×29）/31² C 1/31 D 2/31
- 6. Randomly investigate the birthdays of 100 people (including the elderly, young and middle-aged, children, etc.), and find out the probability that two of them have the same birthday (can be different years)
- 7. When a boat finds a leak, it has entered some water, and the water enters the boat at a constant speed. If 10 people clean the water, it will finish in 3 hours; if 5 people clean the water, it will finish in 8 hours. If it is required to finish in 2 hours, it should be arranged___ A man washes for water
- 8. If a work is done alone, Party A can complete it two days ahead of schedule. Party B can complete it three days ahead of schedule. Now, after two days of cooperation, Party B will continue to do the rest alone, just in time. If cooperation, how many days will it take to complete the project?
- 9. For a project, Party A and Party B work together for 20 days, and Party A has worked together for 2 days after 3 days to complete 1 / 5 of the whole project. How many days does it take for Party A and Party B to work alone? Remember, ”Three days later, it was followed by "three days later, B followed". Just understand.
- 10. For a project, Party A will do it alone in 15 days and Party B will do it alone in 20 days. After three days of cooperation between the two teams, team B will do the rest of the project alone. How many more days will it take to complete? -------------------------------------------------------------------- Please send the formula and solution to me if you know the answer,
- 11. ① Eight chickens and 15 rabbits have () feet ② () chicken and 6 rabbits have 36 feet ③ The chicken and the rabbit have 48 feet ④ How many rabbits and chickens are there in the cage,
- 12. On the Inner Mongolia prairie, there are a group of herdsmen driving a group of cattle and sheep, people and cattle. There are 27 sheep and 100 legs at the same time. How to calculate the number of people, cattle and sheep
- 13. Practical problems in grade four of primary school The two cars left from the two places at the same time and met them two hours later. At this time, they were 20 kilometers away from the midpoint of the two places. It is known that car B travels 60 kilometers per hour and car a how many kilometers per hour
- 14. Next to a straight runway, 51 flags were planted, with an interval of 2 meters. Later, only 26 small flags were planted, with an average interval of how many meters? (both ends are inserted)
- 15. A and B plant trees. It takes 13 more time for a to plant this batch of trees alone than B. if they work together, B will plant 36 more trees than a when they finish the task. How many trees are there in all?
- 16. The total length of a bridge is 161 meters. It is planned to install 16 billboards on the railings on both sides of the bridge. The length of each billboard is 2 meters. The billboards at both ends are 12 meters from the bridge end. The distance between two adjacent billboards is equal. The distance between two adjacent billboards is calculated
- 17. Solving linear equation with one variable Wuhan plans to plant trees on one side of a certain section of the road. It requires one tree to be planted at both ends of the road. If one tree is planted every 5 meters, 21 seedlings will be missing. If one tree is planted every 6 meters, the seedlings will be used up. How many seedlings are there?
- 18. The problem of tree planting is the same as the problem of tree planting, but the topic is not the same The corridor of a dormitory is 15 meters long, with four colored flags. According to this calculation, the corridor of an office building is 27 meters long, how many colored flags should be inserted &It takes eight minutes to saw a piece of wood into three sections. If the time for each section is the same, how many minutes does it take to saw seven sections? &Uncle Zhang is walking on the path full of telephone poles at the same speed. It took him 22 minutes to walk from the first telephone pole to the 12th telephone pole. If he walked for 36 minutes, which telephone pole should he walk to?
- 19. There is a fulcrum O in two shoulder poles ab of the same length, OA ≠ ob, Ma = MX in Figure 1 and MB = MX in Figure 2. Find the value of MX A__________ o___ B | | | | mx mb A__________ o__ B | | | | ma mx Find what MX equals,
- 20. Lever and pulley Now that we have learned lever, we know that lever can be divided into labor-saving lever, equal arm lever and labor-intensive lever. Why should we introduce pulley? What are the advantages of pulley compared with lever?