20-(20× 5-76) ÷ (5+1) =16 (road)
There are 45 students in Class One, of whom 2/5 are boys and14 are girls. 15 students, several boys and several girls.
Solution: If there are X boys, there are (45-x) girls.
2/5x+ 1/4 (45-x)= 15
2/5x + 4/45 -4/x = 15
x=25
Female: 45-25=20 (person)
A train is 200 meters long. It takes 42 seconds to cross a 430-meter-long tunnel and 25 seconds to cross a platform at the same speed. How long is this platform?
(200+430)÷42×25-200
=375-200
=175m
4. It takes 15 days for Party A to do a job alone, and 12 days for Party B to do a job alone. This work is jointly completed by Party A and Party B, and Party B will rest for 7 days during the construction period. How many days can it be completed?
Solution: It takes X days to complete the work, so Party A and Party B will work together for (X-6) days and Party A will work alone for 6 days. According to the meaning of the question, it can be concluded that A can complete115. B112, thus obtaining the formula:
( 1/ 15+ 1/ 12)(X-6)+ 1/ 15 * 6 = 1
The solution is X= 10.
5. Ben rode his bike to a city at the speed of X and returned at the speed of Y. What is the average speed of his whole trip?
The answer is 2xy/x+y, why? )
Solution: let the total distance be s, then the time to go is S/X and the time to come back is s/y.
Then the average speed is 2s/(s/x+s/y) = 2/(1/x+1/y) = 2xy/(x+y).
6. In the swimming pool, pupils account for 30% of the students who take part in swimming. After another group of students came, the total number of students increased by 20%, and primary school students accounted for 40% of the total number of students.
7. Divide 37 into three numbers, A, B and C, so that the product of A, B and C is 1440, and the product of A and B is more than C 12. What are the numbers of A, B and C?
Solution: decompose 1440 into prime factors:
1440= 12× 12× 10
=2×2×3×2×2×3×2×5
=(2×2×2)×(3×3)×(2×2×5)
=8×9×20
If the numbers A and B are 8 and 9, respectively, and the number C is 20, then:
8×9=72,
20×3+ 12=72
Just meet the conditions in the question.
A: The numbers A, B and C are 8, 9 and 20 respectively.
On the 8.800-meter roundabout, put a colorful flag every 50 meters. Later, some colorful flags were added to shorten the interval of colorful flags, and the colorful flags at the starting point did not move. After re-plugging, I found that the colorful flags on all sides did not move. How many meters is the interval between colorful flags now?
Insert a colorful flag every 50 meters around the 800-meter roundabout, * * * insert 800÷50= 16. After reinsertion, four of them are still, and the distance between any two adjacent ones is 50× (16÷ 4) = 200m. After reinsertion, every two adjacent ones.
9. The primary school organized a spring outing, and the students decided to divide into several buses that can take up to 32 people. If you plan to take 22 people in each car, one person has no seat; If you drive one less car, these students will be evenly distributed to the remaining cars. How many students are there? How many buses are there?
If one car is missing, then 22 people in this car will get off. If the people in other cars don't move, there will be 22+ 1=23 people. There was one more person, and the remaining 23 people should just be assigned to the remaining vehicles. Because people are individuals and cannot be separated, these 23 people are only evenly distributed.
Note that only average allocation means that each car is allocated to the same number of people, and 23 is an odd number. Only 1 and 23 are divisible by 23. Only 23 is excluded from these two figures.
So: 22+ 1 = 23
23+ 1 = 24 & lt； Automobile >
23 * 23 = 529 < people >
A: Originally, 24 buses were rented, with 529 teachers and students in the school.
10, a cube, the volume is 133 1 cm3. What is the side length of this cube? (suitable for sixth grade)
Solution: decompose 133 1 into prime factors:
133 1= 1 1× 1 1× 1 1
Answer: The side length of this cube is 1 1 cm.
1 1 Li Ming is a stamp collector. He collected one eleventh of the total number of stamps, and later he collected fifteen more. At that time, stamp sheetlets accounted for one ninth of the total number of stamps. How many stamps has Li Mingyi collected?
First find the invariant: stamps that are not sheetlets.
Is the original sheetlet110?
Is the sheetlet 1/8 now?
Not a sheetlet:15/(1/8-110) = 600.
Sheetlet: 600* 1/8=75 sheets
* * *: 600+75 = 675 (sheets)
12, two piles of sand, the first pile is 25 tons, and the second pile is 2 1 ton. After these two piles used the same parts, the rest of the second pile was 3/4 of the first pile, and each pile used more.
Assume that x tons are used.
(25-x)3/4=2 1-x
x=9
It needs 9 tons.
13. The number of apples bought in kindergarten is three times that of pears. I ate 10 pears and 6 apples, and some apples were just five times as many as pears. How many apples and pears did you buy?
Suppose you buy x pears and then three apples.
5(x- 10)=3x-6
x=22
So there are 22 pears and 66 apples. ***88.
14. Draw the largest square in a circle. It is known that the area of a circle is 628 square centimeters. Find the area of this square.
Solution: the area of a circle divided by π is the square of R, that is, the square area of 1/4, and the square of R multiplied by 4 is the square area.
Formula: 628 ÷ 3.14 = 200m2 (the square of r is also the square area of 1/4).
200*4=800 square meters
The area of a square is 800 square meters.
Note: draw the largest square in a circle, and the diagonal of the square is the diameter.
15. Draw the largest circle in a square. It is known that the area of this square is 20 square centimeters. What is the area of this circle?
16, Xiao Ming reads story books. The ratio of pages read on the first day to total pages is 3: 7. If he reads 15 page again, it is exactly half of this book. How many pages are there in this book?
Let the total number of pages be x: 3x/7+ 15 = x/2.
The solution of x: 7x/14-6x/14 =15.
x/ 14= 15
X=2 10 (page)
17, a clothing store sells a certain kind of clothing, and it can only be sold when it knows that the price is more than 20% higher than the purchase price. In order to get higher profits, the owner of the shop marked the price 80% higher than the purchase price. If you want to buy this kind of clothing in 360 yuan, how much can the store reduce the price at most?
The actual purchase price of clothes marked as 360 yuan is: 360÷( 1+80%)=200 yuan.
The lowest selling price is: 200×( 1+20%)=240 yuan.
The lowest price that can be lowered is 360-240= 120 yuan.
18, Uncle Li surrounded a semi-circular chicken farm with a radius of 10 meter by the wall. How long did he use the fence? What is the solution of area? The formula for calculating the circumference is c=πd, π=3. 14. Because it is a semicircle, it is 1/2 πd, (d=2r).
From the formula, we can find out how long the fence is: 2 * 3.14 *10 * 0.5 = 31.4 square meters.
According to the formula for calculating the area of a circle, S=πR? You can find the area of a circle, because it is a semicircle, so the area is half of the whole circle.
S=3. 14× 10？ × 0.5 =157m2!
19, the number of books in shelf A is 4/5 of that in shelf B. After borrowing 1 12 from these two shelves, the number of books in shelf A is 4/7 of that in shelf B. How many books are there in each shelf? (It takes a process to solve the equation)
The number of books on shelf A is 4/5 of that on shelf B, so we assume that there are 4x and 5x books on shelf A and shelf B, respectively.
(4x- 1 12)/(5x- 1 12)= 4/7
4(5x- 1 12)= 7(4x- 1 12)
x=42
4x= 168
5x=2 10
It turns out that there are 168 and 2 19 books on shelf A and shelf B respectively.
Class 20.6 1 Subscribe to Mathematics Newspaper. The number of people who subscribe to the window newspaper accounts for 40% of the grade, the number of people who subscribe to the math newspaper accounts for 40%, and the number of people who subscribe to the language newspaper accounts for three quarters. Both newspapers are subscribed by 15 people, and there are several people in the whole grade.
The number of subscribers to the Chinese Mathematics Journal is15 ÷ (40%+3/4-1) =15 ÷15% =100 (person).
The whole grade is: 100÷40%=250 (person)
Grade 2 1, grade 6, three classes. 1 class accounts for the whole grade 1/3. The ratio of Class Two to Class Three is 1: 13. There are eight fewer students in Class Two than in Class Three. How many students are there in each of the three classes?
The original problem should be that the ratio of Class Two to Class Three is 1 1: 13.
8/(13-11) = 44 *1= 44 (person) 4* 13=52 (person)1-
(44+52)/(2/3)*( 1/3)=48 (person)
A: There are 48 students in Class One, 44 students in Class Two and 52 students in Class Three.
22. Uncle Zhang's family planted 36 Chinese rose flowers, with 5/ 12 chrysanthemum trees and 3/8 orchid trees. How many orchids (40) did Uncle Zhang plant?
The water content of 23 or 4 tons of grapes in Xinjiang is 99%, and it is 98% after arriving in Nanjing. How many tons of grapes are left after arriving in Nanjing?
4 ×( 1-99%)=0.04 ton.
0.04( 1-98%)= 2 tons.
24. For every 3m increase in the length and width of the rectangular experimental field, its area will increase by 99m. Now it is necessary to fence around the expanded experimental field.
This problem needs to be checked whether the calculation is correct.
How long does it take to prepare a fence?
Circumference = (99-3× 3) ÷ 3× 2 = 60m
The original length, width and x y problem means (x+3) (y+3)-xy = 99 > > & gtx+y = 30 & gt； & gt& gt2*(x+3+y+3 )=72
25. The three sides of a triangle are 3 cm, 4 cm and 5 cm respectively. What is the height of the hypotenuse of this triangle in centimeters?
This is a right triangle (3 and 4 are base and height), and its area is 4×3÷2=6 square centimeters.
Use area unchanged:
According to the triangle area formula, the height on the hypotenuse is 6×2÷5=2.4 square centimeters.
26. Cars travel 40 kilometers per hour, and bicycles travel 1 kilometer per line, which is 2.5 minutes longer than cars. What's the speed of the bike?
60/40÷(60/40+2.5)=
27. On the map with the scale of 1: 5000000, it is measured that the distance between Party A and Party B is 9 cm, and the bus and truck leave from Party A and Party B at the same time and meet at 6 o'clock. The speed ratio of bus to truck is 8: 7. What is the speed of the bus?
The distance between the two places is 9 ÷1/5000000 = 45000000 cm = 450 km.
Bus speed is
450÷6×8/(8+7)
=75×8/ 15
=40 km/h
28. The volume of the cylindrical oil drum is 60 cubic decimeters, the bottom area is 7.5 square decimeters, and it contains three-fifths of the oil. How high is the oil level?
Solution: Oil level height: 60× 3/5 ÷ 7.5 = 4.8 decimeters.
30. Use five cuboids with a length of 10 cm, a width of 5 cm and a height of 4 cm to make a cuboid with the largest surface area. What is its surface area?
Solution: 5× 4 = 20 cm2.
﹙5- 1﹚×2=8
20× 8 = 160 cm2
( 10×5+ 10×4+5×4(2×5 = 1 100 cm2)
1100-160 = 940 square centimeters.
3 1. Make a cuboid with the smallest surface area with three cuboids of 5cm, 3cm wide and 2cm high.
To minimize the surface area, stack the largest surface (5x3) when spelling.
The rectangle is 5 cm long, 3 cm wide and 6 cm high.
Surface area: (5×3+5×6+3×6)×2= 126 cm2.
Volume: 5×3×6=90 cubic centimeters
32. The students walked 80% of the way from school to the park and just arrived at the Children's Palace. On the way back, a quarter of the journey passed through the Children's Palace. How many kilometers is the school from the park?
1/4=25%
25%-( 1-80%)=5%
0.3/5% = 6 km
33. The passenger train is 200 meters long and the freight train is 280 meters long. They travel in opposite directions on parallel tracks, from meeting to leaving in the rear 18s.
It is known that the speed of passenger cars and trucks is 5: 3. How many kilometers do two cars travel per second?
Speed sum = (200+280) ÷ 18 = 80/3m/s
Bus speed = 80/3 ÷ (5+3) × 5 = 50/3m/s.
Freight car speed =80/3-50/3= 10 m/s
34. A group of five students visited the Children's Palace, which happened to be divided into four groups. Each group is led by a teacher. How many people visited the Children's Palace?
35. There used to be 54 students in the sixth grade (1) class, and boys accounted for 5/9 of the class. Later, the boys changed a few people. At this time, boys account for the whole class 13/25. How many boys have been transferred?
54-54× (1-5/9) ÷ (1-13/25) = 4 (person)
(This question uses invariants. )
The little monkey picked 50 bananas. It is very greedy. It eats one every 1 meter. The monkey's house is 50 meters away from the forest. How many bananas can it take home at most? (0)
37. There are 45 students in Class One, Grade Five, among whom there are more boys than girls 1/7. Later, some boys transferred to other schools. At this time, the ratio of boys to girls is 9: 7. How many students are there in the class now?
38. Zhang Kuan has a rectangular iron sheet with a length of 6 cm and a length of 12 cm. What is the volume of a rectangular box without a lid? (Length, width and height are all whole centimeters)
Set the height to 1 cm: 1×4× 10=40 cubic centimeters.
Let the height be 2cm: 2× 2× 8 = 32cm3.
39. Add natural numbers such as 1, 2, 3, 4, 5 ... to get 20 12. It turned out that a number was missing. Which one is it?
There are n numbers, take one.
By (1+2+). . . +n)=20 12+a
(n+ 1)n=4024+2a=63*64=4032
∴a=(4032-4024)/2=4
40. The passenger train is 200 meters long and the freight train is 280 meters long. They travel in opposite directions on parallel tracks, from meeting to leaving in the rear 18s.
It is known that the speed of passenger cars and trucks is 5: 3. How many kilometers do two cars travel per second?
Speed sum = (200+280) ÷ 18 = 80/3m/s
Bus speed = 80/3 ÷ (5+3) × 5 = 50/3m/s.
Freight car speed =80/3-50/3= 10 m/s
4 1, the middle of a book has been torn off, and the sum of the following page numbers is exactly 1200. This book has () pages, and the page numbers on the torn one are () and ().
Solution: Suppose this book has N pages, and the page number on the torn one is M. Since a book has 2 pages, N is a multiple of 2.
N (n+1)/2 =1200+x+(x+1), the solution is n = 50 and x = 37.
So this book has (50) pages, and the page numbers on the torn one are (37) and (38).
42, there are three non-zero numbers, the sum of all three digits that can be composed is 3 108, and the sum of these three digits is ().
Method 1:
Let three numbers be x, y and z respectively.
The values of the three digits that can be composed are
100X+ 10Y+Z
100X+ 10Z+Y
100Y+ 10Z+X
100Y+ 10X+Z
100Z+ 10X+Y
100Z+ 10Y+X
Six values add up to 222(X+Y+Z)=3 108.
X+Y+Z= 14
43. The speed of the ship in still water is per hour15km. It takes 8 hours to sail from upstream A to downstream B, and the water speed is 3km per hour. Does it take () hours to return from B to A?
The distance between Party A and Party B is 8( 15+3)= 144.
The time required for countercurrent is144/(15-3) =12 hours.
It took 8 hours to drive from upstream A to downstream B at the speed of15+3 =18 km/h.
Then the distance is 18× 8 = 144 km.
The speed from downstream B to upstream A is15-3 =12 km/h.
The time is 144 ÷ 12 = 12 hours.
44. There is 2 liters of water in the conical container, and the water level is exactly half the height of the cone. How many liters of water can this container hold?
(8- 1)x2= 14
Note: In this case, the volume ratio is always 8: 1.
45. Build a road. The whole length1/2km was built on the first day. The next day, complete the remaining 1 km. Built on the third day1/4km. At this time, there are still 20 kilometers left, and the total length of the road can be calculated.
Reverse reduction
After the third day, the remaining 20 kilometers.
After the second day, the remaining (20+1) ÷ (1-1/4) = 28 km.
Remaining after the first day (28-1) ÷ (1-1/3) = 81/2km.
Before the first day, the original (81/2+2) ÷ (1-kloc-0//2) = 85 km.
This road is 85 kilometers long.
46. The sum, difference, product and quotient of the ages of a pair of twin sisters this year are 100. How old are they this year?
If the age is x, then:
2X+0+X*X+ 1= 100
The solution is x = 9.
47. Divide 14 by the sum of several natural numbers, and then find the product of these numbers. What is the biggest product that can be found?
[Analysis] According to the "core law",14 = 3+3+2, and the maximum product is 3× 3× 3× 3× 2 = 162.
48. A cloth bag contains several gloves of the same size and different colors. Gloves come in three known colors: black, white and gray. How many gloves do I have to bring to ensure that the three pairs of gloves are the same color?
4+3+3= 10.
The worst way is to take four gloves, three gloves and three gloves respectively, and take 10 gloves to ensure that the two pairs are the same.
There are only three kinds of gloves. If we want the same topic, we won't make him the same. The pigeon coop works like this.
The worst way is to take three samples first, so there is only one pair of black or white or gray, 3x3=9.
Take another one and add it casually. There are four identical ones, that is, two identical pairs.
49. The hour hand of a clock is 20 centimeters long. If you walk for a day and a night, how long will it take for its tip to walk? How big is the area swept by the hour hand?
Distance: 2 * 3.14 * 20 * 2 = 251.2cm.
Area: 3.14 * 20 * 20 * 2 = 2512cm2.
50. There were 28 more boys than girls in the math contest, and all the girls won, 3/4 boys won and 42 boys and girls won. How many boys and girls do you want to take part in the competition?
Equation:
Solution: suppose there is X man in the competition.
x+(x+28)×3/4=42
The solution is x= 12.
12+28=40
Arithmetic:
(42-28)/( 1+3/4)
=2 1*4/7
= 12 (person)
12+28=40 (person)
A: There are 40 girls taking part in the competition.
This is my personal arrangement, I hope it will help you.
Teacher training is a powerful measure to promote the rapid growth of teachers' profession. In order to make the training effective, the