According to the meaning of the question, if he cuts wood 10-7=3 days and he cuts wood 20-5= 15 rubles, then he can cut wood 15/3=5 rubles a day, that is, if he cuts wood 10 days, he can cut wood.
That is, the price of this book =50-20=30 rubles.
0.999999999 or 1, which is the longer period?
1/3 = 0.333333 period
1/3*3= 1
0.3333333333...*3=0.99999999999999 ...
So, the same size.
An old lady sells live ducks, and three buyers come. After a while, she wants to pack all the ducks. A buyer said, "I want to buy half of the two baskets of ducks." Another buyer said, "I'll buy his remaining half." The third buyer said, "I want to buy their remaining half." The old lady thought the three men were joking. How can a lively duck sell for half? How much did the three of them buy?
10-7 = 3 days
20-5 = 15 rubles
Explain that if you work less than three days, you will be given less 15 rubles.
15 ÷ 3 = 5, that is, firewood is 5 rubles per day.
7× 5-5 = 30 rubles
The price of fast food books is 30 rubles.
2 2 2 2 2 2 2 2 2 2 2 2=2008
This question is a question I answered before. Can you have a look?
(2+2+2+2+2)^(2+2/2)*2+2*2*2
Is the power of the previous number.
Interesting problems in mathematics
Ask an old man how much onions are sold at 50 cents a catty (it can be sold in 50 yuan 100 catty).
Here comes a tall man and a short man. The tall one said that I only need 20 cents a catty of onion leaves, and the short one said that I only need 30 cents a catty of onion leaves.
So the old man cut 50 Jin of onion and 50 Jin of onion leaves for them. The tall one was given to 10 yuan and the short one to 15 yuan, which added up to 25 yuan. What happened?
50 kg green onion +50 kg green onion leaves = 100 kg green onion.
But speaking of which,
Onion 1 kg+onion leaves 1 kg = 2 kg of onion.
Onion 2 jiao 1 kg+onion leaf 3 jiao 1 kg = onion 5 jiao 2 kg = onion 2.5 jiao 1 kg.
Because the total weight of onion is 100 Jin.
Calculate 100 Jin onion *2.5 angle =25 yuan.
There are six piles of peaches. Divide the first pile among eight people equally, leaving five. Divide the second pile among eight people equally, leaving four; Divide the third pile among eight people equally, leaving three; Divide the fourth pile among eight people equally, leaving seven; Divide the fifth pile to 8 people on average, leaving1; The sixth pile is as many as the second. If you put six piles of peaches together and give them to eight people equally, can you just finish eating them? Why?
Don't worry about the part that can be divided, just consider whether the rest of each pile can be divided into 8 people.
5+4+3+7+ 1+4 = 24 is a multiple of 8 and can be divisible.
5+3=8,7+ 1=8,4+4=8
1. Guess this number.
There is a number whose meaning and shape are the same whether viewed horizontally, vertically or vice versa. Can you guess this number?
How to break wooden chopsticks
Give you a hammer, a piece of paper and a table. Can you break a wooden chopstick with these three things? The first one is 0. The second is to fold the paper in half several times, then put one end of the chopsticks on it and hit the place where the chopsticks hang with a hammer.
Have you ever heard of the problem of "chickens and rabbits in the same cage" This question is one of the famous and interesting questions in ancient China. About 1500 years ago, this interesting question was recorded in Sun Tzu's calculation. The book says: "Today, chickens and rabbits are in the same cage, with 35 heads above and 94 feet below. What are the geometric figures of chickens and rabbits? " These four sentences mean: there are several chickens and rabbits in a cage, counting from the top, there are 35 heads; It's 94 feet from the bottom. How many chickens and rabbits are there in each cage?
Can you answer this question? Do you want to know how to answer this question in Sunzi Suanjing?
The solution is as follows: If you cut off half a foot of each chicken and rabbit, then each chicken will become a "one-horned chicken" and each rabbit will become a "two-legged rabbit". In this way, the total number of feet of (1) chickens and rabbits will change from 94 to 47; (2) If there is a rabbit in the cage, the total number of feet is more than the total number of heads 1. So the difference between the total number of feet 47 and the total number of heads 35 is the number of rabbits, that is, 47-35 = 12 (only). Obviously, the number of chickens is 35- 12 = 20.
This idea is novel and peculiar, and its "foot-cutting method" has also amazed mathematicians at all times and all over the world. This way of thinking is called transformation. Transformation means that when solving a problem, the conditions or problems in the problem are deformed and transformed until they are finally classified as solved problems.
Honghua Shirt Factory plans to produce 400 shirts every day, which will be completed in 60 days. The actual number of shirts produced every day is 65438+0.5 times of the original plan. How many days did it actually take to complete the task of making these shirts?
To analyze and understand how many days it takes to complete the task of making these shirts, we must know the total number of these shirts and the actual number of them produced every day. Knowing that the original plan was to produce 400 pieces a day and complete them in 60 days, you can work out the total number of these shirts. Knowing that the number of pieces actually produced every day is 65438+ 0.5 times of the original planned number, we can find out the number of pieces actually produced every day.
The actual number of days to complete these shirt-making tasks is:
400×60÷(400× 1.5)
=24000÷600
=40 days
You can also think of it this way: the total number of shirts to be produced is fixed, so the number of days required to complete this batch of shirts is inversely proportional to the number of shirts produced every day. It can be concluded that the number of days actually completed for this batch of shirts is 1.5 times, which is exactly 60 days. Therefore, it is concluded that the number of days actually needed to make this batch of shirts is:
60÷ 1.5=40 (days)
Answer: It actually took 40 days to complete the task of making these shirts.
Dongfeng Machinery Factory originally planned to produce 240 pieces per day, which was completed in 18 days. Actually, it was completed three days ahead of schedule. How many more parts are actually produced every day than originally planned?
Analysis and solutions require how many more parts are actually produced every day than originally planned. First, find out the number of parts actually produced every day, and then subtract the number of parts planned to be produced every day:
240× 18÷( 18-3)-240
=4320÷ 15-240
=288-240
=48 (pieces)
You can also think of it this way: the total number of parts actually completed and planned is the same. According to the meaning of inverse ratio, the number of parts produced every day is inversely proportional to the number of days it takes to complete this batch of parts. Therefore, the ratio of the number of days originally planned to complete the task to the number of days actually completed is 18: (18-3), that is, 6: 5, that is, the ratio of the number of parts actually produced every day to the number of parts originally planned to be produced every day. The number of parts actually produced every day is 6/5 of the number of parts originally planned to be produced every day. Therefore, the number of parts actually produced every day is more than originally planned:
=48 (pieces)
You can also think of it this way: the total number of parts produced is 240× 18=4320 (pieces); This number is decomposed into prime factors, and then the decomposed prime factors are appropriately grouped to represent the product of the original planned daily production number and the number of completed days and the product of the actual daily production number and the actual number of completed days respectively.
4320=25×33×5
= (24× 3× 5 )× (2× 32) ... The quantity and completion of the original planned daily output.
Tiande products
= (25× 32 )× (3× 5) ... Actual daily output and days of completion.
product
Then find out how much the actual daily output exceeds the original plan:
25×32-24×3×5
=288-240
=48 (pieces)
A: Actually, 48 more units are produced every day than originally planned.
Example 47 In the "Creation Cup" exhibition of Chunguang Primary School, 36 pieces are not in grade six, 37 pieces are not in grade five, and 45 pieces are known to be in grade five and six. So, how many items are there in grade five and grade six respectively?
Analysis and solutions According to the known information, 36 items are not in the sixth grade, that is, 1 ~ 4 grade plus 36 items in the fifth grade. There are 37 items that are not in the fifth grade, that is,1~ fourth grade plus sixth grade has 37 items.
Comparing the above two situations, it can be concluded that there are 37-36= 1 exhibit in Grade 6 compared with Grade 5.
I also know that there are 45 exhibits in grade five and grade six, so I found that the exhibits in grade five are
(45- 1)÷2=44÷2=22 (pieces)
The exhibits in grade six are
(45+ 1)÷2=46÷2=23 (pieces)
A: There are 22 exhibits in Grade Five and 23 in Grade Six.
Parts Processing Group of Machinery Factory 1 Master, 6 apprentices, 7 apprentices. Each apprentice can process 50 parts every day, and the number of parts processed by the master every day is 24 more than the average number of parts processed by seven people in the whole group every day. How many parts does the master process in a day?
The number of parts processed by the analysis and solution master every day is 24 more than the average number of parts processed by seven people in the whole group every day. Distribute these 24 parts to six apprentices, plus 50 parts that apprentices process every day, which is exactly the average number of parts that seven people process every day. This number plus 24 is the number of parts processed by the master every day.
24÷6+50+24
=4+50+24
=54+24
=78 (pieces)
A: The master processes 78 parts every day.
The children's wear factory produces red shirts and yellow shirts. Each red shirt needs 2 buttons, and each yellow shirt needs 4 buttons. Shirts of two colors are packed in a box of 30 pieces, and each box of clothes needs 72 buttons. How many red shirts and yellow shirts are there in each box?
Analysis and solution It is known that each yellow coat needs 4 buttons and each red coat needs 2 buttons. If you divide the yellow coat in two, it becomes a "semi-yellow coat". At this time, both the red coat and the "semi-yellow coat" need two buttons. It is known that each box of two-color coats needs 72 buttons. Therefore, it can be found that there are 72÷2=36 red shirts and "semi-yellow shirts". In fact, there are 30 shirts of two colors in each box, and 36 are 6 more than 30, which means that 6 yellow shirts are split in two, so there are 6 yellow shirts in each box. Then, the number of red shirts per box is 30-6.
The formula is:
72÷2-30=36-30=6 (pieces)
30-6=24 (pieces)
You can also think like this:
Take two buttons from each of the 30 coats in each box, so that there are no buttons on the red coat and there are two buttons left on the yellow coat. * * * Remove 2×30=60 buttons. At this time, there are 72-60= 12 buttons left on the coat in the box. Because there are only two buttons left on each yellow coat, there are 12 buttons left.
The formula is:
(72-2×30)÷(4-2)
=(72-60)÷2
= 12÷2
=6 (pieces)
30-6=24 (pieces)
There are 24 red shirts and 6 yellow shirts in each box.
There are apples and peaches in the master's basket. There are three times as many apples as peaches. A group of naughty little monkeys took eight apples and three peaches when their owners were not looking. When the owner found out, the peaches had been taken away by the little monkeys, and there were 10 apples left. How many naughty little monkeys are there?
The number of apples in the basket is three times that of peaches. Each little monkey took three peaches and they were all taken away. So if each little monkey takes nine apples, he can also take all the apples (because the number of apples is just three times that of peaches). But each little monkey only took eight apples, leaving 10 apples, which just shows that this group of little monkeys has 65433 apples.
A: There are 10 naughty monkeys.
Example 5 1 bright primary school originally planned to burn 91800kg of coal in 92 days. If you save more than planned every day,
The analysis and solution require that the saved coal can burn for several days, so it is necessary to know how much coal is saved and the amount of coal burned every day after saving.
How many kilograms of coal has a * * * saved?
How many days can the saved coal burn?
5400÷450= 12 (days)
You can also think like this:
17 sets, so the actual daily coal saving is 1 set, and the actual daily coal consumption is 16 sets. Originally planned to burn coal 192 days, one * * can save 192 unit of coal, and can also burn:
192÷ 16= 12 (days)
Answer: The saved coal can be burned again 12 days.
Example 52 has 1993 people and flour 1993 Jin. 1/2 people took all the flour, the second person took 1/3 of the remaining flour, and the third person took the remaining 1/4. .......
Yes So 1993 How many Jin of flour did this man take?
It is not appropriate to analyze and solve this problem by step-by-step calculation. 1993 Jin of flour was taken away by12, and the rest was of course12. This calculation is decimal, and it is more complicated to calculate how many kilograms of flour are left after the second person takes it away. Therefore, it is necessary to consider the whole and solve the problem with a comprehensive formula.
Answer: 1993 people took 1 kg flour.
Analyze and solve the problem according to the meaning, starting from day 10 and the ninth day.
=40 (bag)
You can also think like this:
The flour was eaten for 10 days, and the pile of flour was divided into 10 piles on average. Flour was eaten on 1 day.
The 1 pile eaten every day is divided into 10 piles on average, and the pile eaten that day is exactly 4 bags. Therefore, this batch of flour is available.
4× 10=40 (bag)
Answer: This batch of flour used to have 40 bags.
There are two containers. The first container contains 1 liter of water, and the second container is empty. Pour 1/2 water from the first container into the second container, then pour 1/3 water from the second container back into the first container, and then pour 1/3 water from the first container.
According to the meaning of the question, the number of times to pour and the amount of water in two cups are listed in the table below.
It is not difficult to see from the above table that the water in the first container is 1, 3, 5, ... after being poured by an odd number. Of course, after pouring 1993 times, the water in the first container is also 1/2 liters.
Can also be calculated in the form of columns:
Children in kindergarten celebrate Children's Day on June 1st, and aunts give apples to children. At first, each child was given three apples. As a result, 15 people only got two apples. Later I bought 40 apples and distributed them to the children. As a result, I happen to have four apples each. How many children are there in kindergarten?
Analysis and problem solving tell us that at first, each child was divided into three parts, and as a result, 15 children were only divided into two parts, that is to say, each child was divided into three parts, and 15 apples were missing. Later, I bought 40 apples and distributed them to the children. As a result, just four apples were distributed to each child. Take out 15 of these 40 apples and give it to those children who only got two apples at first. At this time,
(40- 15)÷(4-3)
=25÷ 1
= 25 (person)
A: There are 25 children in a kindergarten.
A box filled with solid balls weighs 12kg. After taking out the solid ball of 1/4 from the box, the remaining solid ball weighs 9.5kg. How much does the box weigh?
Analysis and solution A box is filled with solid balls, and the box weighs * * *12 kg; After taking out 1/4 of the solid ball from the box, the remaining 3/4 of the solid ball weighs 9.5 kg. It can be concluded that the weight of the solid ball is1/4kg (12-9.5), so the total weight of the solid ball is:
= 10 (kg)
The weight of the box is:
12- 10=2 (kg)
This box weighs 2 kilograms.
Analysis and solution take the total length of the rope as "1" and fold the rope into three strands, that is, use1/3 of the rope length; When the rope is folded into four strands, it is measured by the rope length of 1/4. The difference of remaining rope length outside the well is the difference of rope length 1/3 and rope length 1/4. So the total length of the rope is:
You can also think like this:
Exactly the length of the rope.
Exactly the length of the rope.
The depth of the well is good.
So the depth of the well is:
Students take part in camping activities. A classmate went to ask the teacher in charge of logistics for a bowl. The teacher asked him how much he had taken in the exam, and he said 55. He asked again, "How many people eat?" He said, "One person has 1 rice bowl, two people have 1 vegetable bowl and three people have 1 soup bowl." Please count how many bowls this classmate took to camping activities.
Analysis and solution: first calculate how many bowls 1 person needs on average, and then calculate how many people need 55 bowls. The formula is
You can do the same.
When eating, each person has 1 rice bowls, and how many rice bowls are needed means how many people take part in camping activities. The title also said that two people 1 vegetable bowl, three people 1 soup bowl. We know that the least common multiple of 2 and 3 is 6, that is, when six people eat, there are six rice bowls, three vegetable bowls and two soup bowls.
So, we divided the people who participated in the camping activities into groups of 6 people, and each group used 1 1 bowl for dinner.
From 55÷ 1 1=5, we can know that people who eat are divided into five groups, so we find that this classmate has to lead the bowl for 6×5=30 people.
A: This classmate brought bowls to 30 people who took part in camping activities.
Two years older. How old is father? How old is mom? How old is the son?
Analysis and problem solving tell us that the age of the son is 3/ 10 of the mother's age and 2/7 of the father's age, which is the mother's age.
3/ 10 equals 2/7 of the father's age. Therefore, the mother's age is 2 1/70, and the father is older than the mother 1 year.
The title tells us that father is two years older than mother, so we can see that mother is 40 years old and father
A: Father is 42 years old, mother is 40 years old, and son is 12 years old.
There are some boys and some girls in the classroom. The teacher asked them the number. A boy told the old man.
Analysis and problem solving tell us that the number of boys is the number of girls except 1 boy.
The title also tells us that excluding 1 girls, the number of girls is 3/5 of the number of boys.
The number of girls, excluding 1 girls, is exactly 9 girls. The denominator part of 15 just represents the number of boys, excluding the boys of 1, but just the boys of 14.
It is concluded that there are 15 boys and 10 girls in the classroom.
A: Boys in the classroom 15, girls 10.
There are some books in the bookstore. On the first day, 1/2 was sold out. The next day, I brought 900 books. On the third day, 40 books were sold more than the existing books, leaving 800 books. How many books are there in the bookstore?
Analysis and solutions According to the conditions given in the question, we can go back and find out the number of original books in the bookstore.
Suppose that the number of books sold on the third day is 40 less than the existing books (1/3),
So we can know how many books are in the bookstore before the third day of sale.
Suppose 900 books were not delivered the next day, and the bookstore sold the original books on the first day.
Find out the number of original books in the bookstore.
=720 (Ben)
There are 720 books in the bookstore.
There are 7 bags of rice in Example 62. Their weights are12kg,15kg,17kg, 20kg, 22kg, 24kg and 26kg respectively. Party A takes one bag first, and the rest is taken by Party B, Party C and Party D. It is known that Party B and Party C have the same weight, and both of them are taken by Party D.. ..
Analysis and problem solving tell us that A takes one bag first, and then B, C and D take the rest. It is known that B and C take the same weight, both of which are twice the weight of D, so B, C and D take five times the weight of D..
The total weight of 7 bags of rice is
12+15+17+20+22+24+26 =136 (kg)
136 MINUS the multiple of 5, the rest is the kilograms of the weight taken by A. In other words, 136 MINUS the weight of the bag of rice taken by A, the remaining weight must be a multiple of 5. In order for a number subtracted from 136 to be divisible by 5, the single digit of this number must be 1 or 6.
A: The weight of the bag of rice that A took first was 26 kilograms.
There are several piles of Weiqi players, each pile has the same number of Weiqi players, and each pile has 28% white players. Obviously, half of the players in the first pile are black players. At present, 32% of all the contestants are white. So how many piles of Go players are there?
According to the meaning of the question, the number of white pieces did not change before and after the black pieces were taken away. As the total number of pieces has changed, the percentage of white pieces in the total number of pieces has also changed. The initial white chess pieces accounted for 28% of the total, and later accounted for 32% of the total.
A: It turns out that * * * has four piles of Go.
Learning on the chessboard
Reward score: 25- Question time 2008-10-1915: 24.
32. Learning on the chessboard: In ancient times, in a certain kingdom, there was a wise minister who invented chess and presented it to the king. Since then, the king has been addicted to playing chess. In order to express his gratitude to the clever minister, the king promised to meet one of his requirements. The minister said, "Just put some rice grains on this chessboard. Put 1 grain of rice in the 1 grid; Put 2 grains of rice in the second grid; Put 4 grains of rice in the third box; Then 8 capsules, 16 capsules, 32 capsules ... and so on until box 64. Just a little rice? ! "The king smiled. The minister said, "I'm afraid your treasury doesn't have that much rice!" " "
Because the 63rd power of 2 is equal to 922337203685475808, which is about 9.22* 10/8 power.