1

At noon today, I was doing my math summer homework. Writing, unfortunately, I have a problem. I thought about it for a long time, but I couldn't figure out a way. The question is this:

There is a cuboid, the product of the front and the upper two areas is 209 square centimeters, and the length, width and height are prime numbers. Find its volume.

I saw it and thought: this question is really difficult! Only knowing the product of two surface areas, the volume must also know the length, width and height, but there is no hint at all. How does this start?

Just as I was scratching my head, a colleague of my mother came. He taught me to use the idea of equation to solve it first, but I am not very familiar with this method of equation. So, he taught me another way: list the numbers first, and then exclude them one by one. First, we listed a lot of numbers according to the requirements of the topic, such as: 3, 5, 7, 1 1, and then we began to exclude them, and then we found that only1and 19 were left. At this time, I thought: one of these two numbers is the length of the common side of the front of the cuboid in the question; One is the front of the cuboid, and the other is the division of the previous one.

Sum of side lengths (all lengths are prime numbers). So, I began to tell which number these two numbers were.

The final result is 374 cubic centimeters. My formula is: 209 =119 = 2+171× 2×17 = 374 (cubic centimeter).

Later, I checked this problem with what I learned this semester: prime factor decomposition, and the results are exactly the same.

I am happier than anyone to solve this problem. I also understand the truth that mathematics is full of mysteries, waiting for us to explore.

2

Today, after I signed up for school, I wrapped the book cover and began to calculate the expenses of this semester.

First of all, the tuition fee is 4 10 yuan, plus the drinking water fee in 20 yuan, * * 430 yuan. Then the Olympiad School charges 180 yuan, and it is estimated that it also needs the bus fare in 20 yuan, * * 200 yuan. There is also money for exercise books: 2 volumes of "Classpass" 2 1.5 yuan; English practice 1 9.9 yuan; 2 copies of Examination Paper Course Pass 15.9 yuan; Jiangsu big test paper, 3 books, 2 1 yuan, 21.5+9.9+15.9+13+21= 81.3 (yuan).

Study fee: 430+200+81.3 = 711.3 (Yuan).

Living expenses: I will drink about 5 boxes of milk this semester, 5×30= 150 (yuan). Each meal costs about 2~3 yuan, including 2.5 yuan, 2.5×3×30×5= 1 125 (yuan). "What else?" I bit my pencil and said to myself, "and your school supplies." Hey, mom's home. Yes, there are school supplies.

School supplies: a pencil-box 8 yuan, a pencil-box 3 yuan (very cheap, clearance goods), six pencils 3 yuan, an eraser 0.5 yuan, two triangular rulers 1 yuan, two mechanical pencil 5 yuan, 8+3+0.5+ 1+5=20.5 (yuan).

Total expenditure: 711.3+150+1125+20.5 = 2006.8 (yuan).

Wow, I didn't expect that I, who usually don't spend much money, would let my parents spend 2006.8 yuan this semester. Looks like I have to save money!

three

Xianjiasan brothers

Piggy and knife elder brother came to a magnificent castle along the slide, and the words "Graphic Country" were written on the rostrum.

On the moat bridge in front of the city gate, three brothers, straight line, ray and line segment, stand neatly, welcome guests to visit and introduce themselves enthusiastically.

"I am a straight line with no end points, and I can extend infinitely to both ends, which is unmeasurable."

"I am a ray, with only one endpoint and one end extending infinitely."

I am a line segment with two endpoints and a certain length.

"Simple and clear introduction makes people understand your respective characteristics at a glance." Knife elder brother said.

"Yes, line segments, rays and straight lines can be seen everywhere in life. Among you three brothers, the line segment is the shortest, the straight line is the longest, and the ray is not big. " Pig, show me, too

"No, no, you are only half right," said the straight line at once. "The shortest line segment is good, because his length is fixed. And ray and I are infinitely long. I can't say that I am longer than Ray. "

"Straight lines can extend to both ends, and rays can only extend to one end. Isn't the straight line longer than the ray? " Piggy doesn't understand.

"Then tell me how long I am?" "Unmeasurable" and "How long is the ray?" "I can't measure it." "How much longer am I than Ray?"

"I can't know." It doesn't matter, because we can't measure our own length at all, so we can't compare who is long and who is short. "

"Yes, that's the reason." Piggy nodded again and again.

Mathematics Kingdom

In a faraway place, there is a kingdom of mathematics, and its king is "Infinite (00)".

One day, "Infinite (∞) King held a national meeting, and all the symbolic elves attended the meeting. When Guo Wu suggested that he was not energetic enough and wanted to choose the first minister, the four symbols of "addition (+), subtraction (-), multiplication (×) and division ()" all argued. ...

Symbolic Genie "Multiplication (×)" says first: I am the most useful in the mathematics kingdom! I can magnify any number several times! I can do that too, huh?

The first prime minister "O" spoke calmly: "If you want to be the first minister, you must be modest before you can manage the people well." "O" cleared his throat, faced everyone, and then said, "Suppose you have a first minister who likes to brag, would you be happy?" The First Prime Minister "O" already has many fans, and they all reply: "Unhappy!" "O" turned to "multiply (x)" and whispered, "If you can make any number bigger, wouldn't it be weak in front of me?" "Cheng (x) heard a red face and slipped off the stage.

Sister Jia (+), who symbolizes the spirit "Cheng (X)", stepped onto the platform. She immediately spoke for her brother "multiply (x)": "My brother is the best, he can make all the numbers bigger!" She lowered her head again and whispered, "Except for Prime Minister O ...". The whole audience laughed, and Brother Cheng (X) blew his beard and stared. The "plus sign (+)" sister looked at the "minus sign (-)" sister "except ()" again. She looked up and pointed to "except ()", but it just made the number smaller. The audience burst into laughter again, and "Cheng" has been applauding his sister.

"Except ()" Sister was so angry that she was about to cry! At this time, "Minus (-)" brother also spoke for his sister: "Who said your brother was so difficult that he could only be defeated by" O "? There are many numbers under' O', can't you be defeated by your brother? For example: 0.001× 0.001= 0.00001. What do you say? " He said, lifting his chin triumphantly.

"Jia (+)" Sister was speechless and said cleverly, "What about your sister?"

"Minus (-)" The younger brother came prepared and said unhurriedly, "Sister is really amazing. For example: 0.001÷ 0.001=1. Not only did it not get smaller, but it got bigger! Besides, my sister makes the numbers smaller, which is called modesty. Your brother says he can make the numbers bigger, which is called bragging! "

The elder sister of "plus sign (+)" and the elder brother of "minus sign (-)" both glared at each other as if they were going to eat each other. Besides, there was a flash of lightning between their eyes. Fortunately, Prime Minister, I separated them in time, otherwise they would all fight!

The king "infinite (∞) asked everyone:" Dear people: Who do you want to be your first minister? " There's a lot of talk outside.

The king cleared his throat and everyone was quiet at once. The king asked again, "If you want to do well, you can come up and vote." "good!" Everyone agrees.

The voting has started, and "multiply (×)" by * * * is 143 votes; "Except (÷)" * * is 130 votes; "Minus (-)" * * is 145 votes; "Plus sign (+)"-* * is 150 votes.

When everyone knew the result, the "plus sign (+)" jumped with joy; "Minus (-)" poses as a "grandfather"; "Cheng (×)" is Qingjie; "Except ()" kissed my brother on the cheek.

From then on, when people talk about digital symbols, they should put "plus sign (+)" in front, followed by "minus sign (-)", "multiply (×)" and "divide ()".

Piglets plant trees

One day, the pig was planting flowers. Father Pig saw it and said with a smile, "Son, shall I test you some questions?" The pig said without hesitation, "All right."

So father pig began to ask questions. He asked seriously, "What is 12 χ 60?" The pig immediately said it was equal to 720. "good! The next one is a bit difficult! You should think about it! " Father pig said happily. Piggy said confidently, "No problem! I'm too smart to be defeated! Haha! " "What is easy to deform?" Father pig asked. "It's too simple. It is a rectangle, a square and a parallelogram. " The pig said proudly. "Well, the last question, I'll give you three seeds. When you plant it in our vegetable field, you must plant one on each side. " Father pig said. Little pig said without thinking, "well, it's guaranteed!" " "The pig slowly came to the vegetable field. The pig was dumbfounded. It mumbled, "This vegetable field has six sides, and I only have three seeds. How should I plant it? " The little pig sat there with a sad face. The little rabbit saw the unhappy face of the little pig and asked, "What's wrong with you, little pig?" "My father gave me three seeds to plant in a hexagonal vegetable field. There must be a seed on each side. Little Nutbrown hare thought for a while and said, "Don't worry, I've learned this problem. The question should be like this, like this ... "

Finally, with the help of the little rabbit, the little pig successfully completed the problem given by his father.

The discovery on the license plate

Once, I waited for my mother on the side of the road. Watching the car fly by, I accidentally found an interesting phenomenon: the sum of several numbers on each license plate, MINUS the sum of the numbers, is a multiple of 9.

For example, the license plates on "Yu AE3679" are 3, 6, 7 and 9, and its sum is 25. The sum of two numbers of 25 is 7,25-7 = 18, and18 is a multiple of 9.

The license plates on "Yu AC3388" are 3, 3, 8 and 8, and their sum is 22. The sum of two numbers of 22 is 4, and the result of 22-4 is also 18.

Is this a coincidence? I also verified several license plates, and the calculation results are all multiples of 9.

I carefully observed those numbers and found that when the sum of several numbers is less than or equal to 9, the calculation result is 0.

If the students are interested, come and study!

The most cost-effective trip

The summer vacation is coming, and my parents decided to take me to Qingdao to see the sea during the holiday. In order to book in advance, my father and I went to various travel agencies on Sunday, and each travel agency used different tricks to attract tourists:

1, Century Travel Agency: Four-day tour in Qingdao, only 2020 yuan for five people.

2. Youth Travel Agency: A four-day tour for three people in Qingdao is only 1200 yuan.

3. Shenzhou Travel Agency: Qingdao four-day tour 1 person 398 yuan.

4. Tianzhong Travel Agency: Four-day tour in Qingdao, with two adults 900 yuan and a child 200 yuan.

After my dad finished watching it, let me figure out which one is the most economical. Let me think about it:

Century Travel Agency: 2020÷5=404 yuan, so three people are 3×404= 12 12 yuan.

Youth Travel Agency:13 people in 200 yuan.

Shenzhou Travel Agency: 3×398= 1 194 yuan.

Tianzhong Travel Agency: 900+200= 1 100 Yuan.

So I said to my father, "Tianzhong Travel Agency has the highest cost performance. Our family of three only needs 1 100 yuan. " Dad said happily, "It's up to you, my baby."

Clever identification of boxes

The bear king of the black bear kingdom wants to test the wisdom of ministers. He asked people to bring six boxes, called the ministers together and said, "These six boxes are gifts from the monkey country and the fox country, of which four are from the monkey country and two are from the fox country. Each box is marked with the weight of the tribute, but because of the distance, the numbers on both boxes are blurred, only knowing that the total weight of the tribute in the monkey country is twice that of the fox country. Can you find out that these two boxes are from Fox countries? "

"I can't see the numbers. How can you work it out? " "Just know the total weight of tributes from all countries!" Some ministers are talking about it. Bobo Bear said, "What's so difficult!" King Xiong said, "What can you do? Tell me about it. "

"Add up the units of six numbers, 7+1+2+5+2+6=23, and the unit of the total weight of the tribute is 3." Bobo Xiong said: "Because the total weight of the tributes from the Monkey Kingdom is twice that of the Fox Kingdom, all the tributes should weigh three times as much as the Fox Kingdom. Therefore, it can be inferred that the unit number of the total tribute of the Fox Kingdom can only be 1. Because when the unit number is other numbers, after multiplication, the unit number cannot be 3. Because of six numbers again? The unit number of the sum of 5 and 46 is 1. Therefore, the box marked with these two numbers must be sent by the fox country. "

King Bear was very happy and rewarded Bobo Bear.

four

The problem of "discount" in life

In life, everything is inseparable from mathematics, which is closely related to our lives. If we can't learn math well, you will be cheated if you live in this ever-changing society. If you buy clothes in the market, the clothes are just 75% off, but you didn't learn math well and didn't even notice the 15% off. You will regret it afterwards.

In mathematics, there will inevitably be some problems. In fact, these problems are not very difficult, just adding a little "seasoning" on the original basis to make it very flexible. Such as this question: "A commodity is sold after the cost price is increased by 30%. Later, due to seasonal reasons, it was sold at a 20% discount. After the price reduction, the price of each product is 104 yuan. Is it a loss or a profit to sell a commodity? What is your salary or income? " In fact, this question is flexible, but as long as you clear your mind and think carefully, you will certainly be able to work it out. To solve this problem, first of all, we must find out whether the "ten" units sold at a 30% price increase are the same as those sold at a 20% discount. What is their unit "ten"? When you find out which of these two units "1" is, you will start to calculate the price before the price reduction by reverse strategy, then calculate the cost price, and then compare it with the goods after the price reduction. If it is earned, it is the cost price 104, and if it is lost, it is-104 yuan. The correct expression of this question is as follows:

104÷80%= 130 yuan130 ÷ (160%) = 100 yuan100 yuan <100 yuan.

Therefore, the sale of this commodity is profitable, earning 4 yuan.

You see, this question is simple! In fact, as long as you are good at thinking, there is no problem you can't overcome. Isn't this the saying "where there is a will, there is a way"? Therefore, in the face of difficulties, we should try our best to overcome them instead of running away when we see them.