Math Diary 6th Grade Math Problems are best triggered by one thing

Dongdong, go and do a math test paper! The exam is coming up tomorrow, and you're not in a hurry, I'm really unconscious. My mother started nagging again, and I had no choice but to obey and obediently go to the test papers.

I picked up the pen and started writing the test paper like a fly, but once I got the question, the pen in my hand stopped. The title of this question is as follows: 3 trucks are going to transport 910 tons of cement to a construction site, and it is known that the first truck is 30 tons more than the second one, and the third one is 20 tons less than the second one.

How many tons are carried by each of the 3 trucks? That's a tricky question. Unlike the previous problem-solving strategy we did, there were only two numbers required, but this time three numbers were required.

I thought about it for a long time, and it finally dawned on me and I knew what to do. In fact, the method of doing this kind of question is the same as what I have done before, but in a different form. So, I did it.

Because I don't know how many tons of cement the first truck transports, so first calculate the second truck, use "910 30 20 900 (tons)" the first truck transports 30 tons of cement more than the second truck, so it is necessary to subtract 30 tons, and the third truck transports 20 tons of cement less than the second truck, so we need to add 20 tons, calculate how many tons of cement are transported by the three trucks if all the tons of cement transported by the second truck, and then use "900 3 300 (tons)" to calculate how many tons of cement the second truck transports. Since the title says that the first truck transports 30 tons of cement more than the second truck, and the third truck transports 20 tons less than the second truck, we can directly use "300 30 330 (tons)" to calculate how many tons of cement the first truck transports; Use "300 20 280 (tons)" to calculate how many tons of cement the third truck hauls. In this way, I easily calculated the answer to this question.

Since making this problem, I have summed up a truth - mathematics is alive and ever-changing, and some new question types are just changing the old question type to another form or saying, and only by following it and using the old methods we have learned to solve the new problem type can we explore more mysteries of mathematics and make continuous progress in the kingdom of mathematics.

Let me start by asking what a math diary is.

than in life.

The ratio of sand, cement, and water in concrete is 2:1:1

The ratio of the hand to the heart is 1:1

The ratio of the circumference of the neck to the wrist is 2:1

The ratio of memory to that of the left and right brains is 1:1 million.

Water in the body accounts for 61 8 of body weight

The ratio of sugar to water in sugar water is 1:10 and so on.

The ratio of table to chair is 1:4

Arowana Blended Oil, 1:1:1

The ratio of head length to height in newborns is about 1:4

The Law of Partition This was discovered by the ancient Greek mathematician Pythagoras in the sixth century BC, and later the ancient Greek aesthete Plato called this partition. This is actually a proportional relationship of numbers, that is, a line is divided into two parts, at this time the ratio of the long segment to the short segment is exactly equal to the ratio of the whole line to the long segment, and its numerical ratio is: 1 or 1, that is, the square of the long segment is equal to the product of the full length and the short segment (you can think of the end later).

Grab the game.

Today is another sunny day, I was wandering down the street and suddenly I saw a lot of people gathered not far away. I ran for the past year, and it turned out to be a prize grabber game. "Hmph, what's so fun about grabbing prizes.

I was bored and said that when the person next to me heard this, I hurriedly said: "Although it is not fun to draw prizes, there are heavy prizes, which can attract people." ”

I eagerly asked, "What is it?" "50 yuan.

The man said, his eyes wide. As soon as I heard this, I was excited, "Such a tempting prize, whatever you say, I have to try it." After saying that, I asked the shopkeeper how to do it.

The shopkeeper said: "This is 24 mahjong, mahjong is written under 12 5, 12 10, only 12 mahjong can be caught each time, if the sum of the 12 mahjong bids is 60, then you can win a 50 yuan jackpot." I didn't roll up my sleeves anymore and took out 5 yuan from my pocket and gave it to the shopkeeper.

Even though I could have caught it 10 times, I still didn't get that prize.

When I got home, I thought about it and felt a little wrong. I think, to draw 60 points, then you must catch those 12 mahjong must be marked 5, and the best case is to catch 1 for the first time.

5, 2 5s for the 2nd time, 3 5s for the 3rd time......The 12th time you catch 12 5s, you have to spend at least 6 yuan. But in case the number of mahjong targets is 10 or the sum of some is the same, then how many times do you have to catch how much it costs.

Finally, after some consideration, I finally figured out the problem, and I hurried to the street to find the account, but I had already run away without a trace. Leather shoes that Dad sells.

The day before yesterday, I looked at the shoe rack of my ** shoes and found that the number of old-fashioned leather shoes was decreasing, and the number of new leather shoes was gradually increasing, so I recorded them.

There are 14 pairs of old-fashioned leather shoes and 100 pairs of new-style leather shoes, of which 27% are new casual shoes, 18% are new sports shoes, 21% are new children's shoes, and 32% are ...... new women's shoes

These beautiful new leather shoes are selling well, while the "outdated" products are at a low ebb. Is this weird? When these vintage leather shoes were first made last year, wasn't it flood season? But there is an endless stream of customers who come to buy shoes, and they can sell more than ten pairs a day, what is the reason for this?

After my investigation, I found that my father would promote 1-3 new products every year, and they were often new leather shoes. These figures reflect an improvement in people's living standards and a constant pursuit of perfection. I can also see the strength of social competitiveness and the cruelty of survival of the fittest.

Therefore, we must have good skills from primary school, strive to walk in the forefront of society, and not be eliminated by society. ‘

What is a little diary of mathematics.

The cuboid has 6 faces, so the area is 36*2=72 square centimeters, and you can know that the areas of these three faces are.

So it's clear that the cuboid is three-sided

So the volume is 2*3*6=36 cubic centimeters.

The surface area of the cuboid = 36 * 2 = 72 square centimeters.

Let the three edges be x, y, and z respectively

xy=6，yz=12，xz=18

Multiplication of three formulas; xyz) * (xyz) = 6 * 12 * 18 = 36 * 36 volume xyz = 36 cubic centimeters.

The ratio of the area of the three faces of the same vertex is 1:2:3, and if each part is n, then n+2n+3n=36, n=6The areas of the three faces are 6, 12, 18.

Let the length of the three sides be x,y,z,xy=6,xz=12,yz=18, and the ratio of two to one is: 3x=2y=z.".Substitute 2y=z into yz=18. This results in y=3, x=2, z=6, so the surface area is 2 times 36=72

The volume is 3 times 2 times 6 = 36

Let the length, width and height of the cuboid be a, b, and c, respectively, and according to the question, ab=18, ac=12, bc=6, then a=6, b=3, c=2, then the surface area of this cuboid is s=36*2=72 square centimeters, and the volume v=abc36 cubic centimeters.

Answer: The surface area is 72 square centimeters.

Volume 36 cubic centimeters.

Solution: Let the width of the box be x and the height be y, then according to 1:2:3, the length of 2x can be found and two equations are listed.

2x x square is equal to 2xy equal to 2:3

2xy+xy+2 times x square is equal to 36.

x=3 y=2

The results can be obtained from the volume formula for the surface area of the box.

The first digits are , so the 3rd digit cannot be 1, but can only be 0 Since the 6th digit can no longer be , the 5th digit cannot be 3, and of course, the 5th digit cannot be . So, such a date is.

910 mouths 2 mouths.

form. The 4th position can take any of the 3 8s, and there are 6 ways. After the 4th position is determined, there are 5 ways to take the 6th position. Thus there are 6 5 30 (species), i.e. 30 days in the whole year on the six days when the numbers are not the same.

30 days The first two have been determined to be 91, so the month cannot be a month, if it is 02 months, then the date cannot be 0 days, nor can it be 1 days, 2 days, if it is 30, there will be 0, if it is 31, there will be 1 again. So 02 months are not true.

If it is 03 months, it is 9103**, and the date can be 24, 25, 26, 27, 28.

If it is 04 months, it is 9104**, and the date can be 23, 25, 26, 27, 28.

If it is 05 months, it is 9105**, and the date can be 23, 24, 26, 27, 28.

If it is 06 months, it is 9106**, and the date can be 23, 24, 25, 27, 28.

If it is 07 months, it is 9107**, and the date can be 23, 24, 25, 26, 28.

If it is 08 months, it is 9108**, and the date can be 23, 24, 25, 26, 27.

There are 30 possibilities in total, so it's 30 days.

Detailed enough, right? Haha, I'm tired, hehe

9191 represents 19***, so it can't be January, September, October, November, and December in 1991.

The two-digit number of the month can only be 0*, so the two-digit number of the date can only be 2* or 31.

There are only 28 days in February, that is, 192*-* has two options, 1 has been used, and 2 has also been used, so February does not meet the requirements.

So the month is expressed as 91(2)*, because 1 already has the month of 30 and the 0 in 30 has already been used, so it can only be 2.

March 24 Sun Day (910328) is feasible.

May 23rd (910327) and 28th (910328) are feasible.

The days of July are feasible (910723), (910724), (910725), (910716), (910728).

1 of the 31st day of the month has already been used, so there is only one option - 910*2*

April's feasible; June is feasible.

A total of 6 months, each month has 5 days to be eligible, and the column formula is 5*6

The result is 30 units (days).

A: There are 30 days in a year when the six numbers are not the same.

Let a, b, c d, four digits.

Erection a+b+c=22

a+b+d=20

b+c+d=17

a+c+d=25

Then (a+b+c)+(a+b+d)+(b+c+d=)+(a+c+d)=22+20+17+25=84

Remove the brackets of the same kind of contract: 3a+3b+3c+3d=84, so a+b+c+d=28

The correct answer is 28

Let these numbers be x1, x2, x3, x4, x1+x2+x3=22, x1+x2+x4=20, x1+x3+x4=17, x2+x3+x4=25, and the above four algebraic formulas are added and divided by 3.

x1 + x2 + x3 + x4 = 28, subtract the above three formulas respectively, and obtain.

x4=6x3=8

x2=11x1=3

The three numbers are 3, 11, 8, 6

Let the sum of these four numbers be x, then these four numbers are: x-22, x-20, x-17, x-25, then there is: x-22 + x-20 + x-17 + x-25 = x solution x=28

I think this method is good, and of course there are many other ways to do it together.

Arithmetic: 12 (1 60% 25%) 80 Yuan Xiao Ming: 60% 80 48 Yuan.

Xiaohua: 80-48 32 yuan.

Equation: If there is a total of x yuan, then Xiao Ming has 60% x yuan, Xiao Hua has x-60% x yuan, if Xiao Hua gives Xiao Ming 12 yuan, Xiao Hua has x-60% x+12 so, 25% x = x-60% x + 12

Solution: x=80

Xiao Ming: 60% 80 48 yuan.

Xiaohua: 80-48 32 yuan.

Solution: Let Xiao Ming and Xiao Hua have a total of x yuan.

100％-60％》x-12＝25％x

This is the rest of the money, minus the 12 yuan that Xiao Hua gave to Xiao Ming, and Xiao Hua's remaining money is 25 of the total amount of money

40％x-25％x＝12

15％x＝12

x 80 Xiao Ming 60 *80 48 yuan.

Xiaohua: 80-48 32 yuan.

Let a total of x yuan, Xiao Ming has 60% x yuan, Xiao Hua is x-60%x=40%x 40%x-12=25%xx=80

So Xiao Ming has 80 * 60% = 48 yuan Xiao Hua has 80 * 40% = 32 yuan.

Solution: Let a total of x yuan.

x=80 Ming: 80*RMB).

Xiaohua: 80-48 32 yuan.