Month, day and week

At noon today, I was doing my summer math homework. It says, unfortunately, I met a very difficult 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! Knowing only the product of two areas, the volume must also know the length, width and height, but there is no hint at all. How do we start?

Just as I was scratching my head, a colleague of my mother came. He taught me how to solve the equation first, but I'm not very familiar with this method. So he taught me another way: list the numbers first, and then exclude them one by one. We first listed a lot of numbers according to the requirements of the topic, such as: 3, 5, 7, 1 1 and so on. One is the front of the cuboid, and the other is the division of the previous one.

Sum of sides (both are prime numbers). So, I began to distinguish which of these two numbers are.

The final result is 374 cubic centimeters. My formula is: 209 =11×19 = 2+171× 2×10.

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 that mathematics is full of mysteries, waiting for us to explore.

Math diary 2

Month, day and week

I saw a puzzling math problem tonight. The topic is: 37 students want to cross the river. There is an empty boat at the ferry that can only take five people. How many times must they cross the river with this boat at least?

Careless people often ignore the "empty boat", that is, they forget to have punting, so they can only sit four people at a time. In this way, 37 people subtract one punting classmate, leaving 36 classmates, 36 divided by 4 equals 9, and the classmate who worked as a boatman on the other side for the last time also landed 4, so it takes at least 9 trips.

Math diary III

Month, day and week

In the evening, I saw a problem in the Olympiad Book: the number of apple trees in the orchard is three times that of pear trees. Master Lao Wang fertilizes 50 apple trees and 20 pear trees every day. A few days later, all the pear trees were fertilized, but the remaining 80 apple trees were not fertilized. Excuse me, how many apple and pear trees are there in the orchard?

I'm not intimidated by this question. This question can arouse my interest. I think the apple tree is three times as big as the pear tree. If you want to fertilize two kinds of trees on the same day, Master Lao Wang will fertilize "20×3" apple trees and 20 pear trees every day. In fact, he only fertilizes 50 apple trees every day, which is 10, and the last 80 * * trees. From here, you can get 160 pear trees in 8 days, and according to the first condition, we can know that there are 480 apple trees. This is to solve the problem with the idea of hypothesis, so I think the hypothesis method is really a good way to solve the problem.

Math diary IV

Month, day and week

I met another math problem today, and it took me a lot of effort to solve it. The topic is: there are 30 birds in two trees, and 4 birds fly away from the second tree first. At this time, tree A flew to tree B with three birds, and the birds on the two trees were just equal. How many birds are there in each tree?

As soon as I saw the topic, I knew it was a reduction problem, so I solved it by the method of reduction problem. But when I checked it, I found it was wrong. I began to do it again more seriously. I think there are as many as four trees missing, half of which are 13, and the minus B tree is 14. A tree is 16. The formula is: (30-4) ÷ 2 = 13 (only); 13-3+4 =14 (only); 30- 14 = 16 (only). The answers are: A tree 16, B tree 14.

By solving this problem, I understand that no matter what I do, I should be careful, otherwise, even if I master the solution to the problem, the result will be wrong.

I)

Today, my family went to KFC in Longgang to have a family fun.

When we got there, people were always crowded. We finally ordered good food and found a seat to sit down. Here comes the dish. It's a big set meal. There are 12 chicken legs in it. I thought: how can we split it equally? Then I remembered the division of 12÷3=4. We each have four drumsticks. Later, I ate my mother's 1 chicken leg and my aunt's two chicken legs. My aunt said, "You can't eat this for free. Let me ask you, how many points did you eat? " How many more servings do you have to eat before you can finish them all? "I thought about it and replied," I ate 7/ 12, and then I ate 5/ 12. I ate all of them. "Fortunately, I learned the knowledge of fractions and can answer questions correctly.

(2)

Today, my mother gave me 10 yuan to go shopping in the supermarket. I bought a string of firecrackers, four lollipops, seven balloons and a comb. A * * * uses 2/10+110+2/10+4/10 = 9/10. I have to return one yuan to my mother.

When I got home, my mother ate 1/4 lollipops, my father ate 1/4 lollipops and I ate 1/4 lollipops. I left one and gave it to my brother Xiao Qiang next door. (Author: Xiao Enling)

(3)

Last week, we studied fractions. Fractions have numerator, denominator and fractional line, such as 1/3, where 3 is denominator, 1 is numerator, and the middle horizontal line is fractional line.

Scores are used in many places in life. For example, a book has thirty pages, and each page is 1/30 of a book. Scores can also be added or subtracted! For example, half plus half equals two, which is 1. Why? If you divide a cake into two parts, each part is 1/2 of the cake, and then put the two parts together, there are two pieces 1/2, which is just a cake. When adding and subtracting fractions, if the denominator is the same, only the numerator is added, regardless of the denominator. And the numerator and denominator are 2/2 the same, that is, 65438+.

I also learned to compare the size of fractions. The teacher taught us the formula: numerator is the same as denominator, the fraction with large denominator is small, and the fraction with small denominator is large; The denominator is the same as the numerator, with the larger numerator having a larger score and the smaller numerator having a smaller score.

The teacher also reminded us that when writing scores, we usually write the fractional line first, indicating the average score, then the denominator and finally the numerator.

Math diary 2