Month, day and week

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.

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, forget to have a gondola, so they can only take four people at a time. In this way, 37 people subtract one rowing classmate, leaving 36 students, 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 trees and pear trees are there in the orchard?

I am not intimidated by this question, but it can stimulate my interest. I think the apple tree is three times as big as the pear tree. If two kinds of trees are to be fertilized 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. Therefore, Master Lao Wang has been fertilizing for 8 days. 20 pear trees a day, 8 days is 160 pear trees. According to the first condition, 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, I found something was wrong. I will do it again more seriously. I think there are as many as four missing, half of them are 13, and the restored B-tree is14; 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 and 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 for a family meal.

When we get there, people are always crowded. We finally ordered good food and found a seat to sit down. Here comes the food. This is a sumptuous set meal. There are 12 drumsticks in it. I thought: how to divide 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. I ask you, how much 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 it. "Fortunately, I learned the knowledge of fractions and can answer the questions correctly.

(2)

Today, my mother gave me 10 yuan to go shopping in the supermarket. I bought a string of firecrackers 2/ 10, four lollipops/10, seven balloons 2/ 10, and finally a comb 4/ 10, a *. There is still one yuan left, and I have to pay it back to my mother.

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

(3)

Last week, we studied fractions. Fractions have numerator, denominator and fractional line, for example, 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. Fractions can also be used to add and subtract! For example, half plus half equals two, which is 1. Why is this happening? 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 parts 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 2/2 of the numerator and denominator are the same, which is 1.

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; Denominators are the same as numerators, with large numerator scores larger and small numerator scores smaller.

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

Month Day Week Weather: Sunny Mood: Happy

Today, our whole school went on an autumn outing. I bought many snacks. The snacks I brought this time were eaten a lot by XXX and several classmates.

I ate 3/4 of 2 packets of Hijiro fruit jelly, I finished Sprite, I ate 65,438+0 of Yida gum, we ate 65,438+0 of a bucket of Pinke potato chips and tomato flavor, and we ate 4 candies on a packet of iced lemon hard candy.

What a happy day!