100 interesting math questions in Grade 6 of primary school

100 interesting math questions in Grade 6 of primary school

In the first group of class 1, grade 6, if each person plants 5 trees, there are still 14 trees left; if each person plants 7 trees, there are 4 missing. How many people are in this group? How many trees are there in all?
Do it by arithmetic
First count: (14 + 4) / (7-5) = 9
The idea is as follows: after planting five trees for each person, there are 14 trees left. If each person grows two more trees, there will be four missing. That is to say, if four more trees are added to the original number of trees, there will be just two more trees for each person. Therefore, each person grows two more trees, and there will be 18 more trees for each person. Therefore, the number of people is 18 / 2 = 9
How many trees are planted
9 * 5 + 14 = 59 or 7 * 9 - 4 = 59
Give a bag of sugar to the children. If you give five yuan to each of the children in the big class, six yuan will be missing. If you give four yuan to each of the children in the small class, four yuan will be left. It is known that the big class has two less children than the small class. How many pieces are there in this bag?
(6 + 4 + 4 × 2) / (5-4) = 18 (people) (number of large class)
18 + 2 = 20 (person) (small class)
18 × 5-6 = 84 (pieces)
Assuming that the number of people in the small class is the same as that in the large class, then each person in the small class is given 4 pieces of candy, and then the original 4 pieces will be added to the additional 8 pieces later
Answer: 84
(6 + 4 + 4 * 2) / (5-4) = 18 (large class)
18 + 2 = 20 (small class)
18 * 5-6 = 84 blocks or 20 * 4 + 4 = 84 blocks
Explanation: the key is to understand the meaning of 4 + 4 * 2, which means that if there are as many people in the small class as in the large class, if each person in the small class gets 4 yuan, there will be a total of (4 + 4 * 2) yuan extra
Xiao Ming went to the store to buy exercise books. If he bought 8, he could have 1 yuan left. If he bought 12, he still had 1 yuan left. How much was each exercise book? How much did Xiao Ming bring with him?
Comparing the two times, the difference between the remaining 1 yuan and the remaining 1 yuan is 2 yuan, but the difference between the two times is 12-8 = 4 copies
That is to say, if you use 2 yuan for 4 books, then one book is 2 / 4 = 0.5 yuan
8 * 0.5 + 1 = 5 yuan
Or 12 * 0.5-1 = 5 yuan
Teach the students how to play. Each group is divided into two groups. Each group is divided into six balls, less than 10; each group is divided into four balls, less than 2. How many groups are there? How many balls are there?
How many groups are there
（10－2）÷（6－4)
Li Min's father sold both a and B jackets to one person at the same time. The selling price was a yuan. Among them, a jacket made a profit of 25% and B jacket lost 25%. Please calculate whether the business is a loss or a profit? If so, how much?
Yes, it's 2 A / 15
The cost of a and B is 2A + 2A / 15
Profit means 25% more than cost and loss means 25% less than cost
Cost of a: A / (1 + 25%) = four fifths a
Cost of B: A / (1-25%) = Four Thirds a
The cost of the two is 4 / 5A + 4 / 3A = 32 / 15A = 2 / 15 a
And two clothes are only 2a, so it's a loss
3. There is a rectangle with a volume of 102 cubic decimeters. If the length, width and height are prime numbers, what is the surface area of the rectangle? (to calculate the formula)
1. Group A has three times as many books as group B. if group B gives group a six books, group A has five times as many books as group B. how many books does group A have?
2. It turns out that Xiao Ming's paintings are three times as big as Xiao Hong's. later, they each bought five, so Xiao Ming's paintings are twice as big as Xiao Hong's
1. Have you learned to assume?
Suppose there are x books in group B and 3x books in group A
5(X-6)=3x+6
X = 18 A has 54 copies
2. Suppose Xiao Hong's is x, then Xiao Ming's is 3x
2(X+5)=3X+5
X = 5 Xiaohong has 5 Xiaoming has 15
The sum of divisor and quotient is 170. How much is the divisor?
2.170-8=162 162/(8+1)=18 18*8=144
8. There is a rectangular sports ground. If its length and width are increased by 6 meters, the area will increase by 1236 square meters. What is the perimeter of the original sports ground?
Uncle Liu bought two baskets of apples, and the number of apples in each basket was the same. Basket a sold 150, and basket B sold 194. The remaining apples in basket a were three times as much as that in basket B. how many apples were there in each basket?
194-150 = 44 (pieces) 44 / (3-1) = 22 (pieces) 194 + 22 = 216 (pieces)
8.1236-6 * 6 = 1200 (M2) 1200 / 6 * 2 = 400 (m)
Xiao Li and Xiao Jie ride bicycles from two places 65 kilometers apart. Xiao Li's speed is 15 km / h, and Xiao Jie's speed is 17.5 M / h. After a few hours, are they 32.5 km apart?
(this question is put on the topic of classified discussion, so it should be discussed in different categories. Please answer it by experts and do a good job.)
In the first case, they haven't met yet (the sum of the distances they have traveled is (65km-32.5km)
(65km-32.5km) / (15km / H + 17.5m / h) = 1 hour
In the second case, after meeting each other, they advance to a distance of 32.5Km/
(65 km + 32.5 km) / (15 km / H + 17.5 M / h) = 3 hours
1. There is a pile of candy, of which milk candy accounts for 45%. After adding 16 pieces of fruit candy, milk candy only accounts for 25%
2. There are 77 kilograms of apples and pears. If you take out 5 / 11 and 12 kilograms of apples, the number of apples left is three times that of pears. How many kilograms of apples and pears are there?
3. 9 trees, 10 rows, 3 rows, how to plant?
4. There are two cylindrical containers a and B with the radius of 6cm and 8cm respectively and the depth is equal. Now, container a is filled with water and poured into container B. the water depth is 1cm lower than 2 / 3 of container B. find the depth of the two containers
In 1-500, there are 500 / 2 = 250 numbers divisible by 2
In 1-500, there are 500 / 3 = 166 numbers divisible by 3
In 1-500, there are 71 numbers divisible by 7
In 1-500, there are 500 / 6 = 83 numbers divisible by 6
In 1-500, there are 35 numbers divisible by 14
In 1-500, the number that can be divided by 21 is 500 / 21 = 23
In 1-500, there are 11 numbers divisible by 42
So, in the range of 1-500, it can't be divisible by 2 or 3,
The numbers that can not be divided by 7 are 500-250-166-71 + 83 + 35 + 23-11 = 143

Someone came to the well with a rope to draw water. He tied the rope into a single strand, but the rope was still seven meters long. He tied the rope into a double strand, but the rope was seven meters short. How long is the rope? How deep is the wellhead from the water?

If the wellhead is x meters above the water, then the length of the rope is x + 7 meters. According to the meaning of the title: (x + 7) △ 2 = X-7 & nbsp; & nbsp; X + 7 = 2 (X-7) & nbsp; & nbsp; X + 7 = 2x-14 & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; X = 2121 + 7 = 28 meters. A: the length of the rope is 28 meters, and the wellhead is 21 meters above the water